Fifth task set

  1. I implemented a routine called solveLinearSystemInline, which does the same thing as solveLinearSystem but in an inline fashion without calling rowReduce and backsub. See my software manual entry for solveLinearSystemInline. I then used timing methods to test the performance of the inline solver versus the non-inline one I previously made on diagonally dominant systems. The results for the test are shown in the table below. I did not see any major differences in performance between the two routines. Note that small differences are likely primarily due to the fact that for each matrix size, I run each method on a different randomly generated matrix, which is a weakness in my testing method. Still, my careful memory management helps mitigate performance hits in the non-inline version because matrices and vectors are passed by reference. This likely explains why there is no notable difference.

     | Matrix size | Non-inline time (secondes) | Inline time (secondes) |
 |-------------|----------------------------|------------------------|
 | 100         | 0.0158875                  | 0.0123084              |
 | 200         | 0.0952901                  | 0.09255                |
 | 300         | 0.284401                   | 0.292229               |
 | 400         | 0.652581                   | 0.650894               |
 | 500         | 1.275                      | 1.24139                |
 | 600         | 2.20617                    | 2.14891                |
 | 700         | 3.39894                    | 3.40654                |
 | 800         | 5.18551                    | 5.47892                |
 | 900         | 8.38311                    | 8.01148                |
 | 1000        | 10.5383                    | 10.5108                |
 | 1100        | 13.6662                    | 14.0219                |
 | 1200        | 18.1564                    | 18.5245                |
 | 1300        | 23.4234                    | 24.0034                |
 | 1400        | 28.9636                    | 29.5553                |
 | 1500        | 36.7691                    | 38.355                 |
 | 10k         | 10296.4                    | 10090.4                |

    The code that I used to test the systems is given below. The code was slightly modified to change the size to 10k for the final test. For the timing methods, I #-included chrono from the C++ standard library.

         for (unsigned int size = 100; size < 1600; size += 100) {
         DenseArray<double>* A_7 = new DenseArray<double>(size);
         A_7->makeRandomDD(-100.0, 100.0);
         Vector<double>* b_7 = new Vector<double>(size);
         b_7->makeRandom(-100.0, 100.0);
         auto normalStart = std::chrono::high_resolution_clock::now();
         Vector<double> x_a7 = solveLinearSystem(*A_7, *b_7);
         auto normalEnd = std::chrono::high_resolution_clock::now();
         std::chrono::duration<double> normalTime = normalEnd - normalStart;
         std::cout << "Normal time for " << size << ": " << normalTime.count() << std::endl;

         DenseArray<double>* A_8 = new DenseArray<double>(size);
         A_8->makeRandomDD(-100.0, 100.0);
         Vector<double>* b_8 = new Vector<double>(size);
         b_8->makeRandom(-100.0, 100.0);
         auto inlineStart = std::chrono::high_resolution_clock::now();
         Vector<double> x_a8 = solveLinearSystemInline(*A_8, *b_8);
         auto inlineEnd = std::chrono::high_resolution_clock::now();
         std::chrono::duration<double> inlineTime = inlineEnd - inlineStart;
         std::cout << "Inline time for " << size << ": " << inlineTime.count() << std::endl;
     }
  2. I implemented a routine called lu that gives the LU-factorization of a square matrix. I used scaled partial pivoting to improve the robustness of the method. See my software manual entry
  3. I created routine called luSolve that takes the L and U matrices which can be found using the lu method as well as a left-hand b vector, then computes and returns the solution of the system of equations using the backsub and forwardsub methods. I did not do the LU factorization inside the routine so that the LU factorization can be performed once and reused for many calls of luSolve (for example I use it like this in my inverse iteration routine used for finding eigenvalues). See my software manual entry
  4. I implemented a routine that generates and returns a symmetric, positive definite matrix of the dimensionality of a given integer. See my software manual entry. Here is an example usage making a 110x110 matrix: 
     std::cout << "SPD_large: " << std::endl;
 Array<double>* SPD_large = getRandomSPDArray(10);
 SPD_large->print();

    Output from the code above:

     SPD_large: 
 3.35958e+07 4.50597e+07 2.48781e+07 5.61644e+07 1.42094e+07 4.47804e+07 2.59573e+07 3.04581e+07 4.05466e+07 4.20314e+06 2.58153e+07 2.01592e+07 2.23831e+07 4.93081e+07 1.53519e+07 2.39142e+07 9.93611e+06 4.04512e+07 3.74477e+07 89092.8 1.78977e+07 3.2621e+06 5.5796e+06 2.00697e+07 5.36971e+07 9.46821e+06 3.73399e+07 2.80245e+07 2.73813e+07 5.79155e+07 4.51189e+07 3.01521e+06 4.50134e+07 1.20351e+07 1.21778e+06 1.261e+06 5.68156e+07 2.71751e+07 3.17191e+07 3.94003e+07 3.13782e+07 5.75344e+07 1.59769e+06 5.37613e+07 4.88806e+07 1.69496e+07 1.97136e+07 854861 5.74008e+07 5.71613e+07 943954 1.73367e+07 2.46152e+06 6.52355e+06 3.74064e+07 5.61586e+07 1.59918e+07 1.67844e+07 2.62213e+07 4.33731e+07 1.67381e+07 1.33784e+07 4.63883e+07 3.78968e+06 2.54135e+07 4.7606e+07 5.05068e+06 2.42673e+07 1.68193e+07 3.67697e+07 5.70572e+06 4.81974e+07 3.63423e+07 7.30341e+06 4.39969e+07 2.7261e+07 2.4253e+07 5.74861e+06 2.81159e+07 2.3692e+07 4.94803e+06 2.90598e+07 4.10286e+07 7.40955e+06 3.55834e+07 2.04732e+07 5.60632e+06 5.15752e+07 3.72576e+07 3.18276e+07 3.69864e+07 5.39957e+07 4.5206e+07 2.54128e+07 5.77853e+07 1.26577e+07 1.5057e+07 4.87416e+06 3.6925e+07 3.18762e+07 4.16439e+07 4.26307e+07 2.21118e+07 2.00243e+07 4.99341e+07 8.14685e+06 4.72854e+07 1.62253e+07 1.38955e+07 1.74394e+07 
 4.50597e+07 1.07864e+08 5.57564e+07 1.30578e+08 4.63669e+07 9.12539e+07 6.34742e+07 9.24856e+07 9.22365e+07 2.67084e+07 6.16585e+07 3.38407e+07 9.50378e+07 8.84553e+07 8.1105e+07 5.84177e+07 3.54386e+07 6.09404e+07 9.44594e+07 2.80227e+07 7.45638e+07 1.76147e+07 1.59984e+07 5.9261e+07 1.11532e+08 4.50061e+07 7.28861e+07 8.67791e+07 5.63463e+07 1.19761e+08 1.26217e+08 4.43866e+07 8.10165e+07 3.53647e+07 2.83564e+07 4.9643e+07 1.26619e+08 9.18306e+07 7.32605e+07 7.22466e+07 4.96708e+07 1.34919e+08 2.83469e+07 7.58405e+07 7.67658e+07 4.05838e+07 5.65178e+07 3.4464e+07 1.01524e+08 8.21092e+07 6.24867e+07 2.94795e+07 2.19835e+07 9.61702e+06 8.87405e+07 1.33516e+08 5.46231e+07 8.38863e+07 7.36863e+07 1.10969e+08 5.70389e+07 5.32945e+07 8.64879e+07 6.03151e+07 8.86592e+07 1.14844e+08 4.109e+07 6.86693e+07 6.00664e+07 1.1435e+08 6.31756e+07 1.09737e+08 1.02661e+08 2.26544e+07 1.07837e+08 1.01686e+08 6.32383e+07 1.77467e+07 6.72823e+07 8.70221e+07 2.21155e+07 6.09009e+07 1.16502e+08 4.4099e+07 7.05179e+07 5.86336e+07 3.10062e+07 1.25141e+08 7.36518e+07 1.04692e+08 8.9502e+07 1.30691e+08 8.91189e+07 9.82496e+07 1.22138e+08 3.11696e+07 6.64854e+07 1.66191e+07 9.9839e+07 5.76837e+07 6.21014e+07 9.41465e+07 8.96806e+07 8.7022e+07 1.16801e+08 5.09095e+07 1.1984e+08 3.34307e+07 6.86562e+07 4.05141e+07 
 2.48781e+07 5.57564e+07 1.23399e+08 1.6008e+08 7.85058e+07 1.31858e+08 7.61928e+07 1.34178e+08 7.86871e+07 8.96379e+07 1.00925e+08 8.23418e+07 1.14162e+08 7.52198e+07 8.91849e+07 4.00669e+07 3.93302e+07 4.81698e+07 7.85577e+07 1.00082e+08 6.64034e+07 1.24344e+07 1.8896e+07 6.82267e+07 1.14342e+08 1.17692e+08 6.42335e+07 7.30372e+07 8.42149e+07 7.10075e+07 1.09953e+08 4.93598e+07 7.54915e+07 6.07564e+07 3.68451e+07 1.11076e+08 9.54517e+07 1.13038e+08 1.15581e+08 9.87072e+07 7.30023e+07 1.19342e+08 4.09643e+07 5.74905e+07 1.19131e+08 9.7639e+07 5.46359e+07 1.83762e+07 1.45809e+08 1.00683e+08 1.18458e+08 3.96174e+07 7.01964e+07 7.68042e+06 1.07844e+08 8.73753e+07 2.82089e+07 1.29156e+08 8.49809e+07 1.12424e+08 1.24732e+08 1.19502e+08 1.29273e+08 6.01389e+07 8.30951e+07 6.89553e+07 4.15414e+07 1.03115e+08 1.06562e+08 5.99587e+07 6.17376e+07 8.24006e+07 1.0387e+08 7.01917e+07 9.69696e+07 8.29155e+07 7.06675e+07 7.61739e+07 6.87815e+07 7.63917e+07 3.67726e+07 5.75659e+07 1.16009e+08 1.06969e+08 6.52463e+07 5.12583e+07 2.17494e+07 9.34552e+07 5.07411e+07 1.0673e+08 1.30447e+08 7.831e+07 9.65588e+07 1.19636e+08 1.05939e+08 1.04222e+08 1.1316e+08 7.20484e+07 1.10174e+08 9.00479e+07 9.94969e+07 1.39402e+08 1.29527e+08 6.32817e+07 1.1243e+08 5.39018e+07 1.13687e+08 1.07666e+08 1.30076e+08 1.07037e+08 
 5.61644e+07 1.30578e+08 1.6008e+08 2.55728e+08 1.1626e+08 1.97369e+08 1.41763e+08 2.00016e+08 1.53669e+08 1.08323e+08 1.47557e+08 1.23984e+08 1.83694e+08 1.56027e+08 1.60351e+08 8.83869e+07 7.05051e+07 9.88755e+07 1.62928e+08 1.22258e+08 1.21563e+08 3.49175e+07 5.0476e+07 1.28801e+08 1.92313e+08 1.65735e+08 1.31176e+08 1.39844e+08 1.28678e+08 1.78747e+08 2.17961e+08 8.41356e+07 1.5558e+08 1.02778e+08 6.76336e+07 1.48442e+08 2.05041e+08 1.82897e+08 1.73127e+08 1.55088e+08 1.15889e+08 2.25577e+08 6.0567e+07 1.24252e+08 1.77982e+08 1.40694e+08 1.1574e+08 5.64818e+07 2.3957e+08 1.71945e+08 1.7874e+08 6.24048e+07 1.09963e+08 2.73863e+07 1.91206e+08 1.80671e+08 7.15155e+07 1.98983e+08 1.43393e+08 2.00193e+08 1.74108e+08 1.57732e+08 2.04105e+08 1.11184e+08 1.65404e+08 1.50133e+08 8.42945e+07 1.66822e+08 1.55907e+08 1.62315e+08 1.29905e+08 1.7669e+08 1.8427e+08 1.10248e+08 1.77544e+08 1.70247e+08 1.29336e+08 8.96624e+07 1.20006e+08 1.50402e+08 6.96016e+07 1.23415e+08 2.12807e+08 1.53066e+08 1.24302e+08 1.05284e+08 6.15075e+07 1.95818e+08 1.02438e+08 1.78401e+08 1.92389e+08 1.81439e+08 1.60803e+08 2.04488e+08 2.12399e+08 1.49084e+08 1.77498e+08 9.30715e+07 1.943e+08 1.31576e+08 1.48663e+08 2.17482e+08 2.11367e+08 1.40928e+08 2.06124e+08 9.01821e+07 2.04452e+08 1.31839e+08 1.79844e+08 1.47334e+08 
 1.42094e+07 4.63669e+07 7.85058e+07 1.1626e+08 1.02784e+08 1.44401e+08 1.0311e+08 1.16474e+08 1.00295e+08 1.15303e+08 1.25371e+08 8.09803e+07 1.20411e+08 1.24984e+08 9.82726e+07 7.24175e+07 5.7956e+07 5.94399e+07 9.08564e+07 8.33245e+07 7.55722e+07 8.34655e+07 7.22496e+07 1.26384e+08 8.37658e+07 1.53527e+08 8.87511e+07 1.20788e+08 9.66085e+07 1.39753e+08 1.64753e+08 1.02346e+08 7.77797e+07 6.47079e+07 6.70648e+07 1.30513e+08 1.52408e+08 1.44639e+08 8.55329e+07 9.78987e+07 9.84883e+07 1.54204e+08 7.2127e+07 5.74457e+07 1.24383e+08 1.30746e+08 1.05348e+08 3.60239e+07 1.25086e+08 1.31015e+08 1.19348e+08 5.42527e+07 1.24865e+08 6.97075e+07 1.15537e+08 1.26394e+08 7.58979e+07 1.54237e+08 1.17913e+08 1.07407e+08 1.39185e+08 1.27862e+08 1.04999e+08 1.10213e+08 1.35869e+08 8.98274e+07 7.92713e+07 1.33473e+08 1.05198e+08 1.08104e+08 8.50562e+07 8.18858e+07 1.07503e+08 1.17529e+08 8.92802e+07 8.55707e+07 1.00939e+08 1.04923e+08 5.64046e+07 1.19273e+08 8.96226e+07 7.93988e+07 1.08426e+08 1.23852e+08 5.84704e+07 7.75577e+07 6.42773e+07 1.34368e+08 4.48045e+07 9.15549e+07 1.5207e+08 1.27289e+08 1.23063e+08 1.10754e+08 1.32748e+08 1.29664e+08 1.36412e+08 5.72146e+07 1.158e+08 1.1972e+08 1.00128e+08 1.35666e+08 1.77091e+08 1.26415e+08 1.05859e+08 5.48655e+07 1.46796e+08 1.17093e+08 1.59789e+08 1.39032e+08 
 4.47804e+07 9.12539e+07 1.31858e+08 1.97369e+08 1.44401e+08 2.45514e+08 1.71595e+08 1.85337e+08 1.76193e+08 1.69527e+08 1.93859e+08 1.53438e+08 2.00583e+08 2.27816e+08 1.30423e+08 1.4035e+08 1.167e+08 1.38887e+08 1.61838e+08 1.5459e+08 1.24576e+08 1.14665e+08 1.06982e+08 1.84743e+08 1.7922e+08 2.22594e+08 1.72882e+08 1.75433e+08 1.65775e+08 2.38601e+08 2.44939e+08 1.56335e+08 1.47593e+08 1.26704e+08 1.05054e+08 1.95183e+08 2.43542e+08 2.19401e+08 1.64827e+08 1.98211e+08 1.73235e+08 2.72262e+08 1.30717e+08 1.15874e+08 2.36302e+08 2.15846e+08 1.78965e+08 6.3094e+07 2.28509e+08 2.38261e+08 1.75433e+08 8.6859e+07 1.91693e+08 9.34473e+07 1.87627e+08 2.2724e+08 1.30644e+08 2.26001e+08 1.96146e+08 1.70194e+08 2.00827e+08 2.19561e+08 1.97262e+08 1.69738e+08 2.17589e+08 1.58642e+08 1.06978e+08 1.97356e+08 1.71517e+08 1.8538e+08 1.05659e+08 1.32102e+08 1.93866e+08 1.48832e+08 1.55719e+08 1.4026e+08 1.79281e+08 1.54883e+08 1.00812e+08 1.86857e+08 1.45486e+08 1.44526e+08 1.89742e+08 1.95956e+08 1.39001e+08 1.11143e+08 8.7994e+07 2.27394e+08 1.06454e+08 1.85168e+08 2.60038e+08 2.20856e+08 2.30759e+08 1.67391e+08 2.19076e+08 1.99571e+08 2.03482e+08 1.04529e+08 2.1153e+08 1.86031e+08 1.87366e+08 2.14646e+08 2.40874e+08 1.75299e+08 1.78081e+08 8.86432e+07 2.55267e+08 1.7756e+08 2.43526e+08 2.33526e+08 
 2.59573e+07 6.34742e+07 7.61928e+07 1.41763e+08 1.0311e+08 1.71595e+08 2.44501e+08 1.5215e+08 2.14064e+08 1.31913e+08 1.43462e+08 2.31809e+08 1.97019e+08 2.6324e+08 1.52995e+08 2.04982e+08 1.59181e+08 2.07997e+08 2.22006e+08 1.62926e+08 1.27688e+08 1.67211e+08 2.0566e+08 2.38433e+08 1.76736e+08 2.59991e+08 2.48663e+08 1.32312e+08 1.34238e+08 3.097e+08 2.42095e+08 1.48788e+08 1.98838e+08 1.76718e+08 1.45543e+08 1.97575e+08 2.96564e+08 2.34616e+08 2.19414e+08 2.27655e+08 1.68389e+08 2.50336e+08 1.46713e+08 1.64429e+08 2.27764e+08 2.58093e+08 2.56798e+08 1.82798e+08 2.83607e+08 2.13932e+08 2.07226e+08 1.24758e+08 2.92374e+08 1.03304e+08 2.51377e+08 2.01143e+08 1.8984e+08 2.31999e+08 2.03072e+08 2.09424e+08 1.88059e+08 2.30023e+08 2.04783e+08 2.12644e+08 2.91362e+08 1.50188e+08 1.4141e+08 2.34285e+08 1.86591e+08 2.48285e+08 1.89964e+08 1.95616e+08 2.1281e+08 2.24394e+08 1.62673e+08 1.68598e+08 2.41202e+08 1.09816e+08 8.65235e+07 2.12059e+08 1.90269e+08 2.07424e+08 2.25003e+08 2.15401e+08 1.81984e+08 1.22014e+08 1.70782e+08 2.33326e+08 1.38943e+08 1.77279e+08 2.03763e+08 2.14463e+08 1.8248e+08 2.04398e+08 2.70837e+08 2.7279e+08 2.68188e+08 1.29276e+08 2.65791e+08 1.45197e+08 1.80518e+08 1.90883e+08 2.28201e+08 2.33165e+08 1.73992e+08 1.3102e+08 2.75388e+08 1.73368e+08 2.40836e+08 2.75513e+08 
 3.04581e+07 9.24856e+07 1.34178e+08 2.00016e+08 1.16474e+08 1.85337e+08 1.5215e+08 2.01089e+08 1.65755e+08 1.42173e+08 1.77288e+08 1.51523e+08 2.0841e+08 1.90756e+08 1.54141e+08 1.4733e+08 1.14204e+08 1.28428e+08 1.53226e+08 1.67658e+08 1.36061e+08 1.05659e+08 1.12418e+08 1.65861e+08 1.87833e+08 2.30244e+08 1.77509e+08 1.70326e+08 1.31082e+08 1.93382e+08 2.14014e+08 1.21049e+08 1.3526e+08 1.00118e+08 8.96442e+07 1.98081e+08 2.46521e+08 2.46582e+08 2.04401e+08 1.7235e+08 1.24965e+08 2.22872e+08 1.20486e+08 1.24463e+08 1.93075e+08 1.99651e+08 1.50225e+08 1.20793e+08 2.14919e+08 1.67432e+08 2.05287e+08 1.06132e+08 1.90545e+08 5.63862e+07 2.08479e+08 1.92035e+08 1.17948e+08 2.36892e+08 1.69335e+08 2.04889e+08 2.11709e+08 2.12443e+08 1.87448e+08 1.55736e+08 2.08621e+08 1.59769e+08 1.11388e+08 2.01073e+08 1.79809e+08 1.56973e+08 1.53422e+08 1.70838e+08 1.94796e+08 1.49285e+08 1.95852e+08 1.67869e+08 1.82242e+08 1.22005e+08 1.17139e+08 1.93773e+08 1.17095e+08 1.22151e+08 2.00887e+08 1.81094e+08 1.35155e+08 1.31003e+08 1.11668e+08 2.05443e+08 1.24237e+08 2.04104e+08 2.35908e+08 1.7713e+08 1.68612e+08 2.01367e+08 2.13749e+08 2.05568e+08 2.33612e+08 1.20715e+08 2.04443e+08 1.52103e+08 1.75185e+08 2.21845e+08 2.36876e+08 1.77989e+08 2.04436e+08 1.36521e+08 2.57498e+08 1.96123e+08 2.58526e+08 2.11609e+08 
 4.05466e+07 9.22365e+07 7.86871e+07 1.53669e+08 1.00295e+08 1.76193e+08 2.14064e+08 1.65755e+08 2.6882e+08 1.65473e+08 2.17487e+08 2.00701e+08 2.70088e+08 2.89293e+08 2.15418e+08 2.58037e+08 1.55082e+08 2.46866e+08 2.42109e+08 2.17408e+08 1.93136e+08 2.28677e+08 2.09381e+08 2.32323e+08 2.41033e+08 2.52464e+08 3.08646e+08 2.17572e+08 1.53228e+08 3.4976e+08 2.84781e+08 2.11301e+08 2.40312e+08 1.74911e+08 1.63822e+08 2.52684e+08 3.41662e+08 2.92003e+08 2.51235e+08 2.28362e+08 2.29027e+08 2.73182e+08 1.57786e+08 2.40037e+08 2.74329e+08 2.46787e+08 2.64271e+08 2.26795e+08 3.00285e+08 2.10331e+08 2.28779e+08 1.69826e+08 3.1966e+08 1.63571e+08 2.78656e+08 2.6962e+08 2.01243e+08 2.57966e+08 2.23128e+08 2.53501e+08 1.92329e+08 2.89637e+08 2.14891e+08 2.6874e+08 3.0983e+08 2.51489e+08 1.88247e+08 2.89247e+08 2.05329e+08 2.43942e+08 2.40894e+08 2.30243e+08 2.47276e+08 2.02388e+08 2.10819e+08 1.73439e+08 2.50034e+08 1.62239e+08 1.57338e+08 2.79042e+08 2.21531e+08 2.09709e+08 2.35624e+08 2.32415e+08 2.08478e+08 1.88037e+08 1.73002e+08 2.84046e+08 1.76244e+08 2.28679e+08 2.94571e+08 2.44484e+08 2.16234e+08 2.17097e+08 2.85837e+08 3.00173e+08 2.72215e+08 1.81713e+08 3.00529e+08 2.02956e+08 2.03705e+08 2.45374e+08 2.89147e+08 2.79461e+08 2.48621e+08 1.60254e+08 3.53978e+08 2.59903e+08 3.22493e+08 2.96646e+08 
 4.20314e+06 2.67084e+07 8.96379e+07 1.08323e+08 1.15303e+08 1.69527e+08 1.31913e+08 1.42173e+08 1.65473e+08 2.57487e+08 2.64625e+08 1.31534e+08 2.15341e+08 2.19356e+08 1.92477e+08 2.31867e+08 1.50365e+08 1.3499e+08 1.36084e+08 1.91278e+08 1.36349e+08 2.038e+08 1.66232e+08 2.00211e+08 1.86885e+08 2.43759e+08 2.28693e+08 2.23965e+08 2.10672e+08 2.15059e+08 2.65025e+08 2.3592e+08 1.31604e+08 1.42667e+08 1.51515e+08 2.56915e+08 2.2177e+08 2.59253e+08 1.77478e+08 2.10871e+08 1.94506e+08 2.68354e+08 1.94818e+08 1.41487e+08 2.37603e+08 2.2169e+08 1.86944e+08 1.93738e+08 2.04367e+08 1.80125e+08 2.66368e+08 1.42789e+08 2.92223e+08 1.64338e+08 2.27506e+08 1.90657e+08 1.74176e+08 2.39311e+08 2.28432e+08 1.92459e+08 2.19764e+08 2.80169e+08 1.4728e+08 2.45431e+08 2.69523e+08 1.89502e+08 2.02942e+08 2.94367e+08 2.31522e+08 2.06671e+08 1.95741e+08 1.88264e+08 2.38024e+08 1.88134e+08 1.49682e+08 1.15345e+08 2.0875e+08 2.2415e+08 1.19635e+08 2.65529e+08 2.33758e+08 1.28477e+08 1.44709e+08 2.31894e+08 1.50814e+08 1.94031e+08 1.46938e+08 1.8601e+08 1.68824e+08 1.68887e+08 3.02813e+08 1.81401e+08 2.20998e+08 1.91971e+08 2.37286e+08 2.60285e+08 2.08616e+08 1.95898e+08 2.05464e+08 2.561e+08 2.06485e+08 2.58302e+08 3.21845e+08 2.374e+08 1.61138e+08 1.15534e+08 3.15384e+08 2.88456e+08 3.39684e+08 2.49056e+08 
 2.58153e+07 6.16585e+07 1.00925e+08 1.47557e+08 1.25371e+08 1.93859e+08 1.43462e+08 1.77288e+08 2.17487e+08 2.64625e+08 3.60995e+08 1.74976e+08 2.91035e+08 3.34399e+08 2.75888e+08 3.21137e+08 1.95059e+08 1.93232e+08 2.11969e+08 2.75235e+08 2.15262e+08 2.59726e+08 2.34983e+08 2.22078e+08 2.92235e+08 3.09772e+08 3.35886e+08 3.65634e+08 2.50255e+08 3.00493e+08 3.60185e+08 3.03647e+08 2.31794e+08 1.96603e+08 1.84224e+08 3.04452e+08 3.54526e+08 3.39824e+08 2.31419e+08 2.40447e+08 2.53911e+08 3.50734e+08 2.4774e+08 2.49024e+08 2.88339e+08 2.83597e+08 2.38121e+08 2.66082e+08 2.88388e+08 2.74862e+08 3.51113e+08 1.81747e+08 3.64437e+08 2.32495e+08 3.09286e+08 2.58435e+08 2.10784e+08 3.16945e+08 2.56456e+08 2.4244e+08 2.72059e+08 3.57235e+08 2.55004e+08 2.93851e+08 3.35814e+08 2.85008e+08 2.8997e+08 3.54535e+08 2.88293e+08 2.79708e+08 2.91856e+08 2.85537e+08 3.07965e+08 2.05663e+08 2.56752e+08 2.09287e+08 3.03574e+08 2.8468e+08 2.36316e+08 3.80792e+08 3.18329e+08 2.0202e+08 2.36394e+08 3.16949e+08 2.48412e+08 2.95256e+08 1.91438e+08 3.10314e+08 2.41465e+08 2.59871e+08 4.36465e+08 2.82335e+08 2.73099e+08 2.72461e+08 3.0784e+08 3.50006e+08 2.72901e+08 2.82508e+08 2.87249e+08 3.24477e+08 2.82515e+08 3.60392e+08 4.3618e+08 3.07576e+08 3.06969e+08 1.60772e+08 4.14038e+08 3.69276e+08 4.45452e+08 3.34955e+08 
 2.01592e+07 3.38407e+07 8.23418e+07 1.23984e+08 8.09803e+07 1.53438e+08 2.31809e+08 1.51523e+08 2.00701e+08 1.31534e+08 1.74976e+08 2.78205e+08 2.08745e+08 3.01007e+08 1.63154e+08 2.57123e+08 1.98832e+08 2.35262e+08 2.3627e+08 2.30038e+08 1.4377e+08 1.76982e+08 2.4847e+08 2.21414e+08 2.3078e+08 3.01898e+08 2.95312e+08 1.66137e+08 1.47741e+08 2.95766e+08 2.31705e+08 1.6756e+08 2.20566e+08 2.12603e+08 1.55863e+08 2.18559e+08 3.19365e+08 2.54641e+08 2.59522e+08 2.55259e+08 1.77813e+08 2.54235e+08 1.97808e+08 1.97698e+08 2.4327e+08 3.04731e+08 2.63374e+08 2.3218e+08 3.19257e+08 2.51126e+08 2.56481e+08 1.46997e+08 3.35541e+08 1.09589e+08 2.77278e+08 1.78354e+08 2.09705e+08 2.56223e+08 1.98824e+08 2.04513e+08 2.10904e+08 2.88465e+08 2.65014e+08 2.14874e+08 3.03338e+08 1.5063e+08 1.74997e+08 2.43362e+08 2.27617e+08 2.52929e+08 2.142e+08 2.26447e+08 2.3593e+08 2.24816e+08 1.99795e+08 1.92297e+08 3.00054e+08 1.41615e+08 1.34138e+08 2.44708e+08 2.34097e+08 2.28932e+08 2.53785e+08 2.67852e+08 2.43554e+08 1.45225e+08 1.84977e+08 2.48234e+08 1.8843e+08 2.15461e+08 2.62155e+08 2.1802e+08 1.84646e+08 2.35079e+08 2.72523e+08 3.29339e+08 2.96058e+08 1.95577e+08 2.95062e+08 1.70825e+08 2.2841e+08 2.21799e+08 2.47689e+08 2.28956e+08 2.13556e+08 1.57175e+08 2.97429e+08 2.25402e+08 2.9879e+08 3.40123e+08 
 2.23831e+07 9.50378e+07 1.14162e+08 1.83694e+08 1.20411e+08 2.00583e+08 1.97019e+08 2.0841e+08 2.70088e+08 2.15341e+08 2.91035e+08 2.08745e+08 3.89247e+08 3.3934e+08 3.3695e+08 3.50317e+08 2.21559e+08 2.71194e+08 2.87069e+08 3.70387e+08 3.09221e+08 2.76317e+08 2.71309e+08 2.85283e+08 3.56192e+08 3.40805e+08 3.5404e+08 3.29198e+08 2.75795e+08 3.94262e+08 3.83689e+08 3.31178e+08 3.19888e+08 2.57965e+08 2.45036e+08 3.87994e+08 4.1915e+08 4.19075e+08 3.5227e+08 2.66819e+08 3.17946e+08 3.77476e+08 2.36044e+08 2.50112e+08 3.26542e+08 3.04432e+08 3.10727e+08 2.90073e+08 3.37916e+08 2.35426e+08 3.65092e+08 2.47406e+08 4.06753e+08 2.20706e+08 3.56072e+08 3.48752e+08 2.88712e+08 3.97415e+08 2.99012e+08 3.32696e+08 2.84177e+08 4.24785e+08 2.89961e+08 3.40521e+08 3.94989e+08 3.10839e+08 3.21278e+08 3.93193e+08 3.3123e+08 3.34149e+08 3.51349e+08 2.86502e+08 3.67843e+08 2.07381e+08 3.14459e+08 2.92816e+08 3.37759e+08 2.70612e+08 2.5695e+08 3.82463e+08 3.32201e+08 2.88497e+08 3.44011e+08 3.28911e+08 3.11604e+08 2.62105e+08 2.11414e+08 3.73316e+08 2.41957e+08 3.4488e+08 4.22747e+08 3.20015e+08 3.0035e+08 3.34515e+08 3.41892e+08 3.91554e+08 3.48391e+08 3.03551e+08 3.70813e+08 2.94817e+08 2.85093e+08 3.38885e+08 4.20801e+08 3.83898e+08 3.6223e+08 2.08047e+08 4.51811e+08 3.75377e+08 4.78659e+08 3.86214e+08 
 4.93081e+07 8.84553e+07 7.52198e+07 1.56027e+08 1.24984e+08 2.27816e+08 2.6324e+08 1.90756e+08 2.89293e+08 2.19356e+08 3.34399e+08 3.01007e+08 3.3934e+08 5.15761e+08 3.20538e+08 4.82983e+08 3.14552e+08 3.50361e+08 3.63776e+08 3.71313e+08 2.94796e+08 3.40189e+08 4.11613e+08 3.90346e+08 4.19702e+08 4.19818e+08 4.54116e+08 3.99577e+08 3.37497e+08 5.09187e+08 4.73799e+08 3.79359e+08 3.9714e+08 2.9944e+08 2.80932e+08 3.46013e+08 5.3983e+08 4.49285e+08 3.93718e+08 3.59932e+08 3.56968e+08 4.8732e+08 3.17049e+08 3.55326e+08 4.04468e+08 4.2587e+08 4.14879e+08 3.5954e+08 4.44214e+08 4.00556e+08 4.20217e+08 2.80049e+08 5.15119e+08 2.80632e+08 4.29735e+08 3.7541e+08 3.81573e+08 4.13815e+08 3.68921e+08 3.34971e+08 3.48147e+08 4.33031e+08 4.07407e+08 3.58053e+08 4.95413e+08 3.45152e+08 3.77421e+08 4.31644e+08 3.97505e+08 4.578e+08 3.92769e+08 3.97103e+08 4.34893e+08 3.16523e+08 3.60851e+08 3.52042e+08 4.58541e+08 3.12688e+08 2.92497e+08 4.51715e+08 4.58626e+08 3.78065e+08 3.87883e+08 3.9422e+08 3.90295e+08 3.3972e+08 3.29765e+08 4.74881e+08 3.59913e+08 3.6038e+08 5.09372e+08 4.36567e+08 3.89455e+08 3.9207e+08 4.87834e+08 5.05423e+08 4.15866e+08 3.35217e+08 4.21741e+08 3.58519e+08 4.12558e+08 3.81178e+08 4.85773e+08 4.43795e+08 4.20623e+08 2.5257e+08 5.23405e+08 4.30305e+08 5.17372e+08 5.09279e+08 
 1.53519e+07 8.1105e+07 8.91849e+07 1.60351e+08 9.82726e+07 1.30423e+08 1.52995e+08 1.54141e+08 2.15418e+08 1.92477e+08 2.75888e+08 1.63154e+08 3.3695e+08 3.20538e+08 4.4508e+08 3.81391e+08 1.96421e+08 2.23511e+08 3.40818e+08 3.51725e+08 3.29984e+08 2.90734e+08 3.28812e+08 3.16607e+08 3.99922e+08 3.27857e+08 3.09725e+08 3.6551e+08 3.19114e+08 4.00566e+08 4.75253e+08 4.00837e+08 3.73386e+08 2.69804e+08 2.88937e+08 3.71516e+08 4.13534e+08 3.92853e+08 3.4186e+08 2.44417e+08 3.37692e+08 3.8653e+08 2.21324e+08 2.99535e+08 2.85379e+08 2.67156e+08 3.10053e+08 3.08706e+08 3.91606e+08 2.39275e+08 4.27362e+08 2.76649e+08 4.04399e+08 2.57215e+08 3.78777e+08 2.94713e+08 3.4372e+08 4.09232e+08 3.07029e+08 3.54056e+08 2.86068e+08 4.06393e+08 3.5014e+08 3.48423e+08 4.16579e+08 3.17178e+08 4.27832e+08 4.27433e+08 4.00004e+08 4.1632e+08 4.58562e+08 4.0557e+08 3.93751e+08 2.63719e+08 3.17938e+08 3.27659e+08 3.24241e+08 3.18759e+08 3.04396e+08 3.94801e+08 3.84575e+08 3.14146e+08 3.71421e+08 3.55183e+08 3.18505e+08 2.96786e+08 2.53435e+08 3.8496e+08 2.86961e+08 2.71136e+08 4.12003e+08 3.55952e+08 2.84399e+08 4.30744e+08 4.19789e+08 4.26006e+08 3.31983e+08 3.32598e+08 3.68033e+08 3.5889e+08 2.87433e+08 3.41197e+08 4.91645e+08 4.66343e+08 3.9156e+08 2.06316e+08 4.04969e+08 4.18537e+08 4.82575e+08 4.03233e+08 
 2.39142e+07 5.84177e+07 4.00669e+07 8.83869e+07 7.24175e+07 1.4035e+08 2.04982e+08 1.4733e+08 2.58037e+08 2.31867e+08 3.21137e+08 2.57123e+08 3.50317e+08 4.82983e+08 3.81391e+08 6.74177e+08 3.90368e+08 4.80663e+08 4.38389e+08 4.63528e+08 3.51156e+08 4.48257e+08 5.19791e+08 5.23402e+08 5.57792e+08 4.41489e+08 4.92818e+08 4.75184e+08 4.32832e+08 5.73043e+08 5.08509e+08 5.02091e+08 4.69563e+08 3.41747e+08 4.11679e+08 4.46434e+08 5.48281e+08 5.60533e+08 5.12326e+08 4.50858e+08 4.61255e+08 5.1128e+08 3.93718e+08 4.55536e+08 4.82752e+08 5.00967e+08 4.63705e+08 5.00622e+08 5.01775e+08 3.73143e+08 5.24963e+08 4.20916e+08 5.66084e+08 3.815e+08 4.85407e+08 4.36606e+08 5.50801e+08 5.09174e+08 4.80799e+08 4.63387e+08 3.96357e+08 5.52425e+08 4.64178e+08 4.39257e+08 5.78819e+08 4.96625e+08 5.03434e+08 5.67646e+08 5.16975e+08 5.51366e+08 5.15936e+08 5.03811e+08 5.78894e+08 4.02552e+08 4.2975e+08 4.07466e+08 5.33887e+08 4.06804e+08 4.15317e+08 5.25028e+08 6.05895e+08 4.54287e+08 4.47478e+08 4.65394e+08 4.62024e+08 4.4221e+08 3.64006e+08 5.53018e+08 5.5195e+08 4.4857e+08 5.96843e+08 4.54622e+08 4.32833e+08 5.1991e+08 5.89327e+08 5.7927e+08 4.35356e+08 4.05813e+08 4.61791e+08 4.90777e+08 5.04073e+08 4.27629e+08 6.1569e+08 5.96912e+08 5.10596e+08 3.54248e+08 5.88061e+08 5.74044e+08 6.63625e+08 5.64195e+08 
 9.93611e+06 3.54386e+07 3.93302e+07 7.05051e+07 5.7956e+07 1.167e+08 1.59181e+08 1.14204e+08 1.55082e+08 1.50365e+08 1.95059e+08 1.98832e+08 2.21559e+08 3.14552e+08 1.96421e+08 3.90368e+08 3.57743e+08 2.97807e+08 2.61397e+08 3.01749e+08 2.0247e+08 2.61217e+08 2.96307e+08 3.17091e+08 3.79503e+08 3.45868e+08 3.57754e+08 2.94148e+08 3.28284e+08 3.50303e+08 3.83616e+08 3.64098e+08 3.1976e+08 2.66319e+08 2.80989e+08 2.80513e+08 3.56439e+08 3.95631e+08 3.20495e+08 3.26321e+08 2.43597e+08 3.36485e+08 3.41309e+08 2.78179e+08 2.91381e+08 3.6226e+08 3.60284e+08 3.09749e+08 3.401e+08 3.2099e+08 3.47197e+08 2.81339e+08 3.60383e+08 2.19519e+08 3.68431e+08 3.44083e+08 3.24222e+08 3.39503e+08 3.20112e+08 3.32638e+08 2.96039e+08 3.42306e+08 3.64002e+08 2.86849e+08 4.12673e+08 2.79478e+08 3.01275e+08 4.11701e+08 3.91507e+08 3.8694e+08 2.94045e+08 3.74559e+08 4.09758e+08 2.94445e+08 3.01711e+08 3.47299e+08 3.56732e+08 2.34377e+08 2.84585e+08 3.82468e+08 3.59376e+08 2.91525e+08 3.07262e+08 3.00485e+08 3.57495e+08 2.53588e+08 2.26748e+08 3.91851e+08 3.45076e+08 3.29312e+08 3.98159e+08 2.7979e+08 2.98472e+08 3.30876e+08 3.75735e+08 4.12003e+08 3.34045e+08 2.85715e+08 3.36276e+08 3.03261e+08 3.14109e+08 3.41739e+08 3.73077e+08 3.91946e+08 3.20514e+08 2.72142e+08 4.05074e+08 3.67675e+08 4.68869e+08 3.7588e+08 
 4.04512e+07 6.09404e+07 4.81698e+07 9.88755e+07 5.94399e+07 1.38887e+08 2.07997e+08 1.28428e+08 2.46866e+08 1.3499e+08 1.93232e+08 2.35262e+08 2.71194e+08 3.50361e+08 2.23511e+08 4.80663e+08 2.97807e+08 4.84234e+08 3.81647e+08 3.71115e+08 2.65609e+08 3.61114e+08 3.98446e+08 4.49826e+08 4.62247e+08 3.94336e+08 4.14817e+08 3.14735e+08 3.18327e+08 5.20721e+08 3.58344e+08 3.67362e+08 4.20792e+08 2.93907e+08 3.35607e+08 3.65117e+08 4.63238e+08 4.50456e+08 4.24206e+08 4.00105e+08 4.02393e+08 3.76152e+08 2.70738e+08 3.93816e+08 4.36504e+08 4.49294e+08 4.13067e+08 3.73624e+08 4.45447e+08 3.33739e+08 3.60103e+08 3.77888e+08 4.17925e+08 3.08777e+08 4.12957e+08 4.14271e+08 4.07195e+08 4.26311e+08 3.76027e+08 4.34881e+08 3.00257e+08 4.42104e+08 3.79317e+08 3.23922e+08 4.60333e+08 4.40037e+08 3.31038e+08 4.61017e+08 3.79395e+08 4.14984e+08 3.63604e+08 3.57647e+08 4.28494e+08 3.50793e+08 3.52245e+08 2.96327e+08 4.0791e+08 2.66181e+08 3.63193e+08 3.87577e+08 4.25621e+08 4.06575e+08 3.71138e+08 3.65355e+08 3.83169e+08 3.22345e+08 2.19811e+08 4.78948e+08 4.25928e+08 3.84435e+08 4.34267e+08 3.31129e+08 3.40107e+08 3.83561e+08 4.50208e+08 4.55243e+08 3.739e+08 2.94463e+08 4.0722e+08 3.83757e+08 3.6965e+08 3.51208e+08 4.68484e+08 4.49473e+08 4.21422e+08 2.96579e+08 4.61273e+08 3.992e+08 5.19935e+08 4.52811e+08 
 3.74477e+07 9.44594e+07 7.85577e+07 1.62928e+08 9.08564e+07 1.61838e+08 2.22006e+08 1.53226e+08 2.42109e+08 1.36084e+08 2.11969e+08 2.3627e+08 2.87069e+08 3.63776e+08 3.40818e+08 4.38389e+08 2.61397e+08 3.81647e+08 5.85117e+08 4.78334e+08 3.60399e+08 3.66388e+08 4.21289e+08 5.48791e+08 4.67503e+08 4.66127e+08 4.11221e+08 4.02965e+08 3.33231e+08 5.25511e+08 5.58822e+08 5.19644e+08 5.10223e+08 3.44905e+08 4.20098e+08 4.5844e+08 4.5552e+08 4.10768e+08 3.8489e+08 4.77636e+08 4.30095e+08 4.86995e+08 3.40948e+08 4.49765e+08 3.59214e+08 5.33958e+08 4.64828e+08 4.06856e+08 5.22144e+08 3.91733e+08 5.01275e+08 3.68796e+08 4.51383e+08 2.92092e+08 4.62795e+08 3.77102e+08 4.06662e+08 5.54419e+08 4.88436e+08 4.49917e+08 2.91239e+08 4.90355e+08 5.47134e+08 4.60617e+08 5.99987e+08 5.15503e+08 4.18668e+08 5.18772e+08 4.95178e+08 5.48678e+08 5.50951e+08 4.89303e+08 4.45597e+08 3.82526e+08 4.54348e+08 3.89475e+08 4.11284e+08 3.07314e+08 3.90063e+08 4.75457e+08 4.82994e+08 4.21327e+08 3.9794e+08 5.41747e+08 4.22834e+08 3.77743e+08 2.67878e+08 5.72504e+08 3.7742e+08 4.72161e+08 4.4784e+08 4.52346e+08 4.15694e+08 4.99675e+08 6.11019e+08 4.8107e+08 4.113e+08 3.59433e+08 4.4807e+08 4.09114e+08 3.50038e+08 4.57718e+08 5.56984e+08 5.49573e+08 4.39336e+08 2.97434e+08 4.88094e+08 4.20803e+08 5.18994e+08 6.0343e+08 
 89092.8 2.80227e+07 1.00082e+08 1.22258e+08 8.33245e+07 1.5459e+08 1.62926e+08 1.67658e+08 2.17408e+08 1.91278e+08 2.75235e+08 2.30038e+08 3.70387e+08 3.71313e+08 3.51725e+08 4.63528e+08 3.01749e+08 3.71115e+08 4.78334e+08 7.32041e+08 4.4228e+08 4.55986e+08 5.10842e+08 5.85804e+08 6.11999e+08 5.63924e+08 5.01566e+08 4.2321e+08 4.59471e+08 5.21198e+08 5.58089e+08 6.28858e+08 5.36625e+08 3.90083e+08 4.73149e+08 5.49199e+08 4.7404e+08 5.26607e+08 5.78295e+08 4.69244e+08 5.19479e+08 5.31051e+08 4.02878e+08 4.33455e+08 4.57602e+08 6.23762e+08 5.4516e+08 4.90626e+08 5.25308e+08 4.00332e+08 6.14434e+08 4.44804e+08 5.99864e+08 3.94152e+08 5.32609e+08 4.0013e+08 4.1191e+08 6.51874e+08 5.20188e+08 4.96391e+08 4.1471e+08 5.75402e+08 5.89132e+08 4.8074e+08 6.35446e+08 5.43809e+08 4.73102e+08 5.43933e+08 5.76545e+08 5.37617e+08 5.88638e+08 4.25786e+08 4.96764e+08 4.40496e+08 4.97905e+08 4.57444e+08 5.01536e+08 4.77207e+08 5.43147e+08 6.03004e+08 5.88602e+08 4.56596e+08 4.36247e+08 6.29267e+08 4.65472e+08 4.93891e+08 3.41474e+08 6.15097e+08 3.85459e+08 5.56109e+08 5.7542e+08 4.15791e+08 5.01651e+08 5.28112e+08 5.31294e+08 6.07427e+08 5.37025e+08 5.34171e+08 5.14365e+08 4.8065e+08 4.48087e+08 5.50349e+08 6.35053e+08 5.92269e+08 5.79855e+08 3.69607e+08 5.78365e+08 5.87019e+08 6.48673e+08 6.51547e+08 
 1.78977e+07 7.45638e+07 6.64034e+07 1.21563e+08 7.55722e+07 1.24576e+08 1.27688e+08 1.36061e+08 1.93136e+08 1.36349e+08 2.15262e+08 1.4377e+08 3.09221e+08 2.94796e+08 3.29984e+08 3.51156e+08 2.0247e+08 2.65609e+08 3.60399e+08 4.4228e+08 4.18406e+08 3.68803e+08 3.98079e+08 4.34389e+08 4.60803e+08 3.97792e+08 3.67021e+08 4.06338e+08 3.64266e+08 4.5918e+08 5.20624e+08 4.69158e+08 4.10382e+08 3.38612e+08 3.74566e+08 4.87296e+08 4.11371e+08 4.4401e+08 4.70893e+08 3.74677e+08 3.97516e+08 4.6661e+08 3.25567e+08 3.35411e+08 3.41747e+08 4.27189e+08 4.02142e+08 3.19693e+08 4.12233e+08 3.43015e+08 4.66773e+08 3.67363e+08 4.67769e+08 2.89559e+08 4.58526e+08 3.70278e+08 3.72731e+08 4.80457e+08 4.30138e+08 4.17674e+08 3.18245e+08 4.53368e+08 4.30461e+08 4.24852e+08 4.88107e+08 4.29394e+08 4.62309e+08 4.70141e+08 4.94103e+08 4.89328e+08 4.59972e+08 3.69179e+08 4.18611e+08 2.95091e+08 4.06164e+08 3.57557e+08 4.06666e+08 3.47174e+08 3.98603e+08 4.36488e+08 4.65686e+08 3.88583e+08 4.20286e+08 4.36182e+08 4.1538e+08 3.78912e+08 3.049e+08 4.84471e+08 3.55992e+08 4.33361e+08 4.60592e+08 3.98343e+08 3.3777e+08 4.35134e+08 4.51916e+08 4.50756e+08 4.22535e+08 3.50365e+08 3.92669e+08 3.9601e+08 3.80901e+08 4.38867e+08 5.24234e+08 5.05795e+08 4.73838e+08 2.74719e+08 4.66153e+08 4.3223e+08 4.98981e+08 4.94523e+08 
 3.2621e+06 1.76147e+07 1.24344e+07 3.49175e+07 8.34655e+07 1.14665e+08 1.67211e+08 1.05659e+08 2.28677e+08 2.038e+08 2.59726e+08 1.76982e+08 2.76317e+08 3.40189e+08 2.90734e+08 4.48257e+08 2.61217e+08 3.61114e+08 3.66388e+08 4.55986e+08 3.68803e+08 6.87955e+08 5.70853e+08 5.99564e+08 5.25014e+08 5.53885e+08 4.92856e+08 4.82361e+08 4.10396e+08 5.83014e+08 6.4481e+08 5.32313e+08 4.57982e+08 3.33336e+08 5.10212e+08 5.39591e+08 5.47694e+08 6.38407e+08 5.12305e+08 5.26858e+08 4.64815e+08 5.36343e+08 4.77115e+08 5.03525e+08 4.6589e+08 6.18379e+08 5.77135e+08 4.90529e+08 4.60086e+08 4.98173e+08 5.13414e+08 5.24737e+08 6.39548e+08 4.61338e+08 5.63717e+08 3.75554e+08 5.15404e+08 5.55809e+08 5.3332e+08 4.94375e+08 4.32539e+08 5.38125e+08 4.85424e+08 5.74727e+08 6.13235e+08 5.63161e+08 5.15413e+08 6.3327e+08 5.79864e+08 5.49424e+08 5.53773e+08 4.8452e+08 5.06054e+08 5.53351e+08 4.50167e+08 3.21035e+08 5.69481e+08 4.51309e+08 4.23692e+08 5.87016e+08 6.27914e+08 4.10637e+08 4.02804e+08 5.96418e+08 5.00613e+08 4.99733e+08 3.92447e+08 5.7531e+08 4.64608e+08 4.61801e+08 5.75763e+08 3.85381e+08 4.57936e+08 4.40155e+08 4.98369e+08 5.54588e+08 6.03336e+08 3.7383e+08 4.93277e+08 5.99542e+08 4.84402e+08 4.96228e+08 6.32723e+08 6.45116e+08 5.27927e+08 3.63146e+08 6.03825e+08 5.65127e+08 6.26696e+08 6.32549e+08 
 5.5796e+06 1.59984e+07 1.8896e+07 5.0476e+07 7.22496e+07 1.06982e+08 2.0566e+08 1.12418e+08 2.09381e+08 1.66232e+08 2.34983e+08 2.4847e+08 2.71309e+08 4.11613e+08 3.28812e+08 5.19791e+08 2.96307e+08 3.98446e+08 4.21289e+08 5.10842e+08 3.98079e+08 5.70853e+08 6.55804e+08 6.48668e+08 6.01672e+08 5.74442e+08 5.20074e+08 4.62298e+08 4.63679e+08 6.45436e+08 6.26996e+08 5.50226e+08 4.89409e+08 3.99772e+08 5.14703e+08 5.24209e+08 6.02053e+08 5.97445e+08 6.16788e+08 5.34337e+08 5.17007e+08 5.80353e+08 4.53163e+08 4.73174e+08 4.95123e+08 6.31348e+08 5.96094e+08 5.05872e+08 5.50965e+08 5.15204e+08 5.72999e+08 4.98345e+08 6.71466e+08 4.26909e+08 6.12534e+08 3.79193e+08 5.80769e+08 6.01623e+08 5.48344e+08 5.20407e+08 4.42413e+08 5.55934e+08 5.27996e+08 4.93039e+08 6.51253e+08 5.24227e+08 5.81395e+08 5.77026e+08 6.0748e+08 6.52166e+08 5.74494e+08 5.09503e+08 5.13288e+08 5.68159e+08 4.86124e+08 4.07165e+08 5.98797e+08 4.67098e+08 4.74707e+08 5.98213e+08 6.6624e+08 5.11634e+08 5.05517e+08 5.72952e+08 5.26971e+08 5.03556e+08 4.58953e+08 6.20236e+08 5.21616e+08 4.56668e+08 5.47192e+08 4.51765e+08 4.29047e+08 5.54081e+08 5.85768e+08 6.29422e+08 6.01227e+08 4.13761e+08 5.04469e+08 5.79215e+08 5.43392e+08 4.95072e+08 6.58798e+08 6.88975e+08 5.74433e+08 3.74816e+08 6.04771e+08 5.55869e+08 6.15269e+08 6.45935e+08 
 2.00697e+07 5.9261e+07 6.82267e+07 1.28801e+08 1.26384e+08 1.84743e+08 2.38433e+08 1.65861e+08 2.32323e+08 2.00211e+08 2.22078e+08 2.21414e+08 2.85283e+08 3.90346e+08 3.16607e+08 5.23402e+08 3.17091e+08 4.49826e+08 5.48791e+08 5.85804e+08 4.34389e+08 5.99564e+08 6.48668e+08 8.96719e+08 6.7481e+08 7.00507e+08 5.61104e+08 5.38541e+08 5.92835e+08 7.65111e+08 8.14277e+08 6.83324e+08 5.94915e+08 4.66834e+08 6.36876e+08 6.80733e+08 6.42727e+08 7.20069e+08 7.13497e+08 7.07723e+08 6.47417e+08 6.98529e+08 5.41486e+08 5.65007e+08 6.16217e+08 7.80015e+08 6.81352e+08 5.59384e+08 6.99168e+08 6.05041e+08 6.65394e+08 6.18106e+08 7.3957e+08 5.13803e+08 7.02774e+08 5.31909e+08 6.64948e+08 7.92701e+08 7.58939e+08 7.13509e+08 5.51137e+08 6.66945e+08 6.54499e+08 6.08075e+08 8.1895e+08 7.40416e+08 6.28196e+08 7.36048e+08 7.04493e+08 7.75123e+08 6.68806e+08 6.14659e+08 6.14239e+08 7.10822e+08 6.56355e+08 4.67337e+08 6.19476e+08 5.21807e+08 5.26744e+08 7.1424e+08 7.31989e+08 6.03656e+08 5.19919e+08 7.04091e+08 5.66356e+08 6.00666e+08 4.77176e+08 7.86582e+08 6.06414e+08 5.72141e+08 6.26477e+08 5.35609e+08 5.74033e+08 6.61597e+08 7.68896e+08 6.83304e+08 6.5925e+08 4.51134e+08 5.33368e+08 6.8732e+08 6.24292e+08 6.55315e+08 8.1705e+08 8.28711e+08 6.48182e+08 4.57144e+08 7.18283e+08 6.71295e+08 6.71175e+08 7.32379e+08 
 5.36971e+07 1.11532e+08 1.14342e+08 1.92313e+08 8.37658e+07 1.7922e+08 1.76736e+08 1.87833e+08 2.41033e+08 1.86885e+08 2.92235e+08 2.3078e+08 3.56192e+08 4.19702e+08 3.99922e+08 5.57792e+08 3.79503e+08 4.62247e+08 4.67503e+08 6.11999e+08 4.60803e+08 5.25014e+08 6.01672e+08 6.7481e+08 9.90933e+08 7.51042e+08 6.70359e+08 5.94136e+08 7.48649e+08 8.20696e+08 8.62662e+08 7.98034e+08 6.5084e+08 5.64168e+08 6.35937e+08 6.66234e+08 7.56058e+08 7.78187e+08 8.17155e+08 6.89788e+08 6.97699e+08 7.90282e+08 6.1255e+08 6.31357e+08 7.17884e+08 7.42498e+08 7.27874e+08 6.32782e+08 7.95007e+08 7.63295e+08 8.06275e+08 6.71803e+08 7.31265e+08 5.96111e+08 8.02302e+08 6.23825e+08 7.65907e+08 7.7345e+08 6.59184e+08 7.74962e+08 6.41999e+08 7.47481e+08 7.87775e+08 5.67156e+08 7.50544e+08 8.16209e+08 7.56083e+08 7.75553e+08 7.76169e+08 8.53814e+08 6.23222e+08 7.95578e+08 7.24277e+08 6.97785e+08 7.25036e+08 6.08504e+08 6.87753e+08 6.37337e+08 7.66696e+08 8.16558e+08 7.206e+08 6.58549e+08 7.36975e+08 7.34116e+08 7.33378e+08 6.60715e+08 4.71769e+08 8.83631e+08 7.40584e+08 6.14702e+08 7.65168e+08 6.35696e+08 6.3097e+08 8.00297e+08 6.9268e+08 7.17746e+08 7.21664e+08 5.67035e+08 7.19339e+08 8.23213e+08 6.92032e+08 7.17075e+08 8.50407e+08 8.07803e+08 8.58066e+08 5.45115e+08 8.05147e+08 7.24054e+08 8.29791e+08 7.16397e+08 
 9.46821e+06 4.50061e+07 1.17692e+08 1.65735e+08 1.53527e+08 2.22594e+08 2.59991e+08 2.30244e+08 2.52464e+08 2.43759e+08 3.09772e+08 3.01898e+08 3.40805e+08 4.19818e+08 3.27857e+08 4.41489e+08 3.45868e+08 3.94336e+08 4.66127e+08 5.63924e+08 3.97792e+08 5.53885e+08 5.74442e+08 7.00507e+08 7.51042e+08 1.008e+09 6.31255e+08 6.09658e+08 7.10333e+08 8.01871e+08 8.42305e+08 7.81431e+08 6.10618e+08 5.59491e+08 6.07965e+08 8.02737e+08 8.38394e+08 8.19358e+08 7.32621e+08 7.08843e+08 6.5515e+08 7.50736e+08 6.22234e+08 5.27085e+08 6.13384e+08 9.03099e+08 7.56082e+08 6.7983e+08 7.2899e+08 7.63304e+08 8.37793e+08 7.12087e+08 8.35795e+08 6.03052e+08 8.48191e+08 6.0681e+08 7.07278e+08 8.29499e+08 6.87391e+08 7.96621e+08 7.48807e+08 8.073e+08 7.22635e+08 6.148e+08 8.37642e+08 7.97803e+08 6.95848e+08 8.70281e+08 7.53972e+08 7.42716e+08 6.96962e+08 7.35729e+08 6.14696e+08 8.08241e+08 7.3436e+08 5.37935e+08 7.23707e+08 6.13643e+08 6.34531e+08 8.0187e+08 6.68979e+08 6.42908e+08 6.63012e+08 8.60231e+08 6.68388e+08 6.78619e+08 5.38217e+08 8.33427e+08 6.26912e+08 5.97593e+08 7.11068e+08 6.26281e+08 6.32399e+08 7.79873e+08 7.31834e+08 7.58756e+08 8.69524e+08 5.96278e+08 6.69199e+08 7.59369e+08 6.58505e+08 7.31149e+08 8.6062e+08 7.75118e+08 7.15252e+08 5.55895e+08 7.95012e+08 7.35559e+08 8.74804e+08 8.62053e+08 
 3.73399e+07 7.28861e+07 6.42335e+07 1.31176e+08 8.87511e+07 1.72882e+08 2.48663e+08 1.77509e+08 3.08646e+08 2.28693e+08 3.35886e+08 2.95312e+08 3.5404e+08 4.54116e+08 3.09725e+08 4.92818e+08 3.57754e+08 4.14817e+08 4.11221e+08 5.01566e+08 3.67021e+08 4.92856e+08 5.20074e+08 5.61104e+08 6.70359e+08 6.31255e+08 7.37441e+08 5.77365e+08 5.4583e+08 7.35056e+08 7.48694e+08 6.38435e+08 5.82103e+08 4.84139e+08 5.50959e+08 6.27723e+08 6.98662e+08 6.98464e+08 6.59138e+08 6.62782e+08 6.14867e+08 6.78515e+08 6.07093e+08 6.09776e+08 6.18485e+08 7.02903e+08 6.83222e+08 6.43238e+08 6.28178e+08 6.47342e+08 6.64629e+08 5.28353e+08 7.72567e+08 4.94562e+08 7.14317e+08 5.47452e+08 5.80321e+08 6.64067e+08 5.90239e+08 6.13985e+08 5.20849e+08 6.74866e+08 6.0355e+08 5.84109e+08 7.06384e+08 6.69492e+08 6.39806e+08 6.89558e+08 5.93821e+08 7.10302e+08 5.78576e+08 6.63156e+08 5.71765e+08 5.71024e+08 6.48081e+08 4.80592e+08 6.25685e+08 5.03578e+08 5.37264e+08 7.73971e+08 6.93471e+08 5.45304e+08 5.90339e+08 6.46338e+08 6.35273e+08 6.19039e+08 4.70861e+08 7.6845e+08 5.50523e+08 5.64262e+08 6.20149e+08 5.04641e+08 4.86371e+08 5.97765e+08 6.17507e+08 6.78678e+08 6.5463e+08 5.12958e+08 6.27711e+08 6.10111e+08 5.75402e+08 7.02894e+08 6.78876e+08 7.11013e+08 6.8818e+08 4.0002e+08 8.02388e+08 6.33427e+08 7.06855e+08 6.35967e+08 
 2.80245e+07 8.67791e+07 7.30372e+07 1.39844e+08 1.20788e+08 1.75433e+08 1.32312e+08 1.70326e+08 2.17572e+08 2.23965e+08 3.65634e+08 1.66137e+08 3.29198e+08 3.99577e+08 3.6551e+08 4.75184e+08 2.94148e+08 3.14735e+08 4.02965e+08 4.2321e+08 4.06338e+08 4.82361e+08 4.62298e+08 5.38541e+08 5.94136e+08 6.09658e+08 5.77365e+08 8.34691e+08 6.0898e+08 6.97151e+08 8.30155e+08 7.03606e+08 6.5504e+08 5.47898e+08 6.21869e+08 7.66737e+08 7.23125e+08 7.80913e+08 6.53566e+08 6.80054e+08 6.6259e+08 6.76708e+08 6.40676e+08 6.17684e+08 6.08568e+08 6.96263e+08 6.62694e+08 5.92129e+08 6.54358e+08 6.83256e+08 6.95283e+08 5.41664e+08 7.04439e+08 5.57337e+08 7.24798e+08 6.1231e+08 5.88884e+08 7.04166e+08 6.93109e+08 6.73303e+08 6.41632e+08 7.87199e+08 6.35563e+08 6.6239e+08 7.24076e+08 7.85111e+08 7.29174e+08 7.05343e+08 6.72359e+08 7.41485e+08 7.24837e+08 6.62738e+08 5.7546e+08 5.84241e+08 6.98847e+08 5.00947e+08 6.55514e+08 6.05877e+08 6.10887e+08 7.71115e+08 7.82588e+08 6.13631e+08 6.39556e+08 7.46374e+08 6.35181e+08 7.22455e+08 5.07052e+08 8.23053e+08 6.43057e+08 5.84288e+08 7.47868e+08 5.76391e+08 4.95321e+08 6.97732e+08 6.83653e+08 6.97725e+08 6.86305e+08 5.72934e+08 5.4759e+08 6.89991e+08 6.92389e+08 6.97802e+08 8.12637e+08 8.27182e+08 7.61424e+08 4.26989e+08 7.59991e+08 7.2545e+08 8.00859e+08 6.91753e+08 
 2.73813e+07 5.63463e+07 8.42149e+07 1.28678e+08 9.66085e+07 1.65775e+08 1.34238e+08 1.31082e+08 1.53228e+08 2.10672e+08 2.50255e+08 1.47741e+08 2.75795e+08 3.37497e+08 3.19114e+08 4.32832e+08 3.28284e+08 3.18327e+08 3.33231e+08 4.59471e+08 3.64266e+08 4.10396e+08 4.63679e+08 5.92835e+08 7.48649e+08 7.10333e+08 5.4583e+08 6.0898e+08 8.72541e+08 7.56552e+08 8.5526e+08 7.88428e+08 6.76813e+08 6.3562e+08 6.59679e+08 7.46277e+08 7.3713e+08 8.06555e+08 7.87352e+08 7.37195e+08 7.17904e+08 7.89061e+08 6.49304e+08 5.49027e+08 7.21092e+08 7.56617e+08 7.56083e+08 5.98235e+08 7.03398e+08 7.39018e+08 7.50621e+08 7.31301e+08 7.45966e+08 6.31366e+08 8.19951e+08 6.66642e+08 7.25806e+08 7.51966e+08 7.27406e+08 7.85996e+08 7.51464e+08 7.62501e+08 6.59314e+08 5.87357e+08 7.63443e+08 8.1394e+08 7.68971e+08 8.37073e+08 8.21967e+08 8.26736e+08 6.82299e+08 7.47626e+08 6.59114e+08 7.34461e+08 6.90558e+08 5.94692e+08 6.72457e+08 6.62928e+08 6.86946e+08 7.27955e+08 7.20108e+08 6.87211e+08 6.92508e+08 7.2215e+08 7.10291e+08 7.06184e+08 5.45351e+08 8.36312e+08 6.78429e+08 5.69004e+08 6.52069e+08 5.81647e+08 6.44613e+08 7.66742e+08 7.56804e+08 7.09461e+08 7.66974e+08 6.4855e+08 6.29092e+08 7.91206e+08 7.73734e+08 7.07284e+08 8.11122e+08 8.32939e+08 7.31294e+08 5.55797e+08 7.82437e+08 7.2447e+08 8.08744e+08 6.80999e+08 
 5.79155e+07 1.19761e+08 7.10075e+07 1.78747e+08 1.39753e+08 2.38601e+08 3.097e+08 1.93382e+08 3.4976e+08 2.15059e+08 3.00493e+08 2.95766e+08 3.94262e+08 5.09187e+08 4.00566e+08 5.73043e+08 3.50303e+08 5.20721e+08 5.25511e+08 5.21198e+08 4.5918e+08 5.83014e+08 6.45436e+08 7.65111e+08 8.20696e+08 8.01871e+08 7.35056e+08 6.97151e+08 7.56552e+08 1.14654e+09 9.76609e+08 8.59131e+08 8.53402e+08 6.62893e+08 7.79257e+08 8.80308e+08 9.93766e+08 8.90851e+08 9.84199e+08 8.16639e+08 8.67286e+08 8.66914e+08 7.47535e+08 7.80829e+08 8.0747e+08 9.53753e+08 9.13588e+08 7.42591e+08 9.33363e+08 9.43277e+08 8.05303e+08 7.44586e+08 9.66776e+08 7.31453e+08 9.29913e+08 8.24655e+08 9.29402e+08 8.70127e+08 8.41698e+08 8.51113e+08 7.32337e+08 8.81579e+08 8.23301e+08 7.16133e+08 8.94901e+08 9.27702e+08 9.04648e+08 9.4465e+08 7.9387e+08 1.01627e+09 8.30337e+08 8.56088e+08 7.00986e+08 8.94858e+08 8.04371e+08 6.03472e+08 8.66817e+08 6.77702e+08 7.45393e+08 9.04682e+08 8.45595e+08 8.25881e+08 8.97266e+08 8.95313e+08 8.16347e+08 7.49063e+08 6.29673e+08 1.05142e+09 7.61841e+08 6.49095e+08 7.86724e+08 7.91748e+08 6.67256e+08 8.6962e+08 9.49616e+08 8.67246e+08 8.87088e+08 6.6359e+08 8.08866e+08 9.10499e+08 8.53441e+08 7.7158e+08 9.54915e+08 1.06144e+09 8.46815e+08 5.6495e+08 8.84231e+08 8.63027e+08 8.68341e+08 8.89453e+08 
 4.51189e+07 1.26217e+08 1.09953e+08 2.17961e+08 1.64753e+08 2.44939e+08 2.42095e+08 2.14014e+08 2.84781e+08 2.65025e+08 3.60185e+08 2.31705e+08 3.83689e+08 4.73799e+08 4.75253e+08 5.08509e+08 3.83616e+08 3.58344e+08 5.58822e+08 5.58089e+08 5.20624e+08 6.4481e+08 6.26996e+08 8.14277e+08 8.62662e+08 8.42305e+08 7.48694e+08 8.30155e+08 8.5526e+08 9.76609e+08 1.28473e+09 9.73203e+08 8.57729e+08 6.71646e+08 8.48703e+08 9.45759e+08 9.15751e+08 1.0049e+09 8.77943e+08 9.62571e+08 8.58468e+08 1.00169e+09 8.86914e+08 8.10426e+08 7.90982e+08 9.59334e+08 9.39079e+08 7.03554e+08 9.26104e+08 1.00553e+09 9.31003e+08 8.34998e+08 9.93572e+08 6.99067e+08 9.83386e+08 8.04182e+08 8.87258e+08 9.92377e+08 8.98572e+08 8.66077e+08 8.13476e+08 9.03049e+08 9.46513e+08 8.79591e+08 9.88431e+08 9.58307e+08 9.76794e+08 1.03877e+09 1.0325e+09 1.08269e+09 9.05313e+08 1.0194e+09 8.14706e+08 9.03175e+08 8.89601e+08 6.65243e+08 8.37294e+08 7.64068e+08 7.34053e+08 1.01262e+09 9.5046e+08 7.55344e+08 8.57571e+08 9.62519e+08 9.0202e+08 8.22986e+08 6.36807e+08 1.13112e+09 7.97909e+08 7.37094e+08 8.93142e+08 7.76457e+08 7.18071e+08 9.35395e+08 9.73918e+08 9.31676e+08 9.64146e+08 7.08757e+08 8.6705e+08 9.82551e+08 8.39846e+08 9.86698e+08 1.05527e+09 1.12293e+09 8.87177e+08 6.41688e+08 9.68487e+08 9.05895e+08 9.18541e+08 9.46093e+08 
 3.01521e+06 4.43866e+07 4.93598e+07 8.41356e+07 1.02346e+08 1.56335e+08 1.48788e+08 1.21049e+08 2.11301e+08 2.3592e+08 3.03647e+08 1.6756e+08 3.31178e+08 3.79359e+08 4.00837e+08 5.02091e+08 3.64098e+08 3.67362e+08 5.19644e+08 6.28858e+08 4.69158e+08 5.32313e+08 5.50226e+08 6.83324e+08 7.98034e+08 7.81431e+08 6.38435e+08 7.03606e+08 7.88428e+08 8.59131e+08 9.73203e+08 1.19863e+09 9.21171e+08 6.8298e+08 8.16729e+08 9.60926e+08 8.2626e+08 8.47637e+08 7.94323e+08 7.89393e+08 8.89342e+08 9.69285e+08 9.0356e+08 7.35547e+08 6.90956e+08 1.0184e+09 9.54639e+08 8.47786e+08 8.41598e+08 8.23214e+08 9.58224e+08 8.32893e+08 9.45448e+08 7.95185e+08 9.20365e+08 8.35814e+08 8.95276e+08 9.38794e+08 8.57366e+08 8.66834e+08 8.46005e+08 9.25319e+08 9.50459e+08 8.3155e+08 1.01284e+09 9.53162e+08 9.83773e+08 9.98248e+08 9.72283e+08 1.0556e+09 9.08223e+08 9.52129e+08 7.4814e+08 8.74814e+08 8.25857e+08 6.9743e+08 8.59599e+08 8.41242e+08 8.70325e+08 9.86388e+08 9.21089e+08 7.93195e+08 8.03965e+08 9.75171e+08 7.82412e+08 8.43628e+08 6.20649e+08 1.07508e+09 7.39533e+08 6.95103e+08 8.62279e+08 8.14358e+08 8.3054e+08 9.65906e+08 9.1645e+08 9.78053e+08 8.76662e+08 8.11541e+08 7.84259e+08 9.83914e+08 8.27518e+08 8.74868e+08 1.0528e+09 1.0409e+09 8.9397e+08 7.29509e+08 9.21355e+08 9.24899e+08 1.05412e+09 9.29622e+08 
 4.50134e+07 8.10165e+07 7.54915e+07 1.5558e+08 7.77797e+07 1.47593e+08 1.98838e+08 1.3526e+08 2.40312e+08 1.31604e+08 2.31794e+08 2.20566e+08 3.19888e+08 3.9714e+08 3.73386e+08 4.69563e+08 3.1976e+08 4.20792e+08 5.10223e+08 5.36625e+08 4.10382e+08 4.57982e+08 4.89409e+08 5.94915e+08 6.5084e+08 6.10618e+08 5.82103e+08 6.5504e+08 6.76813e+08 8.53402e+08 8.57729e+08 9.21171e+08 1.14517e+09 6.66158e+08 7.86525e+08 8.8692e+08 8.45312e+08 8.68724e+08 8.97892e+08 8.21373e+08 8.87622e+08 8.535e+08 7.84247e+08 8.4511e+08 7.66827e+08 9.15088e+08 9.81448e+08 8.46542e+08 8.59703e+08 7.68728e+08 8.61653e+08 8.2679e+08 9.0127e+08 6.81692e+08 9.43194e+08 7.98841e+08 7.71752e+08 9.04502e+08 8.0405e+08 8.28499e+08 8.39422e+08 8.69017e+08 9.47785e+08 7.63915e+08 9.10414e+08 8.63682e+08 9.02295e+08 9.33177e+08 9.26359e+08 1.00941e+09 9.83238e+08 9.06637e+08 6.86354e+08 7.94496e+08 8.29128e+08 6.91477e+08 8.55035e+08 6.62922e+08 7.80687e+08 8.5758e+08 9.08519e+08 8.96381e+08 8.80148e+08 9.04319e+08 7.81456e+08 8.38653e+08 6.45052e+08 1.03435e+09 7.14007e+08 7.24589e+08 7.88511e+08 7.27018e+08 7.44669e+08 9.18436e+08 9.69561e+08 9.91185e+08 9.52685e+08 8.86679e+08 7.7908e+08 8.63967e+08 8.65543e+08 8.16507e+08 9.43226e+08 1.01174e+09 9.07047e+08 6.76919e+08 8.34755e+08 8.75772e+08 9.58452e+08 9.00285e+08 
 1.20351e+07 3.53647e+07 6.07564e+07 1.02778e+08 6.47079e+07 1.26704e+08 1.76718e+08 1.00118e+08 1.74911e+08 1.42667e+08 1.96603e+08 2.12603e+08 2.57965e+08 2.9944e+08 2.69804e+08 3.41747e+08 2.66319e+08 2.93907e+08 3.44905e+08 3.90083e+08 3.38612e+08 3.33336e+08 3.99772e+08 4.66834e+08 5.64168e+08 5.59491e+08 4.84139e+08 5.47898e+08 6.3562e+08 6.62893e+08 6.71646e+08 6.8298e+08 6.66158e+08 7.46387e+08 5.89616e+08 7.191e+08 6.50996e+08 6.31447e+08 7.09796e+08 6.76913e+08 5.92695e+08 6.68546e+08 6.53438e+08 4.88989e+08 6.11219e+08 7.1316e+08 7.14815e+08 5.77987e+08 7.58805e+08 6.7034e+08 6.44611e+08 5.56814e+08 7.17669e+08 5.61664e+08 7.73646e+08 5.58736e+08 6.17343e+08 6.34159e+08 6.63089e+08 6.99643e+08 6.36114e+08 7.67135e+08 6.38986e+08 6.26546e+08 7.36362e+08 7.15119e+08 6.93812e+08 6.88198e+08 7.10962e+08 8.00322e+08 6.76068e+08 6.06569e+08 5.39518e+08 6.40742e+08 5.98794e+08 5.09156e+08 7.03051e+08 5.27792e+08 6.05304e+08 6.42327e+08 6.42278e+08 7.06953e+08 6.58832e+08 7.36966e+08 6.94901e+08 5.98257e+08 5.00627e+08 7.10941e+08 6.04751e+08 5.14693e+08 5.91428e+08 5.36494e+08 5.23812e+08 6.77614e+08 6.5357e+08 6.99931e+08 6.73803e+08 6.16656e+08 5.64748e+08 6.40194e+08 7.21536e+08 5.77849e+08 7.26985e+08 7.25045e+08 6.43986e+08 5.04239e+08 6.59762e+08 6.03745e+08 6.88987e+08 6.44139e+08 
 1.21778e+06 2.83564e+07 3.68451e+07 6.76336e+07 6.70648e+07 1.05054e+08 1.45543e+08 8.96442e+07 1.63822e+08 1.51515e+08 1.84224e+08 1.55863e+08 2.45036e+08 2.80932e+08 2.88937e+08 4.11679e+08 2.80989e+08 3.35607e+08 4.20098e+08 4.73149e+08 3.74566e+08 5.10212e+08 5.14703e+08 6.36876e+08 6.35937e+08 6.07965e+08 5.50959e+08 6.21869e+08 6.59679e+08 7.79257e+08 8.48703e+08 8.16729e+08 7.86525e+08 5.89616e+08 8.97994e+08 8.57435e+08 7.06578e+08 8.39225e+08 8.29839e+08 8.54815e+08 8.24419e+08 7.36413e+08 8.27069e+08 7.55978e+08 6.84274e+08 8.63873e+08 8.20144e+08 7.56063e+08 7.60579e+08 7.97015e+08 7.99376e+08 7.54487e+08 8.63947e+08 6.22553e+08 8.46853e+08 6.64327e+08 8.10759e+08 8.04404e+08 8.31182e+08 7.72107e+08 7.02799e+08 8.98936e+08 7.56521e+08 7.08651e+08 8.88347e+08 8.48335e+08 8.62828e+08 8.21638e+08 8.73475e+08 9.7444e+08 7.82112e+08 8.77734e+08 6.68715e+08 7.8602e+08 7.15674e+08 6.25236e+08 7.87153e+08 6.53036e+08 6.72035e+08 8.70345e+08 8.98168e+08 8.2566e+08 6.86e+08 7.9427e+08 7.25676e+08 7.54313e+08 5.76302e+08 9.50913e+08 7.46833e+08 6.82582e+08 6.75161e+08 5.69028e+08 5.84016e+08 8.21767e+08 8.45685e+08 8.32968e+08 8.73588e+08 6.56449e+08 6.32708e+08 8.65702e+08 8.29751e+08 7.22236e+08 8.41537e+08 1.0193e+09 8.01165e+08 6.17498e+08 8.51924e+08 7.84836e+08 8.46176e+08 7.91811e+08 
 1.261e+06 4.9643e+07 1.11076e+08 1.48442e+08 1.30513e+08 1.95183e+08 1.97575e+08 1.98081e+08 2.52684e+08 2.56915e+08 3.04452e+08 2.18559e+08 3.87994e+08 3.46013e+08 3.71516e+08 4.46434e+08 2.80513e+08 3.65117e+08 4.5844e+08 5.49199e+08 4.87296e+08 5.39591e+08 5.24209e+08 6.80733e+08 6.66234e+08 8.02737e+08 6.27723e+08 7.66737e+08 7.46277e+08 8.80308e+08 9.45759e+08 9.60926e+08 8.8692e+08 7.191e+08 8.57435e+08 1.16815e+09 9.15622e+08 1.02767e+09 1.00368e+09 9.82314e+08 9.98314e+08 9.31482e+08 9.21522e+08 7.60357e+08 7.63735e+08 1.0794e+09 9.48965e+08 8.56558e+08 9.01497e+08 8.75281e+08 9.59452e+08 8.91311e+08 1.05861e+09 7.44413e+08 1.04298e+09 8.4519e+08 9.20536e+08 9.94754e+08 1.00066e+09 9.42667e+08 8.91072e+08 1.13717e+09 8.67835e+08 9.29511e+08 1.05898e+09 1.00538e+09 9.96838e+08 1.05804e+09 1.00105e+09 1.00139e+09 9.65082e+08 9.03215e+08 7.6315e+08 9.16684e+08 9.11808e+08 6.68861e+08 9.76907e+08 8.49973e+08 7.85126e+08 9.74777e+08 9.71089e+08 8.86334e+08 8.65439e+08 1.00709e+09 8.44337e+08 8.87829e+08 6.92936e+08 1.07345e+09 8.51623e+08 8.50985e+08 8.9393e+08 7.98199e+08 7.43418e+08 9.69308e+08 9.82992e+08 1.02228e+09 1.07571e+09 8.59128e+08 7.499e+08 9.72266e+08 9.53264e+08 9.47087e+08 1.03671e+09 1.12977e+09 9.08207e+08 7.4211e+08 9.81371e+08 9.71113e+08 1.06308e+09 9.79078e+08 
 5.68156e+07 1.26619e+08 9.54517e+07 2.05041e+08 1.52408e+08 2.43542e+08 2.96564e+08 2.46521e+08 3.41662e+08 2.2177e+08 3.54526e+08 3.19365e+08 4.1915e+08 5.3983e+08 4.13534e+08 5.48281e+08 3.56439e+08 4.63238e+08 4.5552e+08 4.7404e+08 4.11371e+08 5.47694e+08 6.02053e+08 6.42727e+08 7.56058e+08 8.38394e+08 6.98662e+08 7.23125e+08 7.3713e+08 9.93766e+08 9.15751e+08 8.2626e+08 8.45312e+08 6.50996e+08 7.06578e+08 9.15622e+08 1.37272e+09 1.15487e+09 1.02564e+09 1.01238e+09 1.03062e+09 1.06466e+09 9.36867e+08 8.62383e+08 8.67011e+08 1.12866e+09 1.08747e+09 8.94353e+08 1.00126e+09 1.04928e+09 9.01539e+08 9.53786e+08 1.07753e+09 8.71786e+08 1.1625e+09 9.36301e+08 1.01043e+09 1.02925e+09 1.05106e+09 1.04099e+09 9.12981e+08 1.14225e+09 9.2694e+08 8.55546e+08 1.08365e+09 1.07012e+09 9.7794e+08 1.10736e+09 9.6149e+08 1.0233e+09 1.05228e+09 1.02871e+09 8.55487e+08 1.05378e+09 9.99364e+08 8.17036e+08 1.10288e+09 8.88172e+08 8.48553e+08 1.06672e+09 9.62372e+08 8.79761e+08 9.49252e+08 9.30381e+08 9.62072e+08 9.50524e+08 7.76599e+08 1.1871e+09 9.82614e+08 8.22887e+08 9.03895e+08 8.90253e+08 9.15893e+08 1.0367e+09 1.12926e+09 1.19367e+09 1.20567e+09 9.17201e+08 8.77773e+08 1.02266e+09 9.98263e+08 9.3042e+08 1.06051e+09 1.21399e+09 1.07822e+09 8.37187e+08 1.11744e+09 1.08556e+09 1.13325e+09 9.65131e+08 
 2.71751e+07 9.18306e+07 1.13038e+08 1.82897e+08 1.44639e+08 2.19401e+08 2.34616e+08 2.46582e+08 2.92003e+08 2.59253e+08 3.39824e+08 2.54641e+08 4.19075e+08 4.49285e+08 3.92853e+08 5.60533e+08 3.95631e+08 4.50456e+08 4.10768e+08 5.26607e+08 4.4401e+08 6.38407e+08 5.97445e+08 7.20069e+08 7.78187e+08 8.19358e+08 6.98464e+08 7.80913e+08 8.06555e+08 8.90851e+08 1.0049e+09 8.47637e+08 8.68724e+08 6.31447e+08 8.39225e+08 1.02767e+09 1.15487e+09 1.3518e+09 1.05277e+09 1.13223e+09 1.0111e+09 1.00929e+09 9.59798e+08 8.91746e+08 9.1097e+08 1.0914e+09 1.05409e+09 9.47497e+08 9.11016e+08 9.80963e+08 9.83393e+08 1.04426e+09 1.07277e+09 8.79556e+08 1.14879e+09 9.38072e+08 9.90933e+08 1.11415e+09 1.11169e+09 1.07548e+09 1.00119e+09 1.15817e+09 9.21539e+08 9.43217e+08 1.11404e+09 1.08412e+09 9.69534e+08 1.13592e+09 1.08184e+09 1.08949e+09 9.90314e+08 1.08108e+09 9.36415e+08 1.04758e+09 9.90645e+08 8.71268e+08 1.07548e+09 9.2989e+08 8.47855e+08 1.07537e+09 1.07216e+09 9.0415e+08 8.5705e+08 8.93515e+08 9.27259e+08 9.99535e+08 7.7375e+08 1.1676e+09 9.96197e+08 9.10246e+08 9.75603e+08 8.34229e+08 8.41609e+08 9.85469e+08 1.04678e+09 1.16986e+09 1.28521e+09 9.40061e+08 9.17762e+08 1.0802e+09 1.05872e+09 9.74417e+08 1.08888e+09 1.30296e+09 1.10072e+09 9.17966e+08 1.15556e+09 1.07961e+09 1.23115e+09 9.87776e+08 
 3.17191e+07 7.32605e+07 1.15581e+08 1.73127e+08 8.55329e+07 1.64827e+08 2.19414e+08 2.04401e+08 2.51235e+08 1.77478e+08 2.31419e+08 2.59522e+08 3.5227e+08 3.93718e+08 3.4186e+08 5.12326e+08 3.20495e+08 4.24206e+08 3.8489e+08 5.78295e+08 4.70893e+08 5.12305e+08 6.16788e+08 7.13497e+08 8.17155e+08 7.32621e+08 6.59138e+08 6.53566e+08 7.87352e+08 9.84199e+08 8.77943e+08 7.94323e+08 8.97892e+08 7.09796e+08 8.29839e+08 1.00368e+09 1.02564e+09 1.05277e+09 1.41124e+09 1.07252e+09 1.03588e+09 9.18293e+08 9.49158e+08 9.00171e+08 9.71625e+08 1.12863e+09 1.06881e+09 9.45729e+08 1.11818e+09 1.08231e+09 9.74052e+08 9.76119e+08 1.17223e+09 7.70229e+08 1.19778e+09 8.38865e+08 1.00014e+09 1.00165e+09 1.06154e+09 1.04536e+09 9.47741e+08 1.16715e+09 1.02646e+09 8.7098e+08 1.03651e+09 1.03178e+09 1.04183e+09 1.02859e+09 1.06624e+09 1.06136e+09 1.01218e+09 9.49208e+08 8.43954e+08 1.08919e+09 9.42211e+08 8.20327e+08 1.10306e+09 8.59183e+08 8.96385e+08 9.7289e+08 9.7886e+08 1.0121e+09 9.87503e+08 1.03161e+09 9.37645e+08 9.92126e+08 8.29743e+08 1.1672e+09 1.00793e+09 9.26537e+08 9.17828e+08 8.35219e+08 7.96769e+08 1.04813e+09 1.12101e+09 1.15693e+09 1.22411e+09 9.80578e+08 8.53836e+08 9.87017e+08 1.17065e+09 9.20068e+08 1.01136e+09 1.23295e+09 1.08906e+09 8.84945e+08 1.0138e+09 1.17332e+09 1.05283e+09 9.67698e+08 
 3.94003e+07 7.22466e+07 9.87072e+07 1.55088e+08 9.78987e+07 1.98211e+08 2.27655e+08 1.7235e+08 2.28362e+08 2.10871e+08 2.40447e+08 2.55259e+08 2.66819e+08 3.59932e+08 2.44417e+08 4.50858e+08 3.26321e+08 4.00105e+08 4.77636e+08 4.69244e+08 3.74677e+08 5.26858e+08 5.34337e+08 7.07723e+08 6.89788e+08 7.08843e+08 6.62782e+08 6.80054e+08 7.37195e+08 8.16639e+08 9.62571e+08 7.89393e+08 8.21373e+08 6.76913e+08 8.54815e+08 9.82314e+08 1.01238e+09 1.13223e+09 1.07252e+09 1.4708e+09 1.10783e+09 1.1018e+09 1.11795e+09 9.19272e+08 1.00633e+09 1.23882e+09 1.16616e+09 1.02482e+09 1.07871e+09 1.23953e+09 1.06714e+09 1.04145e+09 1.14535e+09 8.79835e+08 1.22029e+09 8.58795e+08 1.00464e+09 1.10535e+09 1.25071e+09 1.0717e+09 9.40179e+08 1.27569e+09 1.04824e+09 1.08384e+09 1.18642e+09 1.19405e+09 1.05765e+09 1.09782e+09 1.20672e+09 1.23075e+09 1.03333e+09 1.08862e+09 9.02987e+08 1.07613e+09 1.02229e+09 8.53802e+08 1.07511e+09 9.30314e+08 8.31193e+08 1.07358e+09 1.18929e+09 9.85908e+08 8.64738e+08 1.06359e+09 1.07394e+09 1.10876e+09 7.89764e+08 1.26005e+09 1.09412e+09 1.09593e+09 9.42132e+08 8.67205e+08 9.18125e+08 1.05939e+09 1.20293e+09 1.24622e+09 1.29796e+09 1.02616e+09 1.0304e+09 1.05551e+09 1.13103e+09 1.07701e+09 1.03529e+09 1.30286e+09 1.03269e+09 9.45893e+08 1.12417e+09 1.06835e+09 1.09611e+09 1.07883e+09 
 3.13782e+07 4.96708e+07 7.30023e+07 1.15889e+08 9.84883e+07 1.73235e+08 1.68389e+08 1.24965e+08 2.29027e+08 1.94506e+08 2.53911e+08 1.77813e+08 3.17946e+08 3.56968e+08 3.37692e+08 4.61255e+08 2.43597e+08 4.02393e+08 4.30095e+08 5.19479e+08 3.97516e+08 4.64815e+08 5.17007e+08 6.47417e+08 6.97699e+08 6.5515e+08 6.14867e+08 6.6259e+08 7.17904e+08 8.67286e+08 8.58468e+08 8.89342e+08 8.87622e+08 5.92695e+08 8.24419e+08 9.98314e+08 1.03062e+09 1.0111e+09 1.03588e+09 1.10783e+09 1.33753e+09 1.05727e+09 8.97461e+08 8.99301e+08 9.32174e+08 1.10042e+09 1.0977e+09 9.34596e+08 1.02163e+09 1.00445e+09 9.97103e+08 9.85059e+08 1.10443e+09 8.66878e+08 1.12254e+09 8.83351e+08 9.82266e+08 1.04922e+09 1.10167e+09 1.02407e+09 8.3565e+08 1.24179e+09 9.69799e+08 9.5973e+08 1.11241e+09 1.08104e+09 1.06797e+09 1.03183e+09 1.04656e+09 1.01914e+09 1.00927e+09 9.55604e+08 8.5791e+08 9.84873e+08 9.31887e+08 7.58393e+08 1.0097e+09 1.07655e+09 8.51353e+08 1.06228e+09 1.19402e+09 1.02062e+09 9.01906e+08 9.51755e+08 8.77087e+08 1.04773e+09 7.21385e+08 1.28504e+09 1.00852e+09 9.55415e+08 9.71773e+08 8.53365e+08 8.87395e+08 1.1232e+09 1.08746e+09 1.23402e+09 1.1444e+09 1.01845e+09 8.54772e+08 1.0247e+09 9.94191e+08 1.02528e+09 1.04712e+09 1.29317e+09 1.09159e+09 7.97906e+08 1.09576e+09 1.09167e+09 1.09709e+09 9.47904e+08 
 5.75344e+07 1.34919e+08 1.19342e+08 2.25577e+08 1.54204e+08 2.72262e+08 2.50336e+08 2.22872e+08 2.73182e+08 2.68354e+08 3.50734e+08 2.54235e+08 3.77476e+08 4.8732e+08 3.8653e+08 5.1128e+08 3.36485e+08 3.76152e+08 4.86995e+08 5.31051e+08 4.6661e+08 5.36343e+08 5.80353e+08 6.98529e+08 7.90282e+08 7.50736e+08 6.78515e+08 6.76708e+08 7.89061e+08 8.66914e+08 1.00169e+09 9.69285e+08 8.535e+08 6.68546e+08 7.36413e+08 9.31482e+08 1.06466e+09 1.00929e+09 9.18293e+08 1.1018e+09 1.05727e+09 1.44751e+09 1.12706e+09 8.63736e+08 9.4375e+08 1.27326e+09 1.14962e+09 1.00684e+09 1.05211e+09 1.12497e+09 1.14203e+09 1.04135e+09 1.14096e+09 8.84538e+08 1.14081e+09 9.31686e+08 1.05074e+09 1.1148e+09 1.13698e+09 1.10659e+09 1.06391e+09 1.12932e+09 1.09076e+09 1.10792e+09 1.20489e+09 1.13182e+09 1.09068e+09 1.14108e+09 1.22947e+09 1.21472e+09 1.06274e+09 1.11601e+09 1.08044e+09 1.00223e+09 1.02962e+09 8.47317e+08 1.12443e+09 9.89636e+08 8.86142e+08 1.11854e+09 1.18312e+09 9.05839e+08 1.02279e+09 1.10464e+09 1.07672e+09 1.10488e+09 7.85131e+08 1.29931e+09 9.62261e+08 9.86793e+08 1.0687e+09 1.04239e+09 1.0875e+09 1.18044e+09 1.18432e+09 1.21475e+09 1.1921e+09 9.85191e+08 1.02396e+09 1.14557e+09 1.108e+09 1.15063e+09 1.21153e+09 1.22239e+09 1.15362e+09 8.67617e+08 1.28447e+09 1.01072e+09 1.14973e+09 1.01905e+09 
 1.59769e+06 2.83469e+07 4.09643e+07 6.0567e+07 7.2127e+07 1.30717e+08 1.46713e+08 1.20486e+08 1.57786e+08 1.94818e+08 2.4774e+08 1.97808e+08 2.36044e+08 3.17049e+08 2.21324e+08 3.93718e+08 3.41309e+08 2.70738e+08 3.40948e+08 4.02878e+08 3.25567e+08 4.77115e+08 4.53163e+08 5.41486e+08 6.1255e+08 6.22234e+08 6.07093e+08 6.40676e+08 6.49304e+08 7.47535e+08 8.86914e+08 9.0356e+08 7.84247e+08 6.53438e+08 8.27069e+08 9.21522e+08 9.36867e+08 9.59798e+08 9.49158e+08 1.11795e+09 8.97461e+08 1.12706e+09 1.54134e+09 9.77746e+08 9.16961e+08 1.38762e+09 1.15377e+09 1.16609e+09 1.08684e+09 1.27947e+09 1.13535e+09 1.08569e+09 1.26394e+09 8.90262e+08 1.12876e+09 9.81238e+08 1.17508e+09 1.08469e+09 1.15398e+09 1.10369e+09 1.1712e+09 1.2653e+09 1.14966e+09 1.17687e+09 1.2273e+09 1.20807e+09 1.22059e+09 1.12196e+09 1.22098e+09 1.26425e+09 1.07811e+09 1.24163e+09 1.05036e+09 1.12259e+09 1.16421e+09 8.43114e+08 1.18088e+09 8.94104e+08 9.70086e+08 1.17568e+09 1.10104e+09 9.42412e+08 1.01791e+09 1.20219e+09 1.17261e+09 1.07254e+09 8.13437e+08 1.27233e+09 1.0615e+09 1.01752e+09 1.04071e+09 9.01345e+08 1.0746e+09 1.10826e+09 1.22237e+09 1.22167e+09 1.28515e+09 9.85248e+08 9.62652e+08 1.2367e+09 1.20963e+09 1.20611e+09 1.10503e+09 1.34727e+09 1.07137e+09 1.03206e+09 1.28962e+09 1.22699e+09 1.17727e+09 1.08806e+09 
 5.37613e+07 7.58405e+07 5.74905e+07 1.24252e+08 5.74457e+07 1.15874e+08 1.64429e+08 1.24463e+08 2.40037e+08 1.41487e+08 2.49024e+08 1.97698e+08 2.50112e+08 3.55326e+08 2.99535e+08 4.55536e+08 2.78179e+08 3.93816e+08 4.49765e+08 4.33455e+08 3.35411e+08 5.03525e+08 4.73174e+08 5.65007e+08 6.31357e+08 5.27085e+08 6.09776e+08 6.17684e+08 5.49027e+08 7.80829e+08 8.10426e+08 7.35547e+08 8.4511e+08 4.88989e+08 7.55978e+08 7.60357e+08 8.62383e+08 8.91746e+08 9.00171e+08 9.19272e+08 8.99301e+08 8.63736e+08 9.77746e+08 1.12915e+09 8.24551e+08 1.07984e+09 9.474e+08 9.97071e+08 9.92109e+08 9.84334e+08 8.7985e+08 9.56776e+08 9.69092e+08 7.36489e+08 9.49024e+08 7.61672e+08 7.98436e+08 9.07268e+08 9.89662e+08 9.55864e+08 7.96442e+08 1.02151e+09 9.99679e+08 9.22246e+08 1.00113e+09 1.00636e+09 9.15502e+08 9.59412e+08 9.40334e+08 9.7783e+08 9.7906e+08 1.05886e+09 8.49039e+08 9.4117e+08 9.1612e+08 7.10454e+08 9.62617e+08 7.71861e+08 8.70632e+08 9.54e+08 1.0055e+09 8.29892e+08 7.62961e+08 9.74442e+08 8.79134e+08 9.40218e+08 6.24228e+08 1.11104e+09 9.0676e+08 8.13576e+08 8.55795e+08 7.37238e+08 7.49913e+08 8.91009e+08 1.09032e+09 1.0128e+09 1.03984e+09 9.45932e+08 8.34884e+08 9.54085e+08 9.56554e+08 9.37845e+08 9.59748e+08 1.18546e+09 1.04778e+09 7.64739e+08 1.08194e+09 1.03886e+09 1.04326e+09 9.09957e+08 
 4.88806e+07 7.67658e+07 1.19131e+08 1.77982e+08 1.24383e+08 2.36302e+08 2.27764e+08 1.93075e+08 2.74329e+08 2.37603e+08 2.88339e+08 2.4327e+08 3.26542e+08 4.04468e+08 2.85379e+08 4.82752e+08 2.91381e+08 4.36504e+08 3.59214e+08 4.57602e+08 3.41747e+08 4.6589e+08 4.95123e+08 6.16217e+08 7.17884e+08 6.13384e+08 6.18485e+08 6.08568e+08 7.21092e+08 8.0747e+08 7.90982e+08 6.90956e+08 7.66827e+08 6.11219e+08 6.84274e+08 7.63735e+08 8.67011e+08 9.1097e+08 9.71625e+08 1.00633e+09 9.32174e+08 9.4375e+08 9.16961e+08 8.24551e+08 1.20458e+09 1.04615e+09 1.10399e+09 9.28929e+08 9.88501e+08 1.06455e+09 9.74935e+08 9.50864e+08 1.0452e+09 7.55403e+08 1.03765e+09 8.36502e+08 9.22537e+08 9.50747e+08 9.22662e+08 1.01455e+09 1.00902e+09 1.08776e+09 9.29349e+08 9.43208e+08 9.05354e+08 1.06987e+09 9.90508e+08 9.38627e+08 9.87065e+08 9.86242e+08 8.85248e+08 8.19457e+08 8.70971e+08 9.43861e+08 8.85321e+08 6.76194e+08 8.45641e+08 8.45706e+08 8.05269e+08 8.73751e+08 1.03284e+09 9.42557e+08 9.53037e+08 1.03248e+09 9.1482e+08 9.64004e+08 6.78387e+08 1.14309e+09 8.72619e+08 8.73239e+08 9.00863e+08 7.54955e+08 9.60164e+08 9.65398e+08 9.67162e+08 1.09247e+09 1.09597e+09 9.06386e+08 9.26611e+08 1.0481e+09 1.05035e+09 9.40491e+08 1.00146e+09 1.04156e+09 9.95244e+08 8.34622e+08 1.16049e+09 1.03307e+09 1.01846e+09 8.99706e+08 
 1.69496e+07 4.05838e+07 9.7639e+07 1.40694e+08 1.30746e+08 2.15846e+08 2.58093e+08 1.99651e+08 2.46787e+08 2.2169e+08 2.83597e+08 3.04731e+08 3.04432e+08 4.2587e+08 2.67156e+08 5.00967e+08 3.6226e+08 4.49294e+08 5.33958e+08 6.23762e+08 4.27189e+08 6.18379e+08 6.31348e+08 7.80015e+08 7.42498e+08 9.03099e+08 7.02903e+08 6.96263e+08 7.56617e+08 9.53753e+08 9.59334e+08 1.0184e+09 9.15088e+08 7.1316e+08 8.63873e+08 1.0794e+09 1.12866e+09 1.0914e+09 1.12863e+09 1.23882e+09 1.10042e+09 1.27326e+09 1.38762e+09 1.07984e+09 1.04615e+09 1.8701e+09 1.38326e+09 1.31038e+09 1.35569e+09 1.48747e+09 1.31834e+09 1.28139e+09 1.4483e+09 1.13527e+09 1.41111e+09 1.20346e+09 1.28268e+09 1.25738e+09 1.3855e+09 1.38904e+09 1.38454e+09 1.42598e+09 1.36058e+09 1.36285e+09 1.51213e+09 1.51785e+09 1.26116e+09 1.33686e+09 1.36844e+09 1.31699e+09 1.31582e+09 1.22745e+09 1.27127e+09 1.5308e+09 1.27596e+09 1.04469e+09 1.41997e+09 1.24688e+09 1.21612e+09 1.28957e+09 1.32166e+09 1.10727e+09 1.24846e+09 1.56408e+09 1.30698e+09 1.30773e+09 9.33605e+08 1.56988e+09 1.24437e+09 1.30303e+09 1.19624e+09 1.19555e+09 1.26784e+09 1.29948e+09 1.43781e+09 1.51897e+09 1.59378e+09 1.2097e+09 1.18648e+09 1.29913e+09 1.43313e+09 1.38052e+09 1.38008e+09 1.50694e+09 1.26446e+09 1.21807e+09 1.4449e+09 1.35905e+09 1.41653e+09 1.29504e+09 
 1.97136e+07 5.65178e+07 5.46359e+07 1.1574e+08 1.05348e+08 1.78965e+08 2.56798e+08 1.50225e+08 2.64271e+08 1.86944e+08 2.38121e+08 2.63374e+08 3.10727e+08 4.14879e+08 3.10053e+08 4.63705e+08 3.60284e+08 4.13067e+08 4.64828e+08 5.4516e+08 4.02142e+08 5.77135e+08 5.96094e+08 6.81352e+08 7.27874e+08 7.56082e+08 6.83222e+08 6.62694e+08 7.56083e+08 9.13588e+08 9.39079e+08 9.54639e+08 9.81448e+08 7.14815e+08 8.20144e+08 9.48965e+08 1.08747e+09 1.05409e+09 1.06881e+09 1.16616e+09 1.0977e+09 1.14962e+09 1.15377e+09 9.474e+08 1.10399e+09 1.38326e+09 1.50563e+09 1.14664e+09 1.18712e+09 1.29098e+09 1.18657e+09 1.1274e+09 1.21606e+09 9.75933e+08 1.36361e+09 1.04742e+09 1.1155e+09 1.13404e+09 1.21615e+09 1.22508e+09 1.19744e+09 1.24395e+09 1.20142e+09 1.23955e+09 1.25824e+09 1.28438e+09 1.18905e+09 1.23218e+09 1.24456e+09 1.22458e+09 1.20391e+09 1.0529e+09 1.04201e+09 1.31938e+09 1.10541e+09 9.63222e+08 1.11058e+09 1.06002e+09 1.07931e+09 1.18632e+09 1.23025e+09 1.06108e+09 1.17737e+09 1.30348e+09 1.14787e+09 1.2129e+09 8.9803e+08 1.43735e+09 9.985e+08 1.14058e+09 1.02535e+09 1.03151e+09 1.17579e+09 1.21897e+09 1.25026e+09 1.42261e+09 1.4605e+09 1.18713e+09 1.11857e+09 1.21581e+09 1.18985e+09 1.20644e+09 1.19602e+09 1.41167e+09 1.17334e+09 1.09615e+09 1.32378e+09 1.18257e+09 1.25197e+09 1.13352e+09 
 854861 3.4464e+07 1.83762e+07 5.64818e+07 3.60239e+07 6.3094e+07 1.82798e+08 1.20793e+08 2.26795e+08 1.93738e+08 2.66082e+08 2.3218e+08 2.90073e+08 3.5954e+08 3.08706e+08 5.00622e+08 3.09749e+08 3.73624e+08 4.06856e+08 4.90626e+08 3.19693e+08 4.90529e+08 5.05872e+08 5.59384e+08 6.32782e+08 6.7983e+08 6.43238e+08 5.92129e+08 5.98235e+08 7.42591e+08 7.03554e+08 8.47786e+08 8.46542e+08 5.77987e+08 7.56063e+08 8.56558e+08 8.94353e+08 9.47497e+08 9.45729e+08 1.02482e+09 9.34596e+08 1.00684e+09 1.16609e+09 9.97071e+08 9.28929e+08 1.31038e+09 1.14664e+09 1.61356e+09 1.13459e+09 1.11673e+09 1.32443e+09 1.23202e+09 1.31012e+09 1.06791e+09 1.3226e+09 9.99522e+08 1.11086e+09 1.13072e+09 1.17389e+09 1.30713e+09 1.27234e+09 1.39547e+09 1.12107e+09 1.17458e+09 1.39295e+09 1.33427e+09 1.24376e+09 1.13709e+09 1.14166e+09 1.34994e+09 1.23931e+09 1.26229e+09 1.06544e+09 1.22666e+09 1.22657e+09 1.06346e+09 1.20248e+09 1.04306e+09 1.02579e+09 1.27151e+09 1.25526e+09 1.14076e+09 1.01439e+09 1.28985e+09 1.07713e+09 1.29759e+09 9.02329e+08 1.30753e+09 1.11924e+09 1.11994e+09 1.08578e+09 9.88465e+08 1.08359e+09 1.16871e+09 1.28057e+09 1.3741e+09 1.40192e+09 1.25131e+09 1.09798e+09 1.21194e+09 1.29494e+09 1.15548e+09 1.17209e+09 1.40052e+09 1.15597e+09 1.13877e+09 1.4055e+09 1.29477e+09 1.32781e+09 1.09221e+09 
 5.74008e+07 1.01524e+08 1.45809e+08 2.3957e+08 1.25086e+08 2.28509e+08 2.83607e+08 2.14919e+08 3.00285e+08 2.04367e+08 2.88388e+08 3.19257e+08 3.37916e+08 4.44214e+08 3.91606e+08 5.01775e+08 3.401e+08 4.45447e+08 5.22144e+08 5.25308e+08 4.12233e+08 4.60086e+08 5.50965e+08 6.99168e+08 7.95007e+08 7.2899e+08 6.28178e+08 6.54358e+08 7.03398e+08 9.33363e+08 9.26104e+08 8.41598e+08 8.59703e+08 7.58805e+08 7.60579e+08 9.01497e+08 1.00126e+09 9.11016e+08 1.11818e+09 1.07871e+09 1.02163e+09 1.05211e+09 1.08684e+09 9.92109e+08 9.88501e+08 1.35569e+09 1.18712e+09 1.13459e+09 1.65772e+09 1.37147e+09 1.19004e+09 1.09811e+09 1.27392e+09 1.03103e+09 1.36454e+09 1.11886e+09 1.13177e+09 1.08109e+09 1.27651e+09 1.43246e+09 1.23305e+09 1.37426e+09 1.25841e+09 1.21777e+09 1.42759e+09 1.39616e+09 1.14482e+09 1.16464e+09 1.28521e+09 1.28196e+09 1.24147e+09 1.19785e+09 1.14935e+09 1.40051e+09 1.16117e+09 9.74934e+08 1.22797e+09 1.07139e+09 1.10172e+09 1.25641e+09 1.16904e+09 1.15255e+09 1.12991e+09 1.30424e+09 1.196e+09 1.18071e+09 8.12373e+08 1.45766e+09 1.26777e+09 1.10904e+09 1.23927e+09 1.02289e+09 1.04296e+09 1.36337e+09 1.36147e+09 1.52164e+09 1.35792e+09 1.16798e+09 1.14432e+09 1.19602e+09 1.33686e+09 1.20862e+09 1.31854e+09 1.45097e+09 1.1682e+09 1.14839e+09 1.27322e+09 1.36658e+09 1.24481e+09 1.16398e+09 
 5.71613e+07 8.21092e+07 1.00683e+08 1.71945e+08 1.31015e+08 2.38261e+08 2.13932e+08 1.67432e+08 2.10331e+08 1.80125e+08 2.74862e+08 2.51126e+08 2.35426e+08 4.00556e+08 2.39275e+08 3.73143e+08 3.2099e+08 3.33739e+08 3.91733e+08 4.00332e+08 3.43015e+08 4.98173e+08 5.15204e+08 6.05041e+08 7.63295e+08 7.63304e+08 6.47342e+08 6.83256e+08 7.39018e+08 9.43277e+08 1.00553e+09 8.23214e+08 7.68728e+08 6.7034e+08 7.97015e+08 8.75281e+08 1.04928e+09 9.80963e+08 1.08231e+09 1.23953e+09 1.00445e+09 1.12497e+09 1.27947e+09 9.84334e+08 1.06455e+09 1.48747e+09 1.29098e+09 1.11673e+09 1.37147e+09 1.85819e+09 1.2262e+09 1.17772e+09 1.3453e+09 1.07113e+09 1.4543e+09 1.16883e+09 1.25097e+09 1.1443e+09 1.34699e+09 1.25976e+09 1.29171e+09 1.34263e+09 1.29982e+09 1.20969e+09 1.28337e+09 1.34617e+09 1.27614e+09 1.2775e+09 1.37126e+09 1.36225e+09 1.1163e+09 1.25741e+09 1.18121e+09 1.4596e+09 1.19449e+09 1.01946e+09 1.27547e+09 1.1515e+09 1.15607e+09 1.24082e+09 1.14659e+09 1.15882e+09 1.23981e+09 1.44949e+09 1.39726e+09 1.26564e+09 8.66534e+08 1.57271e+09 1.26302e+09 1.21627e+09 1.19452e+09 1.15422e+09 1.22362e+09 1.22931e+09 1.38803e+09 1.50928e+09 1.5452e+09 1.21197e+09 1.18652e+09 1.41059e+09 1.48316e+09 1.30343e+09 1.17849e+09 1.40036e+09 1.21408e+09 1.15019e+09 1.31369e+09 1.34227e+09 1.16436e+09 1.15075e+09 
 943954 6.24867e+07 1.18458e+08 1.7874e+08 1.19348e+08 1.75433e+08 2.07226e+08 2.05287e+08 2.28779e+08 2.66368e+08 3.51113e+08 2.56481e+08 3.65092e+08 4.20217e+08 4.27362e+08 5.24963e+08 3.47197e+08 3.60103e+08 5.01275e+08 6.14434e+08 4.66773e+08 5.13414e+08 5.72999e+08 6.65394e+08 8.06275e+08 8.37793e+08 6.64629e+08 6.95283e+08 7.50621e+08 8.05303e+08 9.31003e+08 9.58224e+08 8.61653e+08 6.44611e+08 7.99376e+08 9.59452e+08 9.01539e+08 9.83393e+08 9.74052e+08 1.06714e+09 9.97103e+08 1.14203e+09 1.13535e+09 8.7985e+08 9.74935e+08 1.31834e+09 1.18657e+09 1.32443e+09 1.19004e+09 1.2262e+09 1.89809e+09 1.3036e+09 1.50034e+09 1.26084e+09 1.5735e+09 1.22853e+09 1.26927e+09 1.35135e+09 1.42841e+09 1.34428e+09 1.47965e+09 1.4089e+09 1.46302e+09 1.27697e+09 1.39084e+09 1.48396e+09 1.48787e+09 1.47893e+09 1.30018e+09 1.54004e+09 1.33457e+09 1.43735e+09 1.26602e+09 1.33352e+09 1.31764e+09 1.23998e+09 1.30459e+09 1.22466e+09 1.25654e+09 1.46972e+09 1.41363e+09 1.33193e+09 1.28196e+09 1.40437e+09 1.37094e+09 1.44173e+09 9.61108e+08 1.40601e+09 1.31329e+09 1.30683e+09 1.3344e+09 1.23703e+09 1.35238e+09 1.53446e+09 1.41625e+09 1.56084e+09 1.54873e+09 1.2222e+09 1.36902e+09 1.50425e+09 1.46629e+09 1.46024e+09 1.49375e+09 1.51207e+09 1.28393e+09 1.20559e+09 1.46766e+09 1.40618e+09 1.50013e+09 1.38056e+09 
 1.73367e+07 2.94795e+07 3.96174e+07 6.24048e+07 5.42527e+07 8.6859e+07 1.24758e+08 1.06132e+08 1.69826e+08 1.42789e+08 1.81747e+08 1.46997e+08 2.47406e+08 2.80049e+08 2.76649e+08 4.20916e+08 2.81339e+08 3.77888e+08 3.68796e+08 4.44804e+08 3.67363e+08 5.24737e+08 4.98345e+08 6.18106e+08 6.71803e+08 7.12087e+08 5.28353e+08 5.41664e+08 7.31301e+08 7.44586e+08 8.34998e+08 8.32893e+08 8.2679e+08 5.56814e+08 7.54487e+08 8.91311e+08 9.53786e+08 1.04426e+09 9.76119e+08 1.04145e+09 9.85059e+08 1.04135e+09 1.08569e+09 9.56776e+08 9.50864e+08 1.28139e+09 1.1274e+09 1.23202e+09 1.09811e+09 1.17772e+09 1.3036e+09 1.5884e+09 1.31754e+09 1.12529e+09 1.42259e+09 1.18007e+09 1.24329e+09 1.28994e+09 1.32683e+09 1.39935e+09 1.40422e+09 1.4134e+09 1.25259e+09 1.23008e+09 1.3289e+09 1.39305e+09 1.23276e+09 1.44026e+09 1.33001e+09 1.26614e+09 1.23978e+09 1.35916e+09 1.17279e+09 1.37576e+09 1.19854e+09 1.08785e+09 1.316e+09 1.13248e+09 1.09506e+09 1.25265e+09 1.21162e+09 1.20267e+09 1.12451e+09 1.25497e+09 1.27097e+09 1.26926e+09 8.68263e+08 1.38693e+09 1.25111e+09 1.16481e+09 1.11025e+09 1.03713e+09 1.21963e+09 1.25528e+09 1.45715e+09 1.45257e+09 1.51563e+09 1.26379e+09 1.17445e+09 1.41405e+09 1.39994e+09 1.30808e+09 1.23932e+09 1.44961e+09 1.18727e+09 1.23792e+09 1.42139e+09 1.35756e+09 1.38475e+09 1.17159e+09 
 2.46152e+06 2.19835e+07 7.01964e+07 1.09963e+08 1.24865e+08 1.91693e+08 2.92374e+08 1.90545e+08 3.1966e+08 2.92223e+08 3.64437e+08 3.35541e+08 4.06753e+08 5.15119e+08 4.04399e+08 5.66084e+08 3.60383e+08 4.17925e+08 4.51383e+08 5.99864e+08 4.67769e+08 6.39548e+08 6.71466e+08 7.3957e+08 7.31265e+08 8.35795e+08 7.72567e+08 7.04439e+08 7.45966e+08 9.66776e+08 9.93572e+08 9.45448e+08 9.0127e+08 7.17669e+08 8.63947e+08 1.05861e+09 1.07753e+09 1.07277e+09 1.17223e+09 1.14535e+09 1.10443e+09 1.14096e+09 1.26394e+09 9.69092e+08 1.0452e+09 1.4483e+09 1.21606e+09 1.31012e+09 1.27392e+09 1.3453e+09 1.50034e+09 1.31754e+09 1.82283e+09 1.24865e+09 1.58364e+09 1.19016e+09 1.38167e+09 1.29792e+09 1.39891e+09 1.37966e+09 1.44396e+09 1.48963e+09 1.32776e+09 1.32021e+09 1.47365e+09 1.38195e+09 1.43147e+09 1.44001e+09 1.3702e+09 1.45411e+09 1.35092e+09 1.3666e+09 1.22272e+09 1.47214e+09 1.22305e+09 1.09075e+09 1.46127e+09 1.20921e+09 1.06888e+09 1.42289e+09 1.34262e+09 1.36025e+09 1.26913e+09 1.44779e+09 1.424e+09 1.34158e+09 1.07324e+09 1.45371e+09 1.31797e+09 1.18408e+09 1.28795e+09 1.16176e+09 1.26559e+09 1.36207e+09 1.46506e+09 1.62939e+09 1.57046e+09 1.2319e+09 1.28081e+09 1.37278e+09 1.56393e+09 1.35532e+09 1.32161e+09 1.54431e+09 1.25179e+09 1.1476e+09 1.51635e+09 1.50515e+09 1.43859e+09 1.34822e+09 
 6.52355e+06 9.61702e+06 7.68042e+06 2.73863e+07 6.97075e+07 9.34473e+07 1.03304e+08 5.63862e+07 1.63571e+08 1.64338e+08 2.32495e+08 1.09589e+08 2.20706e+08 2.80632e+08 2.57215e+08 3.815e+08 2.19519e+08 3.08777e+08 2.92092e+08 3.94152e+08 2.89559e+08 4.61338e+08 4.26909e+08 5.13803e+08 5.96111e+08 6.03052e+08 4.94562e+08 5.57337e+08 6.31366e+08 7.31453e+08 6.99067e+08 7.95185e+08 6.81692e+08 5.61664e+08 6.22553e+08 7.44413e+08 8.71786e+08 8.79556e+08 7.70229e+08 8.79835e+08 8.66878e+08 8.84538e+08 8.90262e+08 7.36489e+08 7.55403e+08 1.13527e+09 9.75933e+08 1.06791e+09 1.03103e+09 1.07113e+09 1.26084e+09 1.12529e+09 1.24865e+09 1.47466e+09 1.38687e+09 1.0956e+09 1.14427e+09 1.08226e+09 1.29532e+09 1.18018e+09 1.28399e+09 1.28117e+09 1.14186e+09 1.08772e+09 1.24648e+09 1.42363e+09 1.1771e+09 1.3128e+09 1.04807e+09 1.26957e+09 1.12391e+09 1.17667e+09 9.82721e+08 1.39612e+09 1.038e+09 1.0714e+09 1.19329e+09 1.15165e+09 1.12407e+09 1.26458e+09 1.17776e+09 1.10612e+09 1.03373e+09 1.14122e+09 1.16953e+09 1.26447e+09 8.7763e+08 1.21901e+09 1.137e+09 1.01518e+09 1.12497e+09 1.05978e+09 1.12478e+09 1.09997e+09 1.16664e+09 1.36251e+09 1.30772e+09 1.0638e+09 1.17804e+09 1.29557e+09 1.40786e+09 1.09635e+09 1.24882e+09 1.37282e+09 1.12152e+09 1.05726e+09 1.20915e+09 1.24757e+09 1.26068e+09 1.05926e+09 
 3.74064e+07 8.87405e+07 1.07844e+08 1.91206e+08 1.15537e+08 1.87627e+08 2.51377e+08 2.08479e+08 2.78656e+08 2.27506e+08 3.09286e+08 2.77278e+08 3.56072e+08 4.29735e+08 3.78777e+08 4.85407e+08 3.68431e+08 4.12957e+08 4.62795e+08 5.32609e+08 4.58526e+08 5.63717e+08 6.12534e+08 7.02774e+08 8.02302e+08 8.48191e+08 7.14317e+08 7.24798e+08 8.19951e+08 9.29913e+08 9.83386e+08 9.20365e+08 9.43194e+08 7.73646e+08 8.46853e+08 1.04298e+09 1.1625e+09 1.14879e+09 1.19778e+09 1.22029e+09 1.12254e+09 1.14081e+09 1.12876e+09 9.49024e+08 1.03765e+09 1.41111e+09 1.36361e+09 1.3226e+09 1.36454e+09 1.4543e+09 1.5735e+09 1.42259e+09 1.58364e+09 1.38687e+09 2.09523e+09 1.41267e+09 1.4513e+09 1.50292e+09 1.64492e+09 1.6067e+09 1.53467e+09 1.74742e+09 1.52296e+09 1.43859e+09 1.7134e+09 1.70126e+09 1.49456e+09 1.75813e+09 1.57519e+09 1.62358e+09 1.4971e+09 1.53135e+09 1.33442e+09 1.75329e+09 1.36421e+09 1.4591e+09 1.58289e+09 1.35167e+09 1.30804e+09 1.63993e+09 1.3921e+09 1.61891e+09 1.5094e+09 1.4927e+09 1.5162e+09 1.51335e+09 1.1831e+09 1.68322e+09 1.5032e+09 1.54966e+09 1.35885e+09 1.33737e+09 1.48992e+09 1.59622e+09 1.65316e+09 1.77063e+09 1.86013e+09 1.42847e+09 1.47623e+09 1.61506e+09 1.89511e+09 1.55229e+09 1.54803e+09 1.76125e+09 1.42811e+09 1.44746e+09 1.6983e+09 1.63567e+09 1.58937e+09 1.36193e+09 
 5.61586e+07 1.33516e+08 8.73753e+07 1.80671e+08 1.26394e+08 2.2724e+08 2.01143e+08 1.92035e+08 2.6962e+08 1.90657e+08 2.58435e+08 1.78354e+08 3.48752e+08 3.7541e+08 2.94713e+08 4.36606e+08 3.44083e+08 4.14271e+08 3.77102e+08 4.0013e+08 3.70278e+08 3.75554e+08 3.79193e+08 5.31909e+08 6.23825e+08 6.0681e+08 5.47452e+08 6.1231e+08 6.66642e+08 8.24655e+08 8.04182e+08 8.35814e+08 7.98841e+08 5.58736e+08 6.64327e+08 8.4519e+08 9.36301e+08 9.38072e+08 8.38865e+08 8.58795e+08 8.83351e+08 9.31686e+08 9.81238e+08 7.61672e+08 8.36502e+08 1.20346e+09 1.04742e+09 9.99522e+08 1.11886e+09 1.16883e+09 1.22853e+09 1.18007e+09 1.19016e+09 1.0956e+09 1.41267e+09 1.62566e+09 1.33094e+09 1.27531e+09 1.3853e+09 1.32416e+09 1.41228e+09 1.4138e+09 1.18861e+09 1.19401e+09 1.46048e+09 1.51385e+09 1.1994e+09 1.35933e+09 1.16297e+09 1.35921e+09 1.15983e+09 1.27347e+09 1.22453e+09 1.35067e+09 1.24523e+09 1.13134e+09 1.26576e+09 1.10299e+09 1.2318e+09 1.28287e+09 1.07354e+09 1.24905e+09 1.23776e+09 1.18408e+09 1.2171e+09 1.20538e+09 8.34108e+08 1.53912e+09 1.2601e+09 1.17856e+09 1.21383e+09 1.13759e+09 1.2422e+09 1.31743e+09 1.38975e+09 1.51868e+09 1.45125e+09 1.03408e+09 1.21726e+09 1.34239e+09 1.46559e+09 1.355e+09 1.28283e+09 1.47806e+09 1.16883e+09 1.26223e+09 1.36721e+09 1.32747e+09 1.39438e+09 1.03986e+09 
 1.59918e+07 5.46231e+07 2.82089e+07 7.15155e+07 7.58979e+07 1.30644e+08 1.8984e+08 1.17948e+08 2.01243e+08 1.74176e+08 2.10784e+08 2.09705e+08 2.88712e+08 3.81573e+08 3.4372e+08 5.50801e+08 3.24222e+08 4.07195e+08 4.06662e+08 4.1191e+08 3.72731e+08 5.15404e+08 5.80769e+08 6.64948e+08 7.65907e+08 7.07278e+08 5.80321e+08 5.88884e+08 7.25806e+08 9.29402e+08 8.87258e+08 8.95276e+08 7.71752e+08 6.17343e+08 8.10759e+08 9.20536e+08 1.01043e+09 9.90933e+08 1.00014e+09 1.00464e+09 9.82266e+08 1.05074e+09 1.17508e+09 7.98436e+08 9.22537e+08 1.28268e+09 1.1155e+09 1.11086e+09 1.13177e+09 1.25097e+09 1.26927e+09 1.24329e+09 1.38167e+09 1.14427e+09 1.4513e+09 1.33094e+09 1.87663e+09 1.38574e+09 1.48851e+09 1.31623e+09 1.4477e+09 1.68392e+09 1.34224e+09 1.34819e+09 1.47459e+09 1.55844e+09 1.53928e+09 1.52979e+09 1.33035e+09 1.57911e+09 1.19609e+09 1.46226e+09 1.34496e+09 1.55933e+09 1.28547e+09 1.18546e+09 1.48223e+09 1.179e+09 1.18259e+09 1.43549e+09 1.22822e+09 1.39072e+09 1.41899e+09 1.43089e+09 1.34332e+09 1.25085e+09 1.06486e+09 1.61729e+09 1.37841e+09 1.28386e+09 1.27746e+09 1.29304e+09 1.35792e+09 1.48236e+09 1.56608e+09 1.50523e+09 1.5617e+09 1.03009e+09 1.31333e+09 1.62159e+09 1.698e+09 1.36634e+09 1.39732e+09 1.64302e+09 1.1558e+09 1.39007e+09 1.4855e+09 1.44011e+09 1.49529e+09 1.27457e+09 
 1.67844e+07 8.38863e+07 1.29156e+08 1.98983e+08 1.54237e+08 2.26001e+08 2.31999e+08 2.36892e+08 2.57966e+08 2.39311e+08 3.16945e+08 2.56223e+08 3.97415e+08 4.13815e+08 4.09232e+08 5.09174e+08 3.39503e+08 4.26311e+08 5.54419e+08 6.51874e+08 4.80457e+08 5.55809e+08 6.01623e+08 7.92701e+08 7.7345e+08 8.29499e+08 6.64067e+08 7.04166e+08 7.51966e+08 8.70127e+08 9.92377e+08 9.38794e+08 9.04502e+08 6.34159e+08 8.04404e+08 9.94754e+08 1.02925e+09 1.11415e+09 1.00165e+09 1.10535e+09 1.04922e+09 1.1148e+09 1.08469e+09 9.07268e+08 9.50747e+08 1.25738e+09 1.13404e+09 1.13072e+09 1.08109e+09 1.1443e+09 1.35135e+09 1.28994e+09 1.29792e+09 1.08226e+09 1.50292e+09 1.27531e+09 1.38574e+09 1.76022e+09 1.51338e+09 1.31128e+09 1.38404e+09 1.64876e+09 1.46198e+09 1.42006e+09 1.57614e+09 1.5258e+09 1.34967e+09 1.53053e+09 1.39011e+09 1.54439e+09 1.32448e+09 1.42838e+09 1.28333e+09 1.48224e+09 1.34446e+09 1.157e+09 1.46167e+09 1.19515e+09 1.24168e+09 1.4637e+09 1.30404e+09 1.41297e+09 1.29591e+09 1.41784e+09 1.23722e+09 1.35759e+09 1.00715e+09 1.63022e+09 1.25177e+09 1.35394e+09 1.31877e+09 1.18486e+09 1.30846e+09 1.42244e+09 1.55596e+09 1.48232e+09 1.58508e+09 1.28749e+09 1.45852e+09 1.52006e+09 1.56816e+09 1.42992e+09 1.53543e+09 1.6646e+09 1.39334e+09 1.3565e+09 1.50738e+09 1.46688e+09 1.57994e+09 1.31281e+09 
 2.62213e+07 7.36863e+07 8.49809e+07 1.43393e+08 1.17913e+08 1.96146e+08 2.03072e+08 1.69335e+08 2.23128e+08 2.28432e+08 2.56456e+08 1.98824e+08 2.99012e+08 3.68921e+08 3.07029e+08 4.80799e+08 3.20112e+08 3.76027e+08 4.88436e+08 5.20188e+08 4.30138e+08 5.3332e+08 5.48344e+08 7.58939e+08 6.59184e+08 6.87391e+08 5.90239e+08 6.93109e+08 7.27406e+08 8.41698e+08 8.98572e+08 8.57366e+08 8.0405e+08 6.63089e+08 8.31182e+08 1.00066e+09 1.05106e+09 1.11169e+09 1.06154e+09 1.25071e+09 1.10167e+09 1.13698e+09 1.15398e+09 9.89662e+08 9.22662e+08 1.3855e+09 1.21615e+09 1.17389e+09 1.27651e+09 1.34699e+09 1.42841e+09 1.32683e+09 1.39891e+09 1.29532e+09 1.64492e+09 1.3853e+09 1.48851e+09 1.51338e+09 2.07587e+09 1.52674e+09 1.46224e+09 1.8158e+09 1.46266e+09 1.59994e+09 1.76178e+09 1.72644e+09 1.40873e+09 1.6745e+09 1.4707e+09 1.75037e+09 1.5018e+09 1.55853e+09 1.44275e+09 1.6924e+09 1.47641e+09 1.3457e+09 1.65662e+09 1.39965e+09 1.44728e+09 1.57393e+09 1.54866e+09 1.47446e+09 1.28884e+09 1.57529e+09 1.49758e+09 1.53383e+09 1.21283e+09 1.67423e+09 1.56142e+09 1.48488e+09 1.5096e+09 1.38475e+09 1.4525e+09 1.49734e+09 1.83334e+09 1.74868e+09 1.77912e+09 1.47871e+09 1.40677e+09 1.65982e+09 1.86231e+09 1.54729e+09 1.51009e+09 1.8833e+09 1.41493e+09 1.43108e+09 1.65574e+09 1.63353e+09 1.67834e+09 1.42038e+09 
 4.33731e+07 1.10969e+08 1.12424e+08 2.00193e+08 1.07407e+08 1.70194e+08 2.09424e+08 2.04889e+08 2.53501e+08 1.92459e+08 2.4244e+08 2.04513e+08 3.32696e+08 3.34971e+08 3.54056e+08 4.63387e+08 3.32638e+08 4.34881e+08 4.49917e+08 4.96391e+08 4.17674e+08 4.94375e+08 5.20407e+08 7.13509e+08 7.74962e+08 7.96621e+08 6.13985e+08 6.73303e+08 7.85996e+08 8.51113e+08 8.66077e+08 8.66834e+08 8.28499e+08 6.99643e+08 7.72107e+08 9.42667e+08 1.04099e+09 1.07548e+09 1.04536e+09 1.0717e+09 1.02407e+09 1.10659e+09 1.10369e+09 9.55864e+08 1.01455e+09 1.38904e+09 1.22508e+09 1.30713e+09 1.43246e+09 1.25976e+09 1.34428e+09 1.39935e+09 1.37966e+09 1.18018e+09 1.6067e+09 1.32416e+09 1.31623e+09 1.31128e+09 1.52674e+09 1.97685e+09 1.55479e+09 1.60462e+09 1.39511e+09 1.45096e+09 1.63534e+09 1.72478e+09 1.2822e+09 1.54296e+09 1.47318e+09 1.55278e+09 1.49694e+09 1.50756e+09 1.43734e+09 1.59275e+09 1.36483e+09 1.34993e+09 1.42388e+09 1.35869e+09 1.24297e+09 1.54936e+09 1.29332e+09 1.50849e+09 1.34169e+09 1.48352e+09 1.4325e+09 1.49468e+09 1.10988e+09 1.66073e+09 1.4054e+09 1.39091e+09 1.30649e+09 1.27303e+09 1.32572e+09 1.61512e+09 1.63923e+09 1.67677e+09 1.60125e+09 1.4375e+09 1.37276e+09 1.50526e+09 1.57869e+09 1.47731e+09 1.53217e+09 1.70876e+09 1.48149e+09 1.40441e+09 1.76479e+09 1.60154e+09 1.66754e+09 1.26155e+09 
 1.67381e+07 5.70389e+07 1.24732e+08 1.74108e+08 1.39185e+08 2.00827e+08 1.88059e+08 2.11709e+08 1.92329e+08 2.19764e+08 2.72059e+08 2.10904e+08 2.84177e+08 3.48147e+08 2.86068e+08 3.96357e+08 2.96039e+08 3.00257e+08 2.91239e+08 4.1471e+08 3.18245e+08 4.32539e+08 4.42413e+08 5.51137e+08 6.41999e+08 7.48807e+08 5.20849e+08 6.41632e+08 7.51464e+08 7.32337e+08 8.13476e+08 8.46005e+08 8.39422e+08 6.36114e+08 7.02799e+08 8.91072e+08 9.12981e+08 1.00119e+09 9.47741e+08 9.40179e+08 8.3565e+08 1.06391e+09 1.1712e+09 7.96442e+08 1.00902e+09 1.38454e+09 1.19744e+09 1.27234e+09 1.23305e+09 1.29171e+09 1.47965e+09 1.40422e+09 1.44396e+09 1.28399e+09 1.53467e+09 1.41228e+09 1.4477e+09 1.38404e+09 1.46224e+09 1.55479e+09 2.0482e+09 1.67965e+09 1.50157e+09 1.51217e+09 1.50833e+09 1.71327e+09 1.46977e+09 1.60813e+09 1.43105e+09 1.56124e+09 1.41178e+09 1.56555e+09 1.44545e+09 1.78704e+09 1.42645e+09 1.28736e+09 1.58865e+09 1.35033e+09 1.36302e+09 1.50239e+09 1.34714e+09 1.43101e+09 1.56511e+09 1.57715e+09 1.5334e+09 1.57388e+09 1.19073e+09 1.65014e+09 1.32884e+09 1.35582e+09 1.50229e+09 1.29824e+09 1.43515e+09 1.55733e+09 1.64965e+09 1.71242e+09 1.80586e+09 1.35687e+09 1.45633e+09 1.63561e+09 1.86852e+09 1.55132e+09 1.52441e+09 1.62669e+09 1.46488e+09 1.5701e+09 1.71161e+09 1.5781e+09 1.69425e+09 1.35683e+09 
 1.33784e+07 5.32945e+07 1.19502e+08 1.57732e+08 1.27862e+08 2.19561e+08 2.30023e+08 2.12443e+08 2.89637e+08 2.80169e+08 3.57235e+08 2.88465e+08 4.24785e+08 4.33031e+08 4.06393e+08 5.52425e+08 3.42306e+08 4.42104e+08 4.90355e+08 5.75402e+08 4.53368e+08 5.38125e+08 5.55934e+08 6.66945e+08 7.47481e+08 8.073e+08 6.74866e+08 7.87199e+08 7.62501e+08 8.81579e+08 9.03049e+08 9.25319e+08 8.69017e+08 7.67135e+08 8.98936e+08 1.13717e+09 1.14225e+09 1.15817e+09 1.16715e+09 1.27569e+09 1.24179e+09 1.12932e+09 1.2653e+09 1.02151e+09 1.08776e+09 1.42598e+09 1.24395e+09 1.39547e+09 1.37426e+09 1.34263e+09 1.4089e+09 1.4134e+09 1.48963e+09 1.28117e+09 1.74742e+09 1.4138e+09 1.68392e+09 1.64876e+09 1.8158e+09 1.60462e+09 1.67965e+09 2.51891e+09 1.63542e+09 1.76834e+09 1.97288e+09 2.02354e+09 1.69027e+09 1.88979e+09 1.644e+09 1.8383e+09 1.65956e+09 1.73074e+09 1.57578e+09 1.8409e+09 1.56097e+09 1.46959e+09 1.91872e+09 1.5937e+09 1.47294e+09 1.84215e+09 1.75126e+09 1.84806e+09 1.58152e+09 1.91895e+09 1.59221e+09 1.72571e+09 1.34114e+09 1.96003e+09 1.67268e+09 1.79565e+09 1.79023e+09 1.56293e+09 1.62601e+09 1.80066e+09 1.9547e+09 1.94147e+09 2.09038e+09 1.69122e+09 1.77268e+09 1.84037e+09 2.08033e+09 1.76074e+09 1.81091e+09 1.96545e+09 1.72737e+09 1.68174e+09 1.99909e+09 2.01884e+09 2.03098e+09 1.65546e+09 
 4.63883e+07 8.64879e+07 1.29273e+08 2.04105e+08 1.04999e+08 1.97262e+08 2.04783e+08 1.87448e+08 2.14891e+08 1.4728e+08 2.55004e+08 2.65014e+08 2.89961e+08 4.07407e+08 3.5014e+08 4.64178e+08 3.64002e+08 3.79317e+08 5.47134e+08 5.89132e+08 4.30461e+08 4.85424e+08 5.27996e+08 6.54499e+08 7.87775e+08 7.22635e+08 6.0355e+08 6.35563e+08 6.59314e+08 8.23301e+08 9.46513e+08 9.50459e+08 9.47785e+08 6.38986e+08 7.56521e+08 8.67835e+08 9.2694e+08 9.21539e+08 1.02646e+09 1.04824e+09 9.69799e+08 1.09076e+09 1.14966e+09 9.99679e+08 9.29349e+08 1.36058e+09 1.20142e+09 1.12107e+09 1.25841e+09 1.29982e+09 1.46302e+09 1.25259e+09 1.32776e+09 1.14186e+09 1.52296e+09 1.18861e+09 1.34224e+09 1.46198e+09 1.46266e+09 1.39511e+09 1.50157e+09 1.63542e+09 2.0144e+09 1.46053e+09 1.47761e+09 1.58504e+09 1.46953e+09 1.65321e+09 1.42733e+09 1.62686e+09 1.43808e+09 1.60344e+09 1.44207e+09 1.6552e+09 1.27928e+09 1.33658e+09 1.60366e+09 1.40924e+09 1.34729e+09 1.54354e+09 1.49599e+09 1.53524e+09 1.56874e+09 1.66083e+09 1.50015e+09 1.48485e+09 1.09786e+09 1.68882e+09 1.26807e+09 1.50112e+09 1.51848e+09 1.51987e+09 1.49043e+09 1.58281e+09 1.66596e+09 1.65477e+09 1.53205e+09 1.4614e+09 1.61161e+09 1.6015e+09 1.6984e+09 1.5416e+09 1.587e+09 1.71644e+09 1.51683e+09 1.49674e+09 1.58021e+09 1.70884e+09 1.61575e+09 1.55973e+09 
 3.78968e+06 6.03151e+07 6.01389e+07 1.11184e+08 1.10213e+08 1.69738e+08 2.12644e+08 1.55736e+08 2.6874e+08 2.45431e+08 2.93851e+08 2.14874e+08 3.40521e+08 3.58053e+08 3.48423e+08 4.39257e+08 2.86849e+08 3.23922e+08 4.60617e+08 4.8074e+08 4.24852e+08 5.74727e+08 4.93039e+08 6.08075e+08 5.67156e+08 6.148e+08 5.84109e+08 6.6239e+08 5.87357e+08 7.16133e+08 8.79591e+08 8.3155e+08 7.63915e+08 6.26546e+08 7.08651e+08 9.29511e+08 8.55546e+08 9.43217e+08 8.7098e+08 1.08384e+09 9.5973e+08 1.10792e+09 1.17687e+09 9.22246e+08 9.43208e+08 1.36285e+09 1.23955e+09 1.17458e+09 1.21777e+09 1.20969e+09 1.27697e+09 1.23008e+09 1.32021e+09 1.08772e+09 1.43859e+09 1.19401e+09 1.34819e+09 1.42006e+09 1.59994e+09 1.45096e+09 1.51217e+09 1.76834e+09 1.46053e+09 2.00774e+09 1.66292e+09 1.74682e+09 1.38679e+09 1.63839e+09 1.59966e+09 1.59848e+09 1.62457e+09 1.44513e+09 1.52187e+09 1.65986e+09 1.31851e+09 1.19687e+09 1.6465e+09 1.38799e+09 1.3111e+09 1.64879e+09 1.54673e+09 1.43191e+09 1.46317e+09 1.63999e+09 1.56713e+09 1.41155e+09 1.178e+09 1.7433e+09 1.32798e+09 1.60239e+09 1.57697e+09 1.37181e+09 1.49095e+09 1.5298e+09 1.68564e+09 1.68144e+09 1.81052e+09 1.54306e+09 1.60647e+09 1.60953e+09 1.63734e+09 1.5947e+09 1.5733e+09 1.76522e+09 1.45223e+09 1.518e+09 1.72999e+09 1.61434e+09 1.72542e+09 1.50828e+09 
 2.54135e+07 8.86592e+07 8.30951e+07 1.65404e+08 1.35869e+08 2.17589e+08 2.91362e+08 2.08621e+08 3.0983e+08 2.69523e+08 3.35814e+08 3.03338e+08 3.94989e+08 4.95413e+08 4.16579e+08 5.78819e+08 4.12673e+08 4.60333e+08 5.99987e+08 6.35446e+08 4.88107e+08 6.13235e+08 6.51253e+08 8.1895e+08 7.50544e+08 8.37642e+08 7.06384e+08 7.24076e+08 7.63443e+08 8.94901e+08 9.88431e+08 1.01284e+09 9.10414e+08 7.36362e+08 8.88347e+08 1.05898e+09 1.08365e+09 1.11404e+09 1.03651e+09 1.18642e+09 1.11241e+09 1.20489e+09 1.2273e+09 1.00113e+09 9.05354e+08 1.51213e+09 1.25824e+09 1.39295e+09 1.42759e+09 1.28337e+09 1.39084e+09 1.3289e+09 1.47365e+09 1.24648e+09 1.7134e+09 1.46048e+09 1.47459e+09 1.57614e+09 1.76178e+09 1.63534e+09 1.50833e+09 1.97288e+09 1.47761e+09 1.66292e+09 2.27247e+09 1.96179e+09 1.44195e+09 1.69102e+09 1.65447e+09 1.86162e+09 1.66572e+09 1.66528e+09 1.55487e+09 1.81664e+09 1.57881e+09 1.46468e+09 1.78529e+09 1.49647e+09 1.53415e+09 1.75501e+09 1.66115e+09 1.72264e+09 1.38475e+09 1.7048e+09 1.44235e+09 1.64174e+09 1.26974e+09 1.89981e+09 1.5713e+09 1.7231e+09 1.66627e+09 1.51791e+09 1.6142e+09 1.6366e+09 1.80923e+09 1.88643e+09 1.92765e+09 1.58677e+09 1.59667e+09 1.63452e+09 1.84391e+09 1.62509e+09 1.73857e+09 1.99737e+09 1.62383e+09 1.59923e+09 1.85726e+09 1.72596e+09 1.93528e+09 1.52339e+09 
 4.7606e+07 1.14844e+08 6.89553e+07 1.50133e+08 8.98274e+07 1.58642e+08 1.50188e+08 1.59769e+08 2.51489e+08 1.89502e+08 2.85008e+08 1.5063e+08 3.10839e+08 3.45152e+08 3.17178e+08 4.96625e+08 2.79478e+08 4.40037e+08 5.15503e+08 5.43809e+08 4.29394e+08 5.63161e+08 5.24227e+08 7.40416e+08 8.16209e+08 7.97803e+08 6.69492e+08 7.85111e+08 8.1394e+08 9.27702e+08 9.58307e+08 9.53162e+08 8.63682e+08 7.15119e+08 8.48335e+08 1.00538e+09 1.07012e+09 1.08412e+09 1.03178e+09 1.19405e+09 1.08104e+09 1.13182e+09 1.20807e+09 1.00636e+09 1.06987e+09 1.51785e+09 1.28438e+09 1.33427e+09 1.39616e+09 1.34617e+09 1.48396e+09 1.39305e+09 1.38195e+09 1.42363e+09 1.70126e+09 1.51385e+09 1.55844e+09 1.5258e+09 1.72644e+09 1.72478e+09 1.71327e+09 2.02354e+09 1.58504e+09 1.74682e+09 1.96179e+09 2.52296e+09 1.60333e+09 1.93719e+09 1.67327e+09 1.91648e+09 1.82844e+09 1.74164e+09 1.66432e+09 2.01924e+09 1.74028e+09 1.51794e+09 1.80245e+09 1.58283e+09 1.78291e+09 1.91936e+09 1.7655e+09 1.79432e+09 1.69153e+09 1.87322e+09 1.70142e+09 1.9108e+09 1.34305e+09 2.1518e+09 1.70438e+09 1.87217e+09 1.76436e+09 1.72677e+09 1.79821e+09 1.8934e+09 2.03431e+09 1.83406e+09 1.99669e+09 1.68325e+09 1.83111e+09 1.86754e+09 2.02849e+09 1.8522e+09 1.93499e+09 2.02417e+09 1.80358e+09 1.82817e+09 1.99003e+09 1.96041e+09 2.08398e+09 1.62854e+09 
 5.05068e+06 4.109e+07 4.15414e+07 8.42945e+07 7.92713e+07 1.06978e+08 1.4141e+08 1.11388e+08 1.88247e+08 2.02942e+08 2.8997e+08 1.74997e+08 3.21278e+08 3.77421e+08 4.27832e+08 5.03434e+08 3.01275e+08 3.31038e+08 4.18668e+08 4.73102e+08 4.62309e+08 5.15413e+08 5.81395e+08 6.28196e+08 7.56083e+08 6.95848e+08 6.39806e+08 7.29174e+08 7.68971e+08 9.04648e+08 9.76794e+08 9.83773e+08 9.02295e+08 6.93812e+08 8.62828e+08 9.96838e+08 9.7794e+08 9.69534e+08 1.04183e+09 1.05765e+09 1.06797e+09 1.09068e+09 1.22059e+09 9.15502e+08 9.90508e+08 1.26116e+09 1.18905e+09 1.24376e+09 1.14482e+09 1.27614e+09 1.48787e+09 1.23276e+09 1.43147e+09 1.1771e+09 1.49456e+09 1.1994e+09 1.53928e+09 1.34967e+09 1.40873e+09 1.2822e+09 1.46977e+09 1.69027e+09 1.46953e+09 1.38679e+09 1.44195e+09 1.60333e+09 2.03666e+09 1.71393e+09 1.53056e+09 1.77928e+09 1.43866e+09 1.46934e+09 1.39792e+09 1.62563e+09 1.59652e+09 1.21791e+09 1.53005e+09 1.39498e+09 1.34848e+09 1.60132e+09 1.5598e+09 1.52616e+09 1.54459e+09 1.54625e+09 1.64071e+09 1.63204e+09 1.25558e+09 1.66764e+09 1.43958e+09 1.5298e+09 1.51125e+09 1.42707e+09 1.46836e+09 1.61378e+09 1.68563e+09 1.75267e+09 1.65674e+09 1.42051e+09 1.52754e+09 1.67642e+09 1.8087e+09 1.53509e+09 1.59778e+09 1.78578e+09 1.39772e+09 1.37357e+09 1.68186e+09 1.71304e+09 1.69823e+09 1.50548e+09 
 2.42673e+07 6.86693e+07 1.03115e+08 1.66822e+08 1.33473e+08 1.97356e+08 2.34285e+08 2.01073e+08 2.89247e+08 2.94367e+08 3.54535e+08 2.43362e+08 3.93193e+08 4.31644e+08 4.27433e+08 5.67646e+08 4.11701e+08 4.61017e+08 5.18772e+08 5.43933e+08 4.70141e+08 6.3327e+08 5.77026e+08 7.36048e+08 7.75553e+08 8.70281e+08 6.89558e+08 7.05343e+08 8.37073e+08 9.4465e+08 1.03877e+09 9.98248e+08 9.33177e+08 6.88198e+08 8.21638e+08 1.05804e+09 1.10736e+09 1.13592e+09 1.02859e+09 1.09782e+09 1.03183e+09 1.14108e+09 1.12196e+09 9.59412e+08 9.38627e+08 1.33686e+09 1.23218e+09 1.13709e+09 1.16464e+09 1.2775e+09 1.47893e+09 1.44026e+09 1.44001e+09 1.3128e+09 1.75813e+09 1.35933e+09 1.52979e+09 1.53053e+09 1.6745e+09 1.54296e+09 1.60813e+09 1.88979e+09 1.65321e+09 1.63839e+09 1.69102e+09 1.93719e+09 1.71393e+09 2.4306e+09 1.81347e+09 1.84172e+09 1.77348e+09 1.82919e+09 1.64504e+09 1.96433e+09 1.56362e+09 1.46522e+09 1.88323e+09 1.55209e+09 1.57405e+09 1.83804e+09 1.61011e+09 1.74782e+09 1.69433e+09 1.76622e+09 1.78579e+09 1.78418e+09 1.41713e+09 1.94652e+09 1.60707e+09 1.7671e+09 1.71579e+09 1.59862e+09 1.84614e+09 1.89379e+09 2.14228e+09 1.9974e+09 1.96254e+09 1.7753e+09 1.86487e+09 1.96026e+09 2.04493e+09 1.91644e+09 1.82267e+09 1.86511e+09 1.64635e+09 1.69323e+09 1.92065e+09 2.05295e+09 1.95689e+09 1.7569e+09 
 1.68193e+07 6.00664e+07 1.06562e+08 1.55907e+08 1.05198e+08 1.71517e+08 1.86591e+08 1.79809e+08 2.05329e+08 2.31522e+08 2.88293e+08 2.27617e+08 3.3123e+08 3.97505e+08 4.00004e+08 5.16975e+08 3.91507e+08 3.79395e+08 4.95178e+08 5.76545e+08 4.94103e+08 5.79864e+08 6.0748e+08 7.04493e+08 7.76169e+08 7.53972e+08 5.93821e+08 6.72359e+08 8.21967e+08 7.9387e+08 1.0325e+09 9.72283e+08 9.26359e+08 7.10962e+08 8.73475e+08 1.00105e+09 9.6149e+08 1.08184e+09 1.06624e+09 1.20672e+09 1.04656e+09 1.22947e+09 1.22098e+09 9.40334e+08 9.87065e+08 1.36844e+09 1.24456e+09 1.14166e+09 1.28521e+09 1.37126e+09 1.30018e+09 1.33001e+09 1.3702e+09 1.04807e+09 1.57519e+09 1.16297e+09 1.33035e+09 1.39011e+09 1.4707e+09 1.47318e+09 1.43105e+09 1.644e+09 1.42733e+09 1.59966e+09 1.65447e+09 1.67327e+09 1.53056e+09 1.81347e+09 2.12244e+09 1.78781e+09 1.70559e+09 1.6115e+09 1.6062e+09 1.74421e+09 1.41496e+09 1.38217e+09 1.67736e+09 1.48407e+09 1.38595e+09 1.65286e+09 1.61325e+09 1.57841e+09 1.51593e+09 1.57238e+09 1.68437e+09 1.5913e+09 1.33683e+09 1.90898e+09 1.53664e+09 1.70448e+09 1.67415e+09 1.42149e+09 1.59723e+09 1.78941e+09 1.8487e+09 2.01613e+09 1.92995e+09 1.72074e+09 1.69493e+09 1.74699e+09 1.87604e+09 1.68335e+09 1.63628e+09 1.83654e+09 1.50793e+09 1.61836e+09 1.73791e+09 1.847e+09 1.79728e+09 1.64492e+09 
 3.67697e+07 1.1435e+08 5.99587e+07 1.62315e+08 1.08104e+08 1.8538e+08 2.48285e+08 1.56973e+08 2.43942e+08 2.06671e+08 2.79708e+08 2.52929e+08 3.34149e+08 4.578e+08 4.1632e+08 5.51366e+08 3.8694e+08 4.14984e+08 5.48678e+08 5.37617e+08 4.89328e+08 5.49424e+08 6.52166e+08 7.75123e+08 8.53814e+08 7.42716e+08 7.10302e+08 7.41485e+08 8.26736e+08 1.01627e+09 1.08269e+09 1.0556e+09 1.00941e+09 8.00322e+08 9.7444e+08 1.00139e+09 1.0233e+09 1.08949e+09 1.06136e+09 1.23075e+09 1.01914e+09 1.21472e+09 1.26425e+09 9.7783e+08 9.86242e+08 1.31699e+09 1.22458e+09 1.34994e+09 1.28196e+09 1.36225e+09 1.54004e+09 1.26614e+09 1.45411e+09 1.26957e+09 1.62358e+09 1.35921e+09 1.57911e+09 1.54439e+09 1.75037e+09 1.55278e+09 1.56124e+09 1.8383e+09 1.62686e+09 1.59848e+09 1.86162e+09 1.91648e+09 1.77928e+09 1.84172e+09 1.78781e+09 2.53297e+09 1.75786e+09 1.90991e+09 1.66138e+09 1.88796e+09 1.75578e+09 1.66764e+09 1.8757e+09 1.57824e+09 1.62184e+09 1.9878e+09 1.91716e+09 1.9454e+09 1.64338e+09 1.82667e+09 1.75753e+09 1.78302e+09 1.44425e+09 2.04166e+09 1.70863e+09 1.72859e+09 1.72069e+09 1.78008e+09 1.69274e+09 1.90331e+09 2.03117e+09 2.0032e+09 1.9344e+09 1.73352e+09 1.93321e+09 1.93696e+09 2.14533e+09 1.75264e+09 1.88958e+09 2.10378e+09 1.71133e+09 1.66384e+09 1.8397e+09 1.92157e+09 1.99953e+09 1.68613e+09 
 5.70572e+06 6.31756e+07 6.17376e+07 1.29905e+08 8.50562e+07 1.05659e+08 1.89964e+08 1.53422e+08 2.40894e+08 1.95741e+08 2.91856e+08 2.142e+08 3.51349e+08 3.92769e+08 4.58562e+08 5.15936e+08 2.94045e+08 3.63604e+08 5.50951e+08 5.88638e+08 4.59972e+08 5.53773e+08 5.74494e+08 6.68806e+08 6.23222e+08 6.96962e+08 5.78576e+08 7.24837e+08 6.82299e+08 8.30337e+08 9.05313e+08 9.08223e+08 9.83238e+08 6.76068e+08 7.82112e+08 9.65082e+08 1.05228e+09 9.90314e+08 1.01218e+09 1.03333e+09 1.00927e+09 1.06274e+09 1.07811e+09 9.7906e+08 8.85248e+08 1.31582e+09 1.20391e+09 1.23931e+09 1.24147e+09 1.1163e+09 1.33457e+09 1.23978e+09 1.35092e+09 1.12391e+09 1.4971e+09 1.15983e+09 1.19609e+09 1.32448e+09 1.5018e+09 1.49694e+09 1.41178e+09 1.65956e+09 1.43808e+09 1.62457e+09 1.66572e+09 1.82844e+09 1.43866e+09 1.77348e+09 1.70559e+09 1.75786e+09 2.19267e+09 1.64606e+09 1.53983e+09 1.78491e+09 1.59746e+09 1.48864e+09 1.68062e+09 1.49842e+09 1.4325e+09 1.82814e+09 1.65263e+09 1.65033e+09 1.54618e+09 1.73922e+09 1.6206e+09 1.63519e+09 1.31435e+09 1.88083e+09 1.48623e+09 1.67169e+09 1.66558e+09 1.48851e+09 1.66713e+09 1.79229e+09 2.02322e+09 1.98391e+09 1.91515e+09 1.90448e+09 1.73468e+09 1.64853e+09 1.67231e+09 1.69559e+09 1.68724e+09 1.89056e+09 1.61206e+09 1.53865e+09 1.6912e+09 1.93691e+09 1.87638e+09 1.72968e+09 
 4.81974e+07 1.09737e+08 8.24006e+07 1.7669e+08 8.18858e+07 1.32102e+08 1.95616e+08 1.70838e+08 2.30243e+08 1.88264e+08 2.85537e+08 2.26447e+08 2.86502e+08 3.97103e+08 4.0557e+08 5.03811e+08 3.74559e+08 3.57647e+08 4.89303e+08 4.25786e+08 3.69179e+08 4.8452e+08 5.09503e+08 6.14659e+08 7.95578e+08 7.35729e+08 6.63156e+08 6.62738e+08 7.47626e+08 8.56088e+08 1.0194e+09 9.52129e+08 9.06637e+08 6.06569e+08 8.77734e+08 9.03215e+08 1.02871e+09 1.08108e+09 9.49208e+08 1.08862e+09 9.55604e+08 1.11601e+09 1.24163e+09 1.05886e+09 8.19457e+08 1.22745e+09 1.0529e+09 1.26229e+09 1.19785e+09 1.25741e+09 1.43735e+09 1.35916e+09 1.3666e+09 1.17667e+09 1.53135e+09 1.27347e+09 1.46226e+09 1.42838e+09 1.55853e+09 1.50756e+09 1.56555e+09 1.73074e+09 1.60344e+09 1.44513e+09 1.66528e+09 1.74164e+09 1.46934e+09 1.82919e+09 1.6115e+09 1.90991e+09 1.64606e+09 2.25615e+09 1.59146e+09 1.75415e+09 1.62662e+09 1.64174e+09 1.80018e+09 1.54961e+09 1.46076e+09 1.83649e+09 1.5943e+09 1.69455e+09 1.5572e+09 1.54341e+09 1.6071e+09 1.60957e+09 1.33205e+09 1.87606e+09 1.68308e+09 1.61181e+09 1.66458e+09 1.52949e+09 1.4583e+09 1.88513e+09 2.03557e+09 1.86939e+09 1.78618e+09 1.59429e+09 1.76068e+09 1.86511e+09 1.92889e+09 1.76063e+09 1.66235e+09 1.92991e+09 1.69332e+09 1.64513e+09 1.84618e+09 1.77292e+09 1.90317e+09 1.63521e+09 
 3.63423e+07 1.02661e+08 1.0387e+08 1.8427e+08 1.07503e+08 1.93866e+08 2.1281e+08 1.94796e+08 2.47276e+08 2.38024e+08 3.07965e+08 2.3593e+08 3.67843e+08 4.34893e+08 3.93751e+08 5.78894e+08 4.09758e+08 4.28494e+08 4.45597e+08 4.96764e+08 4.18611e+08 5.06054e+08 5.13288e+08 6.14239e+08 7.24277e+08 6.14696e+08 5.71765e+08 5.7546e+08 6.59114e+08 7.00986e+08 8.14706e+08 7.4814e+08 6.86354e+08 5.39518e+08 6.68715e+08 7.6315e+08 8.55487e+08 9.36415e+08 8.43954e+08 9.02987e+08 8.5791e+08 1.08044e+09 1.05036e+09 8.49039e+08 8.70971e+08 1.27127e+09 1.04201e+09 1.06544e+09 1.14935e+09 1.18121e+09 1.26602e+09 1.17279e+09 1.22272e+09 9.82721e+08 1.33442e+09 1.22453e+09 1.34496e+09 1.28333e+09 1.44275e+09 1.43734e+09 1.44545e+09 1.57578e+09 1.44207e+09 1.52187e+09 1.55487e+09 1.66432e+09 1.39792e+09 1.64504e+09 1.6062e+09 1.66138e+09 1.53983e+09 1.59146e+09 2.06274e+09 1.69908e+09 1.53522e+09 1.51228e+09 1.70899e+09 1.47933e+09 1.46368e+09 1.84316e+09 1.57481e+09 1.61622e+09 1.63287e+09 1.681e+09 1.64161e+09 1.6431e+09 1.2435e+09 1.81338e+09 1.61664e+09 1.77522e+09 1.78322e+09 1.57944e+09 1.6647e+09 1.74373e+09 1.92196e+09 1.88376e+09 1.76188e+09 1.56319e+09 1.65082e+09 1.69861e+09 1.83152e+09 1.72167e+09 1.72408e+09 1.75205e+09 1.68757e+09 1.57355e+09 1.89277e+09 1.85561e+09 1.95795e+09 1.54044e+09 
 7.30341e+06 2.26544e+07 7.01917e+07 1.10248e+08 1.17529e+08 1.48832e+08 2.24394e+08 1.49285e+08 2.02388e+08 1.88134e+08 2.05663e+08 2.24816e+08 2.07381e+08 3.16523e+08 2.63719e+08 4.02552e+08 2.94445e+08 3.50793e+08 3.82526e+08 4.40496e+08 2.95091e+08 5.53351e+08 5.68159e+08 7.10822e+08 6.97785e+08 8.08241e+08 5.71024e+08 5.84241e+08 7.34461e+08 8.94858e+08 9.03175e+08 8.74814e+08 7.94496e+08 6.40742e+08 7.8602e+08 9.16684e+08 1.05378e+09 1.04758e+09 1.08919e+09 1.07613e+09 9.84873e+08 1.00223e+09 1.12259e+09 9.4117e+08 9.43861e+08 1.5308e+09 1.31938e+09 1.22666e+09 1.40051e+09 1.4596e+09 1.33352e+09 1.37576e+09 1.47214e+09 1.39612e+09 1.75329e+09 1.35067e+09 1.55933e+09 1.48224e+09 1.6924e+09 1.59275e+09 1.78704e+09 1.8409e+09 1.6552e+09 1.65986e+09 1.81664e+09 2.01924e+09 1.62563e+09 1.96433e+09 1.74421e+09 1.88796e+09 1.78491e+09 1.75415e+09 1.69908e+09 2.57483e+09 1.7086e+09 1.59874e+09 1.94591e+09 1.77707e+09 1.79912e+09 1.99691e+09 1.75692e+09 1.78597e+09 1.83822e+09 1.94502e+09 1.78095e+09 1.85912e+09 1.51241e+09 2.14586e+09 1.76435e+09 1.86662e+09 1.78215e+09 1.8032e+09 1.86868e+09 1.81147e+09 2.12563e+09 2.17349e+09 2.2041e+09 1.87948e+09 1.92315e+09 1.90737e+09 2.268e+09 1.83502e+09 1.86086e+09 2.13272e+09 1.72115e+09 1.88737e+09 1.92856e+09 2.07421e+09 2.01595e+09 1.70401e+09 
 4.39969e+07 1.07837e+08 9.69696e+07 1.77544e+08 8.92802e+07 1.55719e+08 1.62673e+08 1.95852e+08 2.10819e+08 1.49682e+08 2.56752e+08 1.99795e+08 3.14459e+08 3.60851e+08 3.17938e+08 4.2975e+08 3.01711e+08 3.52245e+08 4.54348e+08 4.97905e+08 4.06164e+08 4.50167e+08 4.86124e+08 6.56355e+08 7.25036e+08 7.3436e+08 6.48081e+08 6.98847e+08 6.90558e+08 8.04371e+08 8.89601e+08 8.25857e+08 8.29128e+08 5.98794e+08 7.15674e+08 9.11808e+08 9.99364e+08 9.90645e+08 9.42211e+08 1.02229e+09 9.31887e+08 1.02962e+09 1.16421e+09 9.1612e+08 8.85321e+08 1.27596e+09 1.10541e+09 1.22657e+09 1.16117e+09 1.19449e+09 1.31764e+09 1.19854e+09 1.22305e+09 1.038e+09 1.36421e+09 1.24523e+09 1.28547e+09 1.34446e+09 1.47641e+09 1.36483e+09 1.42645e+09 1.56097e+09 1.27928e+09 1.31851e+09 1.57881e+09 1.74028e+09 1.59652e+09 1.56362e+09 1.41496e+09 1.75578e+09 1.59746e+09 1.62662e+09 1.53522e+09 1.7086e+09 2.23178e+09 1.52896e+09 1.6345e+09 1.55709e+09 1.68092e+09 1.96144e+09 1.63759e+09 1.54675e+09 1.5935e+09 1.69967e+09 1.64236e+09 1.74817e+09 1.37938e+09 1.90532e+09 1.68812e+09 1.87621e+09 1.78765e+09 1.59612e+09 1.71317e+09 1.77791e+09 2.02417e+09 1.99789e+09 1.90649e+09 1.73175e+09 1.67898e+09 1.75675e+09 1.89462e+09 1.9116e+09 1.75652e+09 1.95026e+09 1.72725e+09 1.52599e+09 1.9874e+09 1.85533e+09 1.96583e+09 1.61773e+09 
 2.7261e+07 1.01686e+08 8.29155e+07 1.70247e+08 8.55707e+07 1.4026e+08 1.68598e+08 1.67869e+08 1.73439e+08 1.15345e+08 2.09287e+08 1.92297e+08 2.92816e+08 3.52042e+08 3.27659e+08 4.07466e+08 3.47299e+08 2.96327e+08 3.89475e+08 4.57444e+08 3.57557e+08 3.21035e+08 4.07165e+08 4.67337e+08 6.08504e+08 5.37935e+08 4.80592e+08 5.00947e+08 5.94692e+08 6.03472e+08 6.65243e+08 6.9743e+08 6.91477e+08 5.09156e+08 6.25236e+08 6.68861e+08 8.17036e+08 8.71268e+08 8.20327e+08 8.53802e+08 7.58393e+08 8.47317e+08 8.43114e+08 7.10454e+08 6.76194e+08 1.04469e+09 9.63222e+08 1.06346e+09 9.74934e+08 1.01946e+09 1.23998e+09 1.08785e+09 1.09075e+09 1.0714e+09 1.4591e+09 1.13134e+09 1.18546e+09 1.157e+09 1.3457e+09 1.34993e+09 1.28736e+09 1.46959e+09 1.33658e+09 1.19687e+09 1.46468e+09 1.51794e+09 1.21791e+09 1.46522e+09 1.38217e+09 1.66764e+09 1.48864e+09 1.64174e+09 1.51228e+09 1.59874e+09 1.52896e+09 2.06815e+09 1.62897e+09 1.55589e+09 1.49073e+09 1.85058e+09 1.48768e+09 1.69192e+09 1.55867e+09 1.46911e+09 1.45027e+09 1.59038e+09 1.26818e+09 1.79054e+09 1.46769e+09 1.90528e+09 1.51291e+09 1.63736e+09 1.65675e+09 1.71583e+09 1.81987e+09 1.93464e+09 1.78709e+09 1.67199e+09 1.71784e+09 1.57056e+09 1.84445e+09 1.67927e+09 1.56788e+09 1.78612e+09 1.61419e+09 1.52749e+09 1.751e+09 1.68928e+09 1.86254e+09 1.5116e+09 
 2.4253e+07 6.32383e+07 7.06675e+07 1.29336e+08 1.00939e+08 1.79281e+08 2.41202e+08 1.82242e+08 2.50034e+08 2.0875e+08 3.03574e+08 3.00054e+08 3.37759e+08 4.58541e+08 3.24241e+08 5.33887e+08 3.56732e+08 4.0791e+08 4.11284e+08 5.01536e+08 4.06666e+08 5.69481e+08 5.98797e+08 6.19476e+08 6.87753e+08 7.23707e+08 6.25685e+08 6.55514e+08 6.72457e+08 8.66817e+08 8.37294e+08 8.59599e+08 8.55035e+08 7.03051e+08 7.87153e+08 9.76907e+08 1.10288e+09 1.07548e+09 1.10306e+09 1.07511e+09 1.0097e+09 1.12443e+09 1.18088e+09 9.62617e+08 8.45641e+08 1.41997e+09 1.11058e+09 1.20248e+09 1.22797e+09 1.27547e+09 1.30459e+09 1.316e+09 1.46127e+09 1.19329e+09 1.58289e+09 1.26576e+09 1.48223e+09 1.46167e+09 1.65662e+09 1.42388e+09 1.58865e+09 1.91872e+09 1.60366e+09 1.6465e+09 1.78529e+09 1.80245e+09 1.53005e+09 1.88323e+09 1.67736e+09 1.8757e+09 1.68062e+09 1.80018e+09 1.70899e+09 1.94591e+09 1.6345e+09 1.62897e+09 2.59027e+09 1.76071e+09 1.77862e+09 1.936e+09 1.85292e+09 1.98449e+09 1.83603e+09 1.87488e+09 1.7673e+09 1.93307e+09 1.50747e+09 2.04399e+09 1.86763e+09 1.91507e+09 1.99858e+09 1.85534e+09 1.7934e+09 1.93618e+09 2.086e+09 2.10143e+09 2.0382e+09 1.98934e+09 1.95062e+09 1.91944e+09 2.25826e+09 1.78813e+09 1.83726e+09 2.09402e+09 1.82561e+09 1.701e+09 2.02003e+09 1.9958e+09 2.13558e+09 1.78639e+09 
 5.74861e+06 1.77467e+07 7.61739e+07 8.96624e+07 1.04923e+08 1.54883e+08 1.09816e+08 1.22005e+08 1.62239e+08 2.2415e+08 2.8468e+08 1.41615e+08 2.70612e+08 3.12688e+08 3.18759e+08 4.06804e+08 2.34377e+08 2.66181e+08 3.07314e+08 4.77207e+08 3.47174e+08 4.51309e+08 4.67098e+08 5.21807e+08 6.37337e+08 6.13643e+08 5.03578e+08 6.05877e+08 6.62928e+08 6.77702e+08 7.64068e+08 8.41242e+08 6.62922e+08 5.27792e+08 6.53036e+08 8.49973e+08 8.88172e+08 9.2989e+08 8.59183e+08 9.30314e+08 1.07655e+09 9.89636e+08 8.94104e+08 7.71861e+08 8.45706e+08 1.24688e+09 1.06002e+09 1.04306e+09 1.07139e+09 1.1515e+09 1.22466e+09 1.13248e+09 1.20921e+09 1.15165e+09 1.35167e+09 1.10299e+09 1.179e+09 1.19515e+09 1.39965e+09 1.35869e+09 1.35033e+09 1.5937e+09 1.40924e+09 1.38799e+09 1.49647e+09 1.58283e+09 1.39498e+09 1.55209e+09 1.48407e+09 1.57824e+09 1.49842e+09 1.54961e+09 1.47933e+09 1.77707e+09 1.55709e+09 1.55589e+09 1.76071e+09 2.1778e+09 1.5988e+09 1.83909e+09 1.82975e+09 1.66082e+09 1.64927e+09 1.67924e+09 1.50725e+09 1.73822e+09 1.4387e+09 1.90215e+09 1.7266e+09 1.88776e+09 1.83285e+09 1.71353e+09 1.6521e+09 1.82168e+09 1.75791e+09 2.19232e+09 1.79004e+09 1.90968e+09 1.75539e+09 1.73643e+09 1.94267e+09 1.72756e+09 1.79199e+09 1.97342e+09 1.74452e+09 1.59412e+09 1.8876e+09 1.88409e+09 1.93863e+09 1.5672e+09 
 2.81159e+07 6.72823e+07 6.87815e+07 1.20006e+08 5.64046e+07 1.00812e+08 8.65235e+07 1.17139e+08 1.57338e+08 1.19635e+08 2.36316e+08 1.34138e+08 2.5695e+08 2.92497e+08 3.04396e+08 4.15317e+08 2.84585e+08 3.63193e+08 3.90063e+08 5.43147e+08 3.98603e+08 4.23692e+08 4.74707e+08 5.26744e+08 7.66696e+08 6.34531e+08 5.37264e+08 6.10887e+08 6.86946e+08 7.45393e+08 7.34053e+08 8.70325e+08 7.80687e+08 6.05304e+08 6.72035e+08 7.85126e+08 8.48553e+08 8.47855e+08 8.96385e+08 8.31193e+08 8.51353e+08 8.86142e+08 9.70086e+08 8.70632e+08 8.05269e+08 1.21612e+09 1.07931e+09 1.02579e+09 1.10172e+09 1.15607e+09 1.25654e+09 1.09506e+09 1.06888e+09 1.12407e+09 1.30804e+09 1.2318e+09 1.18259e+09 1.24168e+09 1.44728e+09 1.24297e+09 1.36302e+09 1.47294e+09 1.34729e+09 1.3111e+09 1.53415e+09 1.78291e+09 1.34848e+09 1.57405e+09 1.38595e+09 1.62184e+09 1.4325e+09 1.46076e+09 1.46368e+09 1.79912e+09 1.68092e+09 1.49073e+09 1.77862e+09 1.5988e+09 2.37871e+09 1.92181e+09 1.68493e+09 1.75615e+09 1.77067e+09 1.8825e+09 1.60735e+09 1.78406e+09 1.40149e+09 2.0283e+09 1.73181e+09 1.84169e+09 1.86683e+09 1.85986e+09 1.84305e+09 1.83397e+09 1.92417e+09 2.06487e+09 1.90604e+09 1.97201e+09 1.76015e+09 1.84789e+09 2.00125e+09 1.87096e+09 1.86269e+09 1.98269e+09 1.94725e+09 1.68613e+09 1.83944e+09 1.90748e+09 2.0079e+09 1.66914e+09 
 2.3692e+07 8.70221e+07 7.63917e+07 1.50402e+08 1.19273e+08 1.86857e+08 2.12059e+08 1.93773e+08 2.79042e+08 2.65529e+08 3.80792e+08 2.44708e+08 3.82463e+08 4.51715e+08 3.94801e+08 5.25028e+08 3.82468e+08 3.87577e+08 4.75457e+08 6.03004e+08 4.36488e+08 5.87016e+08 5.98213e+08 7.1424e+08 8.16558e+08 8.0187e+08 7.73971e+08 7.71115e+08 7.27955e+08 9.04682e+08 1.01262e+09 9.86388e+08 8.5758e+08 6.42327e+08 8.70345e+08 9.74777e+08 1.06672e+09 1.07537e+09 9.7289e+08 1.07358e+09 1.06228e+09 1.11854e+09 1.17568e+09 9.54e+08 8.73751e+08 1.28957e+09 1.18632e+09 1.27151e+09 1.25641e+09 1.24082e+09 1.46972e+09 1.25265e+09 1.42289e+09 1.26458e+09 1.63993e+09 1.28287e+09 1.43549e+09 1.4637e+09 1.57393e+09 1.54936e+09 1.50239e+09 1.84215e+09 1.54354e+09 1.64879e+09 1.75501e+09 1.91936e+09 1.60132e+09 1.83804e+09 1.65286e+09 1.9878e+09 1.82814e+09 1.83649e+09 1.84316e+09 1.99691e+09 1.96144e+09 1.85058e+09 1.936e+09 1.83909e+09 1.92181e+09 2.9211e+09 2.04669e+09 2.05867e+09 2.01669e+09 2.10822e+09 1.94363e+09 2.04961e+09 1.63224e+09 2.2894e+09 1.97333e+09 2.29045e+09 2.19017e+09 2.10125e+09 2.14904e+09 2.27724e+09 2.38068e+09 2.53809e+09 2.2647e+09 2.17364e+09 2.17393e+09 2.19598e+09 2.18736e+09 2.3342e+09 2.30975e+09 2.38455e+09 2.20479e+09 1.79336e+09 2.3838e+09 2.3552e+09 2.41412e+09 2.12331e+09 
 4.94803e+06 2.21155e+07 3.67726e+07 6.96016e+07 8.96226e+07 1.45486e+08 1.90269e+08 1.17095e+08 2.21531e+08 2.33758e+08 3.18329e+08 2.34097e+08 3.32201e+08 4.58626e+08 3.84575e+08 6.05895e+08 3.59376e+08 4.25621e+08 4.82994e+08 5.88602e+08 4.65686e+08 6.27914e+08 6.6624e+08 7.31989e+08 7.206e+08 6.68979e+08 6.93471e+08 7.82588e+08 7.20108e+08 8.45595e+08 9.5046e+08 9.21089e+08 9.08519e+08 6.42278e+08 8.98168e+08 9.71089e+08 9.62372e+08 1.07216e+09 9.7886e+08 1.18929e+09 1.19402e+09 1.18312e+09 1.10104e+09 1.0055e+09 1.03284e+09 1.32166e+09 1.23025e+09 1.25526e+09 1.16904e+09 1.14659e+09 1.41363e+09 1.21162e+09 1.34262e+09 1.17776e+09 1.3921e+09 1.07354e+09 1.22822e+09 1.30404e+09 1.54866e+09 1.29332e+09 1.34714e+09 1.75126e+09 1.49599e+09 1.54673e+09 1.66115e+09 1.7655e+09 1.5598e+09 1.61011e+09 1.61325e+09 1.91716e+09 1.65263e+09 1.5943e+09 1.57481e+09 1.75692e+09 1.63759e+09 1.48768e+09 1.85292e+09 1.82975e+09 1.68493e+09 2.04669e+09 2.54458e+09 1.88942e+09 1.83264e+09 1.87546e+09 1.71618e+09 1.9288e+09 1.53962e+09 2.15037e+09 1.79889e+09 1.99351e+09 2.00815e+09 1.93483e+09 1.84056e+09 1.98834e+09 1.93817e+09 2.28272e+09 2.00866e+09 2.05655e+09 2.03381e+09 1.89507e+09 2.01809e+09 1.92525e+09 2.00844e+09 2.20355e+09 1.93555e+09 1.49704e+09 2.00902e+09 2.05101e+09 2.08838e+09 1.85324e+09 
 2.90598e+07 6.09009e+07 5.75659e+07 1.23415e+08 7.93988e+07 1.44526e+08 2.07424e+08 1.22151e+08 2.09709e+08 1.28477e+08 2.0202e+08 2.28932e+08 2.88497e+08 3.78065e+08 3.14146e+08 4.54287e+08 2.91525e+08 4.06575e+08 4.21327e+08 4.56596e+08 3.88583e+08 4.10637e+08 5.11634e+08 6.03656e+08 6.58549e+08 6.42908e+08 5.45304e+08 6.13631e+08 6.87211e+08 8.25881e+08 7.55344e+08 7.93195e+08 8.96381e+08 7.06953e+08 8.2566e+08 8.86334e+08 8.79761e+08 9.0415e+08 1.0121e+09 9.85908e+08 1.02062e+09 9.05839e+08 9.42412e+08 8.29892e+08 9.42557e+08 1.10727e+09 1.06108e+09 1.14076e+09 1.15255e+09 1.15882e+09 1.33193e+09 1.20267e+09 1.36025e+09 1.10612e+09 1.61891e+09 1.24905e+09 1.39072e+09 1.41297e+09 1.47446e+09 1.50849e+09 1.43101e+09 1.84806e+09 1.53524e+09 1.43191e+09 1.72264e+09 1.79432e+09 1.52616e+09 1.74782e+09 1.57841e+09 1.9454e+09 1.65033e+09 1.69455e+09 1.61622e+09 1.78597e+09 1.54675e+09 1.69192e+09 1.98449e+09 1.66082e+09 1.75615e+09 2.05867e+09 1.88942e+09 2.66522e+09 2.00907e+09 1.95575e+09 1.80205e+09 1.9935e+09 1.70862e+09 2.22648e+09 1.98942e+09 2.12288e+09 2.00788e+09 1.9252e+09 1.99538e+09 2.13864e+09 2.18838e+09 2.28655e+09 2.06527e+09 2.17047e+09 2.01965e+09 1.99191e+09 2.25972e+09 1.93403e+09 1.98639e+09 2.06684e+09 2.1225e+09 1.71439e+09 2.04339e+09 2.10263e+09 2.18881e+09 1.91931e+09 
 4.10286e+07 1.16502e+08 1.16009e+08 2.12807e+08 1.08426e+08 1.89742e+08 2.25003e+08 2.00887e+08 2.35624e+08 1.44709e+08 2.36394e+08 2.53785e+08 3.44011e+08 3.87883e+08 3.71421e+08 4.47478e+08 3.07262e+08 3.71138e+08 3.9794e+08 4.36247e+08 4.20286e+08 4.02804e+08 5.05517e+08 5.19919e+08 7.36975e+08 6.63012e+08 5.90339e+08 6.39556e+08 6.92508e+08 8.97266e+08 8.57571e+08 8.03965e+08 8.80148e+08 6.58832e+08 6.86e+08 8.65439e+08 9.49252e+08 8.5705e+08 9.87503e+08 8.64738e+08 9.01906e+08 1.02279e+09 1.01791e+09 7.62961e+08 9.53037e+08 1.24846e+09 1.17737e+09 1.01439e+09 1.12991e+09 1.23981e+09 1.28196e+09 1.12451e+09 1.26913e+09 1.03373e+09 1.5094e+09 1.23776e+09 1.41899e+09 1.29591e+09 1.28884e+09 1.34169e+09 1.56511e+09 1.58152e+09 1.56874e+09 1.46317e+09 1.38475e+09 1.69153e+09 1.54459e+09 1.69433e+09 1.51593e+09 1.64338e+09 1.54618e+09 1.5572e+09 1.63287e+09 1.83822e+09 1.5935e+09 1.55867e+09 1.83603e+09 1.64927e+09 1.77067e+09 2.01669e+09 1.83264e+09 2.00907e+09 2.63886e+09 2.08068e+09 2.01966e+09 2.00246e+09 1.64005e+09 2.25865e+09 1.80092e+09 2.20784e+09 2.04904e+09 2.0348e+09 2.07938e+09 2.15378e+09 2.06901e+09 2.25685e+09 2.16765e+09 2.01291e+09 2.14091e+09 1.97714e+09 2.18427e+09 2.16853e+09 1.97203e+09 2.12385e+09 2.03565e+09 1.81401e+09 2.16972e+09 2.06174e+09 2.10779e+09 1.99571e+09 
 7.40955e+06 4.4099e+07 1.06969e+08 1.53066e+08 1.23852e+08 1.95956e+08 2.15401e+08 1.81094e+08 2.32415e+08 2.31894e+08 3.16949e+08 2.67852e+08 3.28911e+08 3.9422e+08 3.55183e+08 4.65394e+08 3.00485e+08 3.65355e+08 5.41747e+08 6.29267e+08 4.36182e+08 5.96418e+08 5.72952e+08 7.04091e+08 7.34116e+08 8.60231e+08 6.46338e+08 7.46374e+08 7.2215e+08 8.95313e+08 9.62519e+08 9.75171e+08 9.04319e+08 7.36966e+08 7.9427e+08 1.00709e+09 9.30381e+08 8.93515e+08 1.03161e+09 1.06359e+09 9.51755e+08 1.10464e+09 1.20219e+09 9.74442e+08 1.03248e+09 1.56408e+09 1.30348e+09 1.28985e+09 1.30424e+09 1.44949e+09 1.40437e+09 1.25497e+09 1.44779e+09 1.14122e+09 1.4927e+09 1.18408e+09 1.43089e+09 1.41784e+09 1.57529e+09 1.48352e+09 1.57715e+09 1.91895e+09 1.66083e+09 1.63999e+09 1.7048e+09 1.87322e+09 1.54625e+09 1.76622e+09 1.57238e+09 1.82667e+09 1.73922e+09 1.54341e+09 1.681e+09 1.94502e+09 1.69967e+09 1.46911e+09 1.87488e+09 1.67924e+09 1.8825e+09 2.10822e+09 1.87546e+09 1.95575e+09 2.08068e+09 2.77889e+09 1.94277e+09 2.08813e+09 1.48923e+09 2.31349e+09 1.79019e+09 2.16618e+09 2.13453e+09 2.1841e+09 2.12114e+09 2.09646e+09 2.15742e+09 2.3223e+09 2.28568e+09 2.1843e+09 2.12271e+09 2.07006e+09 2.21e+09 2.17725e+09 2.19712e+09 2.13437e+09 2.09295e+09 1.83176e+09 2.17653e+09 2.21429e+09 2.20683e+09 2.055e+09 
 3.55834e+07 7.05179e+07 6.52463e+07 1.24302e+08 5.84704e+07 1.39001e+08 1.81984e+08 1.35155e+08 2.08478e+08 1.50814e+08 2.48412e+08 2.43554e+08 3.11604e+08 3.90295e+08 3.18505e+08 4.62024e+08 3.57495e+08 3.83169e+08 4.22834e+08 4.65472e+08 4.1538e+08 5.00613e+08 5.26971e+08 5.66356e+08 7.33378e+08 6.68388e+08 6.35273e+08 6.35181e+08 7.10291e+08 8.16347e+08 9.0202e+08 7.82412e+08 7.81456e+08 6.94901e+08 7.25676e+08 8.44337e+08 9.62072e+08 9.27259e+08 9.37645e+08 1.07394e+09 8.77087e+08 1.07672e+09 1.17261e+09 8.79134e+08 9.1482e+08 1.30698e+09 1.14787e+09 1.07713e+09 1.196e+09 1.39726e+09 1.37094e+09 1.27097e+09 1.424e+09 1.16953e+09 1.5162e+09 1.2171e+09 1.34332e+09 1.23722e+09 1.49758e+09 1.4325e+09 1.5334e+09 1.59221e+09 1.50015e+09 1.56713e+09 1.44235e+09 1.70142e+09 1.64071e+09 1.78579e+09 1.68437e+09 1.75753e+09 1.6206e+09 1.6071e+09 1.64161e+09 1.78095e+09 1.64236e+09 1.45027e+09 1.7673e+09 1.50725e+09 1.60735e+09 1.94363e+09 1.71618e+09 1.80205e+09 2.01966e+09 1.94277e+09 2.51489e+09 1.86797e+09 1.51734e+09 2.08724e+09 1.83945e+09 2.0432e+09 1.94963e+09 1.88327e+09 1.94574e+09 1.96932e+09 2.08835e+09 2.2922e+09 2.12623e+09 2.08002e+09 2.15379e+09 1.95865e+09 2.15631e+09 2.02083e+09 1.87797e+09 2.11298e+09 1.88455e+09 1.72273e+09 2.06239e+09 1.9455e+09 2.02652e+09 1.97071e+09 
 2.04732e+07 5.86336e+07 5.12583e+07 1.05284e+08 7.75577e+07 1.11143e+08 1.22014e+08 1.31003e+08 1.88037e+08 1.94031e+08 2.95256e+08 1.45225e+08 2.62105e+08 3.3972e+08 2.96786e+08 4.4221e+08 2.53588e+08 3.22345e+08 3.77743e+08 4.93891e+08 3.78912e+08 4.99733e+08 5.03556e+08 6.00666e+08 6.60715e+08 6.78619e+08 6.19039e+08 7.22455e+08 7.06184e+08 7.49063e+08 8.22986e+08 8.43628e+08 8.38653e+08 5.98257e+08 7.54313e+08 8.87829e+08 9.50524e+08 9.99535e+08 9.92126e+08 1.10876e+09 1.04773e+09 1.10488e+09 1.07254e+09 9.40218e+08 9.64004e+08 1.30773e+09 1.2129e+09 1.29759e+09 1.18071e+09 1.26564e+09 1.44173e+09 1.26926e+09 1.34158e+09 1.26447e+09 1.51335e+09 1.20538e+09 1.25085e+09 1.35759e+09 1.53383e+09 1.49468e+09 1.57388e+09 1.72571e+09 1.48485e+09 1.41155e+09 1.64174e+09 1.9108e+09 1.63204e+09 1.78418e+09 1.5913e+09 1.78302e+09 1.63519e+09 1.60957e+09 1.6431e+09 1.85912e+09 1.74817e+09 1.59038e+09 1.93307e+09 1.73822e+09 1.78406e+09 2.04961e+09 1.9288e+09 1.9935e+09 2.00246e+09 2.08813e+09 1.86797e+09 2.77612e+09 1.74846e+09 2.34517e+09 1.98646e+09 2.31895e+09 2.13112e+09 1.99401e+09 2.09318e+09 2.20721e+09 2.22135e+09 2.5604e+09 2.19094e+09 2.24946e+09 2.15679e+09 2.01774e+09 2.27276e+09 2.21806e+09 2.094e+09 2.17515e+09 2.1892e+09 1.93616e+09 2.29728e+09 2.20255e+09 2.30818e+09 1.86846e+09 
 5.60632e+06 3.10062e+07 2.17494e+07 6.15075e+07 6.42773e+07 8.7994e+07 1.70782e+08 1.11668e+08 1.73002e+08 1.46938e+08 1.91438e+08 1.84977e+08 2.11414e+08 3.29765e+08 2.53435e+08 3.64006e+08 2.26748e+08 2.19811e+08 2.67878e+08 3.41474e+08 3.049e+08 3.92447e+08 4.58953e+08 4.77176e+08 4.71769e+08 5.38217e+08 4.70861e+08 5.07052e+08 5.45351e+08 6.29673e+08 6.36807e+08 6.20649e+08 6.45052e+08 5.00627e+08 5.76302e+08 6.92936e+08 7.76599e+08 7.7375e+08 8.29743e+08 7.89764e+08 7.21385e+08 7.85131e+08 8.13437e+08 6.24228e+08 6.78387e+08 9.33605e+08 8.9803e+08 9.02329e+08 8.12373e+08 8.66534e+08 9.61108e+08 8.68263e+08 1.07324e+09 8.7763e+08 1.1831e+09 8.34108e+08 1.06486e+09 1.00715e+09 1.21283e+09 1.10988e+09 1.19073e+09 1.34114e+09 1.09786e+09 1.178e+09 1.26974e+09 1.34305e+09 1.25558e+09 1.41713e+09 1.33683e+09 1.44425e+09 1.31435e+09 1.33205e+09 1.2435e+09 1.51241e+09 1.37938e+09 1.26818e+09 1.50747e+09 1.4387e+09 1.40149e+09 1.63224e+09 1.53962e+09 1.70862e+09 1.64005e+09 1.48923e+09 1.51734e+09 1.74846e+09 1.92267e+09 1.79729e+09 1.65016e+09 1.76126e+09 1.69357e+09 1.59339e+09 1.67356e+09 1.65456e+09 1.90418e+09 2.06349e+09 1.81155e+09 1.80946e+09 1.75912e+09 1.63383e+09 1.92532e+09 1.64682e+09 1.55932e+09 1.70217e+09 1.69189e+09 1.58013e+09 1.7925e+09 1.77011e+09 1.71592e+09 1.5937e+09 
 5.15752e+07 1.25141e+08 9.34552e+07 1.95818e+08 1.34368e+08 2.27394e+08 2.33326e+08 2.05443e+08 2.84046e+08 1.8601e+08 3.10314e+08 2.48234e+08 3.73316e+08 4.74881e+08 3.8496e+08 5.53018e+08 3.91851e+08 4.78948e+08 5.72504e+08 6.15097e+08 4.84471e+08 5.7531e+08 6.20236e+08 7.86582e+08 8.83631e+08 8.33427e+08 7.6845e+08 8.23053e+08 8.36312e+08 1.05142e+09 1.13112e+09 1.07508e+09 1.03435e+09 7.10941e+08 9.50913e+08 1.07345e+09 1.1871e+09 1.1676e+09 1.1672e+09 1.26005e+09 1.28504e+09 1.29931e+09 1.27233e+09 1.11104e+09 1.14309e+09 1.56988e+09 1.43735e+09 1.30753e+09 1.45766e+09 1.57271e+09 1.40601e+09 1.38693e+09 1.45371e+09 1.21901e+09 1.68322e+09 1.53912e+09 1.61729e+09 1.63022e+09 1.67423e+09 1.66073e+09 1.65014e+09 1.96003e+09 1.68882e+09 1.7433e+09 1.89981e+09 2.1518e+09 1.66764e+09 1.94652e+09 1.90898e+09 2.04166e+09 1.88083e+09 1.87606e+09 1.81338e+09 2.14586e+09 1.90532e+09 1.79054e+09 2.04399e+09 1.90215e+09 2.0283e+09 2.2894e+09 2.15037e+09 2.22648e+09 2.25865e+09 2.31349e+09 2.08724e+09 2.34517e+09 1.79729e+09 3.11862e+09 2.19456e+09 2.57828e+09 2.35084e+09 2.36431e+09 2.34563e+09 2.49181e+09 2.55467e+09 2.79694e+09 2.53025e+09 2.47732e+09 2.46832e+09 2.26512e+09 2.48621e+09 2.53583e+09 2.34622e+09 2.58392e+09 2.4084e+09 2.30726e+09 2.38926e+09 2.36307e+09 2.45782e+09 2.10391e+09 
 3.72576e+07 7.36518e+07 5.07411e+07 1.02438e+08 4.48045e+07 1.06454e+08 1.38943e+08 1.24237e+08 1.76244e+08 1.68824e+08 2.41465e+08 1.8843e+08 2.41957e+08 3.59913e+08 2.86961e+08 5.5195e+08 3.45076e+08 4.25928e+08 3.7742e+08 3.85459e+08 3.55992e+08 4.64608e+08 5.21616e+08 6.06414e+08 7.40584e+08 6.26912e+08 5.50523e+08 6.43057e+08 6.78429e+08 7.61841e+08 7.97909e+08 7.39533e+08 7.14007e+08 6.04751e+08 7.46833e+08 8.51623e+08 9.82614e+08 9.96197e+08 1.00793e+09 1.09412e+09 1.00852e+09 9.62261e+08 1.0615e+09 9.0676e+08 8.72619e+08 1.24437e+09 9.985e+08 1.11924e+09 1.26777e+09 1.26302e+09 1.31329e+09 1.25111e+09 1.31797e+09 1.137e+09 1.5032e+09 1.2601e+09 1.37841e+09 1.25177e+09 1.56142e+09 1.4054e+09 1.32884e+09 1.67268e+09 1.26807e+09 1.32798e+09 1.5713e+09 1.70438e+09 1.43958e+09 1.60707e+09 1.53664e+09 1.70863e+09 1.48623e+09 1.68308e+09 1.61664e+09 1.76435e+09 1.68812e+09 1.46769e+09 1.86763e+09 1.7266e+09 1.73181e+09 1.97333e+09 1.79889e+09 1.98942e+09 1.80092e+09 1.79019e+09 1.83945e+09 1.98646e+09 1.65016e+09 2.19456e+09 2.60251e+09 2.25517e+09 2.08886e+09 1.90406e+09 1.9875e+09 2.1435e+09 2.26403e+09 2.49495e+09 2.08289e+09 2.07374e+09 2.07341e+09 2.04494e+09 2.31756e+09 1.98519e+09 2.05606e+09 2.07094e+09 1.99058e+09 1.97766e+09 2.04959e+09 2.12215e+09 2.16312e+09 1.8182e+09 
 3.18276e+07 1.04692e+08 1.0673e+08 1.78401e+08 9.15549e+07 1.85168e+08 1.77279e+08 2.04104e+08 2.28679e+08 1.68887e+08 2.59871e+08 2.15461e+08 3.4488e+08 3.6038e+08 2.71136e+08 4.4857e+08 3.29312e+08 3.84435e+08 4.72161e+08 5.56109e+08 4.33361e+08 4.61801e+08 4.56668e+08 5.72141e+08 6.14702e+08 5.97593e+08 5.64262e+08 5.84288e+08 5.69004e+08 6.49095e+08 7.37094e+08 6.95103e+08 7.24589e+08 5.14693e+08 6.82582e+08 8.50985e+08 8.22887e+08 9.10246e+08 9.26537e+08 1.09593e+09 9.55415e+08 9.86793e+08 1.01752e+09 8.13576e+08 8.73239e+08 1.30303e+09 1.14058e+09 1.11994e+09 1.10904e+09 1.21627e+09 1.30683e+09 1.16481e+09 1.18408e+09 1.01518e+09 1.54966e+09 1.17856e+09 1.28386e+09 1.35394e+09 1.48488e+09 1.39091e+09 1.35582e+09 1.79565e+09 1.50112e+09 1.60239e+09 1.7231e+09 1.87217e+09 1.5298e+09 1.7671e+09 1.70448e+09 1.72859e+09 1.67169e+09 1.61181e+09 1.77522e+09 1.86662e+09 1.87621e+09 1.90528e+09 1.91507e+09 1.88776e+09 1.84169e+09 2.29045e+09 1.99351e+09 2.12288e+09 2.20784e+09 2.16618e+09 2.0432e+09 2.31895e+09 1.76126e+09 2.57828e+09 2.25517e+09 3.31774e+09 2.46066e+09 2.35776e+09 2.5974e+09 2.4325e+09 2.56375e+09 2.82433e+09 2.55497e+09 2.56601e+09 2.59648e+09 2.30446e+09 2.55492e+09 2.50601e+09 2.38234e+09 2.41915e+09 2.30781e+09 2.37966e+09 2.6268e+09 2.47923e+09 2.60576e+09 2.37613e+09 
 3.69864e+07 8.9502e+07 1.30447e+08 1.92389e+08 1.5207e+08 2.60038e+08 2.03763e+08 2.35908e+08 2.94571e+08 3.02813e+08 4.36465e+08 2.62155e+08 4.22747e+08 5.09372e+08 4.12003e+08 5.96843e+08 3.98159e+08 4.34267e+08 4.4784e+08 5.7542e+08 4.60592e+08 5.75763e+08 5.47192e+08 6.26477e+08 7.65168e+08 7.11068e+08 6.20149e+08 7.47868e+08 6.52069e+08 7.86724e+08 8.93142e+08 8.62279e+08 7.88511e+08 5.91428e+08 6.75161e+08 8.9393e+08 9.03895e+08 9.75603e+08 9.17828e+08 9.42132e+08 9.71773e+08 1.0687e+09 1.04071e+09 8.55795e+08 9.00863e+08 1.19624e+09 1.02535e+09 1.08578e+09 1.23927e+09 1.19452e+09 1.3344e+09 1.11025e+09 1.28795e+09 1.12497e+09 1.35885e+09 1.21383e+09 1.27746e+09 1.31877e+09 1.5096e+09 1.30649e+09 1.50229e+09 1.79023e+09 1.51848e+09 1.57697e+09 1.66627e+09 1.76436e+09 1.51125e+09 1.71579e+09 1.67415e+09 1.72069e+09 1.66558e+09 1.66458e+09 1.78322e+09 1.78215e+09 1.78765e+09 1.51291e+09 1.99858e+09 1.83285e+09 1.86683e+09 2.19017e+09 2.00815e+09 2.00788e+09 2.04904e+09 2.13453e+09 1.94963e+09 2.13112e+09 1.69357e+09 2.35084e+09 2.08886e+09 2.46066e+09 3.05304e+09 2.15331e+09 2.21108e+09 2.30194e+09 2.39082e+09 2.70031e+09 2.33984e+09 2.43633e+09 2.30555e+09 2.43463e+09 2.39811e+09 2.38931e+09 2.36307e+09 2.34252e+09 2.27222e+09 2.08938e+09 2.45668e+09 2.45545e+09 2.66649e+09 2.4083e+09 
 5.39957e+07 1.30691e+08 7.831e+07 1.81439e+08 1.27289e+08 2.20856e+08 2.14463e+08 1.7713e+08 2.44484e+08 1.81401e+08 2.82335e+08 2.1802e+08 3.20015e+08 4.36567e+08 3.55952e+08 4.54622e+08 2.7979e+08 3.31129e+08 4.52346e+08 4.15791e+08 3.98343e+08 3.85381e+08 4.51765e+08 5.35609e+08 6.35696e+08 6.26281e+08 5.04641e+08 5.76391e+08 5.81647e+08 7.91748e+08 7.76457e+08 8.14358e+08 7.27018e+08 5.36494e+08 5.69028e+08 7.98199e+08 8.90253e+08 8.34229e+08 8.35219e+08 8.67205e+08 8.53365e+08 1.04239e+09 9.01345e+08 7.37238e+08 7.54955e+08 1.19555e+09 1.03151e+09 9.88465e+08 1.02289e+09 1.15422e+09 1.23703e+09 1.03713e+09 1.16176e+09 1.05978e+09 1.33737e+09 1.13759e+09 1.29304e+09 1.18486e+09 1.38475e+09 1.27303e+09 1.29824e+09 1.56293e+09 1.51987e+09 1.37181e+09 1.51791e+09 1.72677e+09 1.42707e+09 1.59862e+09 1.42149e+09 1.78008e+09 1.48851e+09 1.52949e+09 1.57944e+09 1.8032e+09 1.59612e+09 1.63736e+09 1.85534e+09 1.71353e+09 1.85986e+09 2.10125e+09 1.93483e+09 1.9252e+09 2.0348e+09 2.1841e+09 1.88327e+09 1.99401e+09 1.59339e+09 2.36431e+09 1.90406e+09 2.35776e+09 2.15331e+09 2.8663e+09 2.31563e+09 2.17265e+09 2.27001e+09 2.40355e+09 2.13686e+09 2.35983e+09 2.32292e+09 2.10519e+09 2.19126e+09 2.13483e+09 2.24819e+09 2.36057e+09 2.14839e+09 1.92558e+09 2.27693e+09 2.09842e+09 2.32467e+09 2.04366e+09 
 4.5206e+07 8.91189e+07 9.65588e+07 1.60803e+08 1.23063e+08 2.30759e+08 1.8248e+08 1.68612e+08 2.16234e+08 2.20998e+08 2.73099e+08 1.84646e+08 3.0035e+08 3.89455e+08 2.84399e+08 4.32833e+08 2.98472e+08 3.40107e+08 4.15694e+08 5.01651e+08 3.3777e+08 4.57936e+08 4.29047e+08 5.74033e+08 6.3097e+08 6.32399e+08 4.86371e+08 4.95321e+08 6.44613e+08 6.67256e+08 7.18071e+08 8.3054e+08 7.44669e+08 5.23812e+08 5.84016e+08 7.43418e+08 9.15893e+08 8.41609e+08 7.96769e+08 9.18125e+08 8.87395e+08 1.0875e+09 1.0746e+09 7.49913e+08 9.60164e+08 1.26784e+09 1.17579e+09 1.08359e+09 1.04296e+09 1.22362e+09 1.35238e+09 1.21963e+09 1.26559e+09 1.12478e+09 1.48992e+09 1.2422e+09 1.35792e+09 1.30846e+09 1.4525e+09 1.32572e+09 1.43515e+09 1.62601e+09 1.49043e+09 1.49095e+09 1.6142e+09 1.79821e+09 1.46836e+09 1.84614e+09 1.59723e+09 1.69274e+09 1.66713e+09 1.4583e+09 1.6647e+09 1.86868e+09 1.71317e+09 1.65675e+09 1.7934e+09 1.6521e+09 1.84305e+09 2.14904e+09 1.84056e+09 1.99538e+09 2.07938e+09 2.12114e+09 1.94574e+09 2.09318e+09 1.67356e+09 2.34563e+09 1.9875e+09 2.5974e+09 2.21108e+09 2.31563e+09 3.22158e+09 2.21052e+09 2.45608e+09 2.6826e+09 2.43883e+09 2.38043e+09 2.50539e+09 2.39027e+09 2.37392e+09 2.41307e+09 2.1798e+09 2.16863e+09 2.21463e+09 2.17916e+09 2.51986e+09 2.51154e+09 2.29408e+09 2.32418e+09 
 2.54128e+07 9.82496e+07 1.19636e+08 2.04488e+08 1.10754e+08 1.67391e+08 2.04398e+08 2.01367e+08 2.17097e+08 1.91971e+08 2.72461e+08 2.35079e+08 3.34515e+08 3.9207e+08 4.30744e+08 5.1991e+08 3.30876e+08 3.83561e+08 4.99675e+08 5.28112e+08 4.35134e+08 4.40155e+08 5.54081e+08 6.61597e+08 8.00297e+08 7.79873e+08 5.97765e+08 6.97732e+08 7.66742e+08 8.6962e+08 9.35395e+08 9.65906e+08 9.18436e+08 6.77614e+08 8.21767e+08 9.69308e+08 1.0367e+09 9.85469e+08 1.04813e+09 1.05939e+09 1.1232e+09 1.18044e+09 1.10826e+09 8.91009e+08 9.65398e+08 1.29948e+09 1.21897e+09 1.16871e+09 1.36337e+09 1.22931e+09 1.53446e+09 1.25528e+09 1.36207e+09 1.09997e+09 1.59622e+09 1.31743e+09 1.48236e+09 1.42244e+09 1.49734e+09 1.61512e+09 1.55733e+09 1.80066e+09 1.58281e+09 1.5298e+09 1.6366e+09 1.8934e+09 1.61378e+09 1.89379e+09 1.78941e+09 1.90331e+09 1.79229e+09 1.88513e+09 1.74373e+09 1.81147e+09 1.77791e+09 1.71583e+09 1.93618e+09 1.82168e+09 1.83397e+09 2.27724e+09 1.98834e+09 2.13864e+09 2.15378e+09 2.09646e+09 1.96932e+09 2.20721e+09 1.65456e+09 2.49181e+09 2.1435e+09 2.4325e+09 2.30194e+09 2.17265e+09 2.21052e+09 3.09725e+09 2.68888e+09 2.92882e+09 2.38457e+09 2.35148e+09 2.45952e+09 2.4364e+09 2.52282e+09 2.50646e+09 2.65253e+09 2.51751e+09 2.42427e+09 2.30305e+09 2.45833e+09 2.60107e+09 2.53272e+09 2.32037e+09 
 5.77853e+07 1.22138e+08 1.05939e+08 2.12399e+08 1.32748e+08 2.19076e+08 2.70837e+08 2.13749e+08 2.85837e+08 2.37286e+08 3.0784e+08 2.72523e+08 3.41892e+08 4.87834e+08 4.19789e+08 5.89327e+08 3.75735e+08 4.50208e+08 6.11019e+08 5.31294e+08 4.51916e+08 4.98369e+08 5.85768e+08 7.68896e+08 6.9268e+08 7.31834e+08 6.17507e+08 6.83653e+08 7.56804e+08 9.49616e+08 9.73918e+08 9.1645e+08 9.69561e+08 6.5357e+08 8.45685e+08 9.82992e+08 1.12926e+09 1.04678e+09 1.12101e+09 1.20293e+09 1.08746e+09 1.18432e+09 1.22237e+09 1.09032e+09 9.67162e+08 1.43781e+09 1.25026e+09 1.28057e+09 1.36147e+09 1.38803e+09 1.41625e+09 1.45715e+09 1.46506e+09 1.16664e+09 1.65316e+09 1.38975e+09 1.56608e+09 1.55596e+09 1.83334e+09 1.63923e+09 1.64965e+09 1.9547e+09 1.66596e+09 1.68564e+09 1.80923e+09 2.03431e+09 1.68563e+09 2.14228e+09 1.8487e+09 2.03117e+09 2.02322e+09 2.03557e+09 1.92196e+09 2.12563e+09 2.02417e+09 1.81987e+09 2.086e+09 1.75791e+09 1.92417e+09 2.38068e+09 1.93817e+09 2.18838e+09 2.06901e+09 2.15742e+09 2.08835e+09 2.22135e+09 1.90418e+09 2.55467e+09 2.26403e+09 2.56375e+09 2.39082e+09 2.27001e+09 2.45608e+09 2.68888e+09 3.52073e+09 2.94532e+09 2.58845e+09 2.69896e+09 2.5982e+09 2.56334e+09 2.74216e+09 2.68059e+09 2.55214e+09 2.69081e+09 2.51773e+09 2.42262e+09 2.6336e+09 2.77378e+09 2.62083e+09 2.50916e+09 
 1.26577e+07 3.11696e+07 1.04222e+08 1.49084e+08 1.29664e+08 1.99571e+08 2.7279e+08 2.05568e+08 3.00173e+08 2.60285e+08 3.50006e+08 3.29339e+08 3.91554e+08 5.05423e+08 4.26006e+08 5.7927e+08 4.12003e+08 4.55243e+08 4.8107e+08 6.07427e+08 4.50756e+08 5.54588e+08 6.29422e+08 6.83304e+08 7.17746e+08 7.58756e+08 6.78678e+08 6.97725e+08 7.09461e+08 8.67246e+08 9.31676e+08 9.78053e+08 9.91185e+08 6.99931e+08 8.32968e+08 1.02228e+09 1.19367e+09 1.16986e+09 1.15693e+09 1.24622e+09 1.23402e+09 1.21475e+09 1.22167e+09 1.0128e+09 1.09247e+09 1.51897e+09 1.42261e+09 1.3741e+09 1.52164e+09 1.50928e+09 1.56084e+09 1.45257e+09 1.62939e+09 1.36251e+09 1.77063e+09 1.51868e+09 1.50523e+09 1.48232e+09 1.74868e+09 1.67677e+09 1.71242e+09 1.94147e+09 1.65477e+09 1.68144e+09 1.88643e+09 1.83406e+09 1.75267e+09 1.9974e+09 2.01613e+09 2.0032e+09 1.98391e+09 1.86939e+09 1.88376e+09 2.17349e+09 1.99789e+09 1.93464e+09 2.10143e+09 2.19232e+09 2.06487e+09 2.53809e+09 2.28272e+09 2.28655e+09 2.25685e+09 2.3223e+09 2.2922e+09 2.5604e+09 2.06349e+09 2.79694e+09 2.49495e+09 2.82433e+09 2.70031e+09 2.40355e+09 2.6826e+09 2.92882e+09 2.94532e+09 3.99708e+09 2.85919e+09 2.88485e+09 2.81483e+09 2.73338e+09 2.87663e+09 2.83487e+09 2.78918e+09 2.91828e+09 2.73537e+09 2.62199e+09 2.7875e+09 3.02117e+09 2.80176e+09 2.62588e+09 
 1.5057e+07 6.64854e+07 1.1316e+08 1.77498e+08 1.36412e+08 2.03482e+08 2.68188e+08 2.33612e+08 2.72215e+08 2.08616e+08 2.72901e+08 2.96058e+08 3.48391e+08 4.15866e+08 3.31983e+08 4.35356e+08 3.34045e+08 3.739e+08 4.113e+08 5.37025e+08 4.22535e+08 6.03336e+08 6.01227e+08 6.5925e+08 7.21664e+08 8.69524e+08 6.5463e+08 6.86305e+08 7.66974e+08 8.87088e+08 9.64146e+08 8.76662e+08 9.52685e+08 6.73803e+08 8.73588e+08 1.07571e+09 1.20567e+09 1.28521e+09 1.22411e+09 1.29796e+09 1.1444e+09 1.1921e+09 1.28515e+09 1.03984e+09 1.09597e+09 1.59378e+09 1.4605e+09 1.40192e+09 1.35792e+09 1.5452e+09 1.54873e+09 1.51563e+09 1.57046e+09 1.30772e+09 1.86013e+09 1.45125e+09 1.5617e+09 1.58508e+09 1.77912e+09 1.60125e+09 1.80586e+09 2.09038e+09 1.53205e+09 1.81052e+09 1.92765e+09 1.99669e+09 1.65674e+09 1.96254e+09 1.92995e+09 1.9344e+09 1.91515e+09 1.78618e+09 1.76188e+09 2.2041e+09 1.90649e+09 1.78709e+09 2.0382e+09 1.79004e+09 1.90604e+09 2.2647e+09 2.00866e+09 2.06527e+09 2.16765e+09 2.28568e+09 2.12623e+09 2.19094e+09 1.81155e+09 2.53025e+09 2.08289e+09 2.55497e+09 2.33984e+09 2.13686e+09 2.43883e+09 2.38457e+09 2.58845e+09 2.85919e+09 3.28515e+09 2.60326e+09 2.56793e+09 2.38896e+09 2.58676e+09 2.55317e+09 2.4827e+09 2.63864e+09 2.50222e+09 2.41215e+09 2.63328e+09 2.6341e+09 2.61449e+09 2.33642e+09 
 4.87416e+06 1.66191e+07 7.20484e+07 9.30715e+07 5.72146e+07 1.04529e+08 1.29276e+08 1.20715e+08 1.81713e+08 1.95898e+08 2.82508e+08 1.95577e+08 3.03551e+08 3.35217e+08 3.32598e+08 4.05813e+08 2.85715e+08 2.94463e+08 3.59433e+08 5.34171e+08 3.50365e+08 3.7383e+08 4.13761e+08 4.51134e+08 5.67035e+08 5.96278e+08 5.12958e+08 5.72934e+08 6.4855e+08 6.6359e+08 7.08757e+08 8.11541e+08 8.86679e+08 6.16656e+08 6.56449e+08 8.59128e+08 9.17201e+08 9.40061e+08 9.80578e+08 1.02616e+09 1.01845e+09 9.85191e+08 9.85248e+08 9.45932e+08 9.06386e+08 1.2097e+09 1.18713e+09 1.25131e+09 1.16798e+09 1.21197e+09 1.2222e+09 1.26379e+09 1.2319e+09 1.0638e+09 1.42847e+09 1.03408e+09 1.03009e+09 1.28749e+09 1.47871e+09 1.4375e+09 1.35687e+09 1.69122e+09 1.4614e+09 1.54306e+09 1.58677e+09 1.68325e+09 1.42051e+09 1.7753e+09 1.72074e+09 1.73352e+09 1.90448e+09 1.59429e+09 1.56319e+09 1.87948e+09 1.73175e+09 1.67199e+09 1.98934e+09 1.90968e+09 1.97201e+09 2.17364e+09 2.05655e+09 2.17047e+09 2.01291e+09 2.1843e+09 2.08002e+09 2.24946e+09 1.80946e+09 2.47732e+09 2.07374e+09 2.56601e+09 2.43633e+09 2.35983e+09 2.38043e+09 2.35148e+09 2.69896e+09 2.88485e+09 2.60326e+09 3.45796e+09 2.62906e+09 2.29123e+09 2.4265e+09 2.4518e+09 2.4453e+09 2.63556e+09 2.586e+09 2.28992e+09 2.51675e+09 2.68825e+09 2.66754e+09 2.44197e+09 
 3.6925e+07 9.9839e+07 1.10174e+08 1.943e+08 1.158e+08 2.1153e+08 2.65791e+08 2.04443e+08 3.00529e+08 2.05464e+08 2.87249e+08 2.95062e+08 3.70813e+08 4.21741e+08 3.68033e+08 4.61791e+08 3.36276e+08 4.0722e+08 4.4807e+08 5.14365e+08 3.92669e+08 4.93277e+08 5.04469e+08 5.33368e+08 7.19339e+08 6.69199e+08 6.27711e+08 5.4759e+08 6.29092e+08 8.08866e+08 8.6705e+08 7.84259e+08 7.7908e+08 5.64748e+08 6.32708e+08 7.499e+08 8.77773e+08 9.17762e+08 8.53836e+08 1.0304e+09 8.54772e+08 1.02396e+09 9.62652e+08 8.34884e+08 9.26611e+08 1.18648e+09 1.11857e+09 1.09798e+09 1.14432e+09 1.18652e+09 1.36902e+09 1.17445e+09 1.28081e+09 1.17804e+09 1.47623e+09 1.21726e+09 1.31333e+09 1.45852e+09 1.40677e+09 1.37276e+09 1.45633e+09 1.77268e+09 1.61161e+09 1.60647e+09 1.59667e+09 1.83111e+09 1.52754e+09 1.86487e+09 1.69493e+09 1.93321e+09 1.73468e+09 1.76068e+09 1.65082e+09 1.92315e+09 1.67898e+09 1.71784e+09 1.95062e+09 1.75539e+09 1.76015e+09 2.17393e+09 2.03381e+09 2.01965e+09 2.14091e+09 2.12271e+09 2.15379e+09 2.15679e+09 1.75912e+09 2.46832e+09 2.07341e+09 2.59648e+09 2.30555e+09 2.32292e+09 2.50539e+09 2.45952e+09 2.5982e+09 2.81483e+09 2.56793e+09 2.62906e+09 3.4654e+09 2.45678e+09 2.5373e+09 2.40523e+09 2.57217e+09 2.49891e+09 2.43084e+09 2.45856e+09 2.54102e+09 2.60456e+09 2.61657e+09 2.52736e+09 
 3.18762e+07 5.76837e+07 9.00479e+07 1.31576e+08 1.1972e+08 1.86031e+08 1.45197e+08 1.52103e+08 2.02956e+08 2.561e+08 3.24477e+08 1.70825e+08 2.94817e+08 3.58519e+08 3.5889e+08 4.90777e+08 3.03261e+08 3.83757e+08 4.09114e+08 4.8065e+08 3.9601e+08 5.99542e+08 5.79215e+08 6.8732e+08 8.23213e+08 7.59369e+08 6.10111e+08 6.89991e+08 7.91206e+08 9.10499e+08 9.82551e+08 9.83914e+08 8.63967e+08 6.40194e+08 8.65702e+08 9.72266e+08 1.02266e+09 1.0802e+09 9.87017e+08 1.05551e+09 1.0247e+09 1.14557e+09 1.2367e+09 9.54085e+08 1.0481e+09 1.29913e+09 1.21581e+09 1.21194e+09 1.19602e+09 1.41059e+09 1.50425e+09 1.41405e+09 1.37278e+09 1.29557e+09 1.61506e+09 1.34239e+09 1.62159e+09 1.52006e+09 1.65982e+09 1.50526e+09 1.63561e+09 1.84037e+09 1.6015e+09 1.60953e+09 1.63452e+09 1.86754e+09 1.67642e+09 1.96026e+09 1.74699e+09 1.93696e+09 1.64853e+09 1.86511e+09 1.69861e+09 1.90737e+09 1.75675e+09 1.57056e+09 1.91944e+09 1.73643e+09 1.84789e+09 2.19598e+09 1.89507e+09 1.99191e+09 1.97714e+09 2.07006e+09 1.95865e+09 2.01774e+09 1.63383e+09 2.26512e+09 2.04494e+09 2.30446e+09 2.43463e+09 2.10519e+09 2.39027e+09 2.4364e+09 2.56334e+09 2.73338e+09 2.38896e+09 2.29123e+09 2.45678e+09 3.17501e+09 2.54401e+09 2.46819e+09 2.54461e+09 2.56072e+09 2.3312e+09 2.37657e+09 2.65832e+09 2.71259e+09 2.6799e+09 2.39406e+09 
 4.16439e+07 6.21014e+07 9.94969e+07 1.48663e+08 1.00128e+08 1.87366e+08 1.80518e+08 1.75185e+08 2.03705e+08 2.06485e+08 2.82515e+08 2.2841e+08 2.85093e+08 4.12558e+08 2.87433e+08 5.04073e+08 3.14109e+08 3.6965e+08 3.50038e+08 4.48087e+08 3.80901e+08 4.84402e+08 5.43392e+08 6.24292e+08 6.92032e+08 6.58505e+08 5.75402e+08 6.92389e+08 7.73734e+08 8.53441e+08 8.39846e+08 8.27518e+08 8.65543e+08 7.21536e+08 8.29751e+08 9.53264e+08 9.98263e+08 1.05872e+09 1.17065e+09 1.13103e+09 9.94191e+08 1.108e+09 1.20963e+09 9.56554e+08 1.05035e+09 1.43313e+09 1.18985e+09 1.29494e+09 1.33686e+09 1.48316e+09 1.46629e+09 1.39994e+09 1.56393e+09 1.40786e+09 1.89511e+09 1.46559e+09 1.698e+09 1.56816e+09 1.86231e+09 1.57869e+09 1.86852e+09 2.08033e+09 1.6984e+09 1.63734e+09 1.84391e+09 2.02849e+09 1.8087e+09 2.04493e+09 1.87604e+09 2.14533e+09 1.67231e+09 1.92889e+09 1.83152e+09 2.268e+09 1.89462e+09 1.84445e+09 2.25826e+09 1.94267e+09 2.00125e+09 2.18736e+09 2.01809e+09 2.25972e+09 2.18427e+09 2.21e+09 2.15631e+09 2.27276e+09 1.92532e+09 2.48621e+09 2.31756e+09 2.55492e+09 2.39811e+09 2.19126e+09 2.37392e+09 2.52282e+09 2.74216e+09 2.87663e+09 2.58676e+09 2.4265e+09 2.5373e+09 2.54401e+09 3.39029e+09 2.35596e+09 2.50438e+09 2.61085e+09 2.41679e+09 2.57197e+09 2.61937e+09 2.71956e+09 2.62711e+09 2.31638e+09 
 4.26307e+07 9.41465e+07 1.39402e+08 2.17482e+08 1.35666e+08 2.14646e+08 1.90883e+08 2.21845e+08 2.45374e+08 2.58302e+08 3.60392e+08 2.21799e+08 3.38885e+08 3.81178e+08 3.41197e+08 4.27629e+08 3.41739e+08 3.51208e+08 4.57718e+08 5.50349e+08 4.38867e+08 4.96228e+08 4.95072e+08 6.55315e+08 7.17075e+08 7.31149e+08 7.02894e+08 6.97802e+08 7.07284e+08 7.7158e+08 9.86698e+08 8.74868e+08 8.16507e+08 5.77849e+08 7.22236e+08 9.47087e+08 9.3042e+08 9.74417e+08 9.20068e+08 1.07701e+09 1.02528e+09 1.15063e+09 1.20611e+09 9.37845e+08 9.40491e+08 1.38052e+09 1.20644e+09 1.15548e+09 1.20862e+09 1.30343e+09 1.46024e+09 1.30808e+09 1.35532e+09 1.09635e+09 1.55229e+09 1.355e+09 1.36634e+09 1.42992e+09 1.54729e+09 1.47731e+09 1.55132e+09 1.76074e+09 1.5416e+09 1.5947e+09 1.62509e+09 1.8522e+09 1.53509e+09 1.91644e+09 1.68335e+09 1.75264e+09 1.69559e+09 1.76063e+09 1.72167e+09 1.83502e+09 1.9116e+09 1.67927e+09 1.78813e+09 1.72756e+09 1.87096e+09 2.3342e+09 1.92525e+09 1.93403e+09 2.16853e+09 2.17725e+09 2.02083e+09 2.21806e+09 1.64682e+09 2.53583e+09 1.98519e+09 2.50601e+09 2.38931e+09 2.13483e+09 2.41307e+09 2.50646e+09 2.68059e+09 2.83487e+09 2.55317e+09 2.4518e+09 2.40523e+09 2.46819e+09 2.35596e+09 3.25525e+09 2.51e+09 2.65023e+09 2.48549e+09 2.32721e+09 2.67586e+09 2.54665e+09 2.59407e+09 2.46015e+09 
 2.21118e+07 8.96806e+07 1.29527e+08 2.11367e+08 1.77091e+08 2.40874e+08 2.28201e+08 2.36876e+08 2.89147e+08 3.21845e+08 4.3618e+08 2.47689e+08 4.20801e+08 4.85773e+08 4.91645e+08 6.1569e+08 3.73077e+08 4.68484e+08 5.56984e+08 6.35053e+08 5.24234e+08 6.32723e+08 6.58798e+08 8.1705e+08 8.50407e+08 8.6062e+08 6.78876e+08 8.12637e+08 8.11122e+08 9.54915e+08 1.05527e+09 1.0528e+09 9.43226e+08 7.26985e+08 8.41537e+08 1.03671e+09 1.06051e+09 1.08888e+09 1.01136e+09 1.03529e+09 1.04712e+09 1.21153e+09 1.10503e+09 9.59748e+08 1.00146e+09 1.38008e+09 1.19602e+09 1.17209e+09 1.31854e+09 1.17849e+09 1.49375e+09 1.23932e+09 1.32161e+09 1.24882e+09 1.54803e+09 1.28283e+09 1.39732e+09 1.53543e+09 1.51009e+09 1.53217e+09 1.52441e+09 1.81091e+09 1.587e+09 1.5733e+09 1.73857e+09 1.93499e+09 1.59778e+09 1.82267e+09 1.63628e+09 1.88958e+09 1.68724e+09 1.66235e+09 1.72408e+09 1.86086e+09 1.75652e+09 1.56788e+09 1.83726e+09 1.79199e+09 1.86269e+09 2.30975e+09 2.00844e+09 1.98639e+09 1.97203e+09 2.19712e+09 1.87797e+09 2.094e+09 1.55932e+09 2.34622e+09 2.05606e+09 2.38234e+09 2.36307e+09 2.24819e+09 2.1798e+09 2.65253e+09 2.55214e+09 2.78918e+09 2.4827e+09 2.4453e+09 2.57217e+09 2.54461e+09 2.50438e+09 2.51e+09 3.37789e+09 2.78422e+09 2.63461e+09 2.47764e+09 2.75382e+09 2.72456e+09 2.94287e+09 2.42267e+09 
 2.00243e+07 8.7022e+07 6.32817e+07 1.40928e+08 1.26415e+08 1.75299e+08 2.33165e+08 1.77989e+08 2.79461e+08 2.374e+08 3.07576e+08 2.28956e+08 3.83898e+08 4.43795e+08 4.66343e+08 5.96912e+08 3.91946e+08 4.49473e+08 5.49573e+08 5.92269e+08 5.05795e+08 6.45116e+08 6.88975e+08 8.28711e+08 8.07803e+08 7.75118e+08 7.11013e+08 8.27182e+08 8.32939e+08 1.06144e+09 1.12293e+09 1.0409e+09 1.01174e+09 7.25045e+08 1.0193e+09 1.12977e+09 1.21399e+09 1.30296e+09 1.23295e+09 1.30286e+09 1.29317e+09 1.22239e+09 1.34727e+09 1.18546e+09 1.04156e+09 1.50694e+09 1.41167e+09 1.40052e+09 1.45097e+09 1.40036e+09 1.51207e+09 1.44961e+09 1.54431e+09 1.37282e+09 1.76125e+09 1.47806e+09 1.64302e+09 1.6646e+09 1.8833e+09 1.70876e+09 1.62669e+09 1.96545e+09 1.71644e+09 1.76522e+09 1.99737e+09 2.02417e+09 1.78578e+09 1.86511e+09 1.83654e+09 2.10378e+09 1.89056e+09 1.92991e+09 1.75205e+09 2.13272e+09 1.95026e+09 1.78612e+09 2.09402e+09 1.97342e+09 1.98269e+09 2.38455e+09 2.20355e+09 2.06684e+09 2.12385e+09 2.13437e+09 2.11298e+09 2.17515e+09 1.70217e+09 2.58392e+09 2.07094e+09 2.41915e+09 2.34252e+09 2.36057e+09 2.16863e+09 2.51751e+09 2.69081e+09 2.91828e+09 2.63864e+09 2.63556e+09 2.49891e+09 2.56072e+09 2.61085e+09 2.65023e+09 2.78422e+09 3.74632e+09 2.6203e+09 2.5294e+09 2.88286e+09 2.74512e+09 3.00005e+09 2.58441e+09 
 4.99341e+07 1.16801e+08 1.1243e+08 2.06124e+08 1.05859e+08 1.78081e+08 1.73992e+08 2.04436e+08 2.48621e+08 1.61138e+08 3.06969e+08 2.13556e+08 3.6223e+08 4.20623e+08 3.9156e+08 5.10596e+08 3.20514e+08 4.21422e+08 4.39336e+08 5.79855e+08 4.73838e+08 5.27927e+08 5.74433e+08 6.48182e+08 8.58066e+08 7.15252e+08 6.8818e+08 7.61424e+08 7.31294e+08 8.46815e+08 8.87177e+08 8.9397e+08 9.07047e+08 6.43986e+08 8.01165e+08 9.08207e+08 1.07822e+09 1.10072e+09 1.08906e+09 1.03269e+09 1.09159e+09 1.15362e+09 1.07137e+09 1.04778e+09 9.95244e+08 1.26446e+09 1.17334e+09 1.15597e+09 1.1682e+09 1.21408e+09 1.28393e+09 1.18727e+09 1.25179e+09 1.12152e+09 1.42811e+09 1.16883e+09 1.1558e+09 1.39334e+09 1.41493e+09 1.48149e+09 1.46488e+09 1.72737e+09 1.51683e+09 1.45223e+09 1.62383e+09 1.80358e+09 1.39772e+09 1.64635e+09 1.50793e+09 1.71133e+09 1.61206e+09 1.69332e+09 1.68757e+09 1.72115e+09 1.72725e+09 1.61419e+09 1.82561e+09 1.74452e+09 1.94725e+09 2.20479e+09 1.93555e+09 2.1225e+09 2.03565e+09 2.09295e+09 1.88455e+09 2.1892e+09 1.69189e+09 2.4084e+09 1.99058e+09 2.30781e+09 2.27222e+09 2.14839e+09 2.21463e+09 2.42427e+09 2.51773e+09 2.73537e+09 2.50222e+09 2.586e+09 2.43084e+09 2.3312e+09 2.41679e+09 2.48549e+09 2.63461e+09 2.6203e+09 3.28378e+09 2.38417e+09 2.74542e+09 2.67269e+09 2.8437e+09 2.31764e+09 
 8.14685e+06 5.09095e+07 5.39018e+07 9.01821e+07 5.48655e+07 8.86432e+07 1.3102e+08 1.36521e+08 1.60254e+08 1.15534e+08 1.60772e+08 1.57175e+08 2.08047e+08 2.5257e+08 2.06316e+08 3.54248e+08 2.72142e+08 2.96579e+08 2.97434e+08 3.69607e+08 2.74719e+08 3.63146e+08 3.74816e+08 4.57144e+08 5.45115e+08 5.55895e+08 4.0002e+08 4.26989e+08 5.55797e+08 5.6495e+08 6.41688e+08 7.29509e+08 6.76919e+08 5.04239e+08 6.17498e+08 7.4211e+08 8.37187e+08 9.17966e+08 8.84945e+08 9.45893e+08 7.97906e+08 8.67617e+08 1.03206e+09 7.64739e+08 8.34622e+08 1.21807e+09 1.09615e+09 1.13877e+09 1.14839e+09 1.15019e+09 1.20559e+09 1.23792e+09 1.1476e+09 1.05726e+09 1.44746e+09 1.26223e+09 1.39007e+09 1.3565e+09 1.43108e+09 1.40441e+09 1.5701e+09 1.68174e+09 1.49674e+09 1.518e+09 1.59923e+09 1.82817e+09 1.37357e+09 1.69323e+09 1.61836e+09 1.66384e+09 1.53865e+09 1.64513e+09 1.57355e+09 1.88737e+09 1.52599e+09 1.52749e+09 1.701e+09 1.59412e+09 1.68613e+09 1.79336e+09 1.49704e+09 1.71439e+09 1.81401e+09 1.83176e+09 1.72273e+09 1.93616e+09 1.58013e+09 2.30726e+09 1.97766e+09 2.37966e+09 2.08938e+09 1.92558e+09 2.17916e+09 2.30305e+09 2.42262e+09 2.62199e+09 2.41215e+09 2.28992e+09 2.45856e+09 2.37657e+09 2.57197e+09 2.32721e+09 2.47764e+09 2.5294e+09 2.38417e+09 3.26999e+09 2.54661e+09 2.65043e+09 2.70759e+09 2.33733e+09 
 4.72854e+07 1.1984e+08 1.13687e+08 2.04452e+08 1.46796e+08 2.55267e+08 2.75388e+08 2.57498e+08 3.53978e+08 3.15384e+08 4.14038e+08 2.97429e+08 4.51811e+08 5.23405e+08 4.04969e+08 5.88061e+08 4.05074e+08 4.61273e+08 4.88094e+08 5.78365e+08 4.66153e+08 6.03825e+08 6.04771e+08 7.18283e+08 8.05147e+08 7.95012e+08 8.02388e+08 7.59991e+08 7.82437e+08 8.84231e+08 9.68487e+08 9.21355e+08 8.34755e+08 6.59762e+08 8.51924e+08 9.81371e+08 1.11744e+09 1.15556e+09 1.0138e+09 1.12417e+09 1.09576e+09 1.28447e+09 1.28962e+09 1.08194e+09 1.16049e+09 1.4449e+09 1.32378e+09 1.4055e+09 1.27322e+09 1.31369e+09 1.46766e+09 1.42139e+09 1.51635e+09 1.20915e+09 1.6983e+09 1.36721e+09 1.4855e+09 1.50738e+09 1.65574e+09 1.76479e+09 1.71161e+09 1.99909e+09 1.58021e+09 1.72999e+09 1.85726e+09 1.99003e+09 1.68186e+09 1.92065e+09 1.73791e+09 1.8397e+09 1.6912e+09 1.84618e+09 1.89277e+09 1.92856e+09 1.9874e+09 1.751e+09 2.02003e+09 1.8876e+09 1.83944e+09 2.3838e+09 2.00902e+09 2.04339e+09 2.16972e+09 2.17653e+09 2.06239e+09 2.29728e+09 1.7925e+09 2.38926e+09 2.04959e+09 2.6268e+09 2.45668e+09 2.27693e+09 2.51986e+09 2.45833e+09 2.6336e+09 2.7875e+09 2.63328e+09 2.51675e+09 2.54102e+09 2.65832e+09 2.61937e+09 2.67586e+09 2.75382e+09 2.88286e+09 2.74542e+09 2.54661e+09 3.82345e+09 2.90056e+09 3.23721e+09 2.64607e+09 
 1.62253e+07 3.34307e+07 1.07666e+08 1.31839e+08 1.17093e+08 1.7756e+08 1.73368e+08 1.96123e+08 2.59903e+08 2.88456e+08 3.69276e+08 2.25402e+08 3.75377e+08 4.30305e+08 4.18537e+08 5.74044e+08 3.67675e+08 3.992e+08 4.20803e+08 5.87019e+08 4.3223e+08 5.65127e+08 5.55869e+08 6.71295e+08 7.24054e+08 7.35559e+08 6.33427e+08 7.2545e+08 7.2447e+08 8.63027e+08 9.05895e+08 9.24899e+08 8.75772e+08 6.03745e+08 7.84836e+08 9.71113e+08 1.08556e+09 1.07961e+09 1.17332e+09 1.06835e+09 1.09167e+09 1.01072e+09 1.22699e+09 1.03886e+09 1.03307e+09 1.35905e+09 1.18257e+09 1.29477e+09 1.36658e+09 1.34227e+09 1.40618e+09 1.35756e+09 1.50515e+09 1.24757e+09 1.63567e+09 1.32747e+09 1.44011e+09 1.46688e+09 1.63353e+09 1.60154e+09 1.5781e+09 2.01884e+09 1.70884e+09 1.61434e+09 1.72596e+09 1.96041e+09 1.71304e+09 2.05295e+09 1.847e+09 1.92157e+09 1.93691e+09 1.77292e+09 1.85561e+09 2.07421e+09 1.85533e+09 1.68928e+09 1.9958e+09 1.88409e+09 1.90748e+09 2.3552e+09 2.05101e+09 2.10263e+09 2.06174e+09 2.21429e+09 1.9455e+09 2.20255e+09 1.77011e+09 2.36307e+09 2.12215e+09 2.47923e+09 2.45545e+09 2.09842e+09 2.51154e+09 2.60107e+09 2.77378e+09 3.02117e+09 2.6341e+09 2.68825e+09 2.60456e+09 2.71259e+09 2.71956e+09 2.54665e+09 2.72456e+09 2.74512e+09 2.67269e+09 2.65043e+09 2.90056e+09 3.69759e+09 2.98514e+09 2.73452e+09 
 1.38955e+07 6.86562e+07 1.30076e+08 1.79844e+08 1.59789e+08 2.43526e+08 2.40836e+08 2.58526e+08 3.22493e+08 3.39684e+08 4.45452e+08 2.9879e+08 4.78659e+08 5.17372e+08 4.82575e+08 6.63625e+08 4.68869e+08 5.19935e+08 5.18994e+08 6.48673e+08 4.98981e+08 6.26696e+08 6.15269e+08 6.71175e+08 8.29791e+08 8.74804e+08 7.06855e+08 8.00859e+08 8.08744e+08 8.68341e+08 9.18541e+08 1.05412e+09 9.58452e+08 6.88987e+08 8.46176e+08 1.06308e+09 1.13325e+09 1.23115e+09 1.05283e+09 1.09611e+09 1.09709e+09 1.14973e+09 1.17727e+09 1.04326e+09 1.01846e+09 1.41653e+09 1.25197e+09 1.32781e+09 1.24481e+09 1.16436e+09 1.50013e+09 1.38475e+09 1.43859e+09 1.26068e+09 1.58937e+09 1.39438e+09 1.49529e+09 1.57994e+09 1.67834e+09 1.66754e+09 1.69425e+09 2.03098e+09 1.61575e+09 1.72542e+09 1.93528e+09 2.08398e+09 1.69823e+09 1.95689e+09 1.79728e+09 1.99953e+09 1.87638e+09 1.90317e+09 1.95795e+09 2.01595e+09 1.96583e+09 1.86254e+09 2.13558e+09 1.93863e+09 2.0079e+09 2.41412e+09 2.08838e+09 2.18881e+09 2.10779e+09 2.20683e+09 2.02652e+09 2.30818e+09 1.71592e+09 2.45782e+09 2.16312e+09 2.60576e+09 2.66649e+09 2.32467e+09 2.29408e+09 2.53272e+09 2.62083e+09 2.80176e+09 2.61449e+09 2.66754e+09 2.61657e+09 2.6799e+09 2.62711e+09 2.59407e+09 2.94287e+09 3.00005e+09 2.8437e+09 2.70759e+09 3.23721e+09 2.98514e+09 4.0504e+09 2.87486e+09 
 1.74394e+07 4.05141e+07 1.07037e+08 1.47334e+08 1.39032e+08 2.33526e+08 2.75513e+08 2.11609e+08 2.96646e+08 2.49056e+08 3.34955e+08 3.40123e+08 3.86214e+08 5.09279e+08 4.03233e+08 5.64195e+08 3.7588e+08 4.52811e+08 6.0343e+08 6.51547e+08 4.94523e+08 6.32549e+08 6.45935e+08 7.32379e+08 7.16397e+08 8.62053e+08 6.35967e+08 6.91753e+08 6.80999e+08 8.89453e+08 9.46093e+08 9.29622e+08 9.00285e+08 6.44139e+08 7.91811e+08 9.79078e+08 9.65131e+08 9.87776e+08 9.67698e+08 1.07883e+09 9.47904e+08 1.01905e+09 1.08806e+09 9.09957e+08 8.99706e+08 1.29504e+09 1.13352e+09 1.09221e+09 1.16398e+09 1.15075e+09 1.38056e+09 1.17159e+09 1.34822e+09 1.05926e+09 1.36193e+09 1.03986e+09 1.27457e+09 1.31281e+09 1.42038e+09 1.26155e+09 1.35683e+09 1.65546e+09 1.55973e+09 1.50828e+09 1.52339e+09 1.62854e+09 1.50548e+09 1.7569e+09 1.64492e+09 1.68613e+09 1.72968e+09 1.63521e+09 1.54044e+09 1.70401e+09 1.61773e+09 1.5116e+09 1.78639e+09 1.5672e+09 1.66914e+09 2.12331e+09 1.85324e+09 1.91931e+09 1.99571e+09 2.055e+09 1.97071e+09 1.86846e+09 1.5937e+09 2.10391e+09 1.8182e+09 2.37613e+09 2.4083e+09 2.04366e+09 2.32418e+09 2.32037e+09 2.50916e+09 2.62588e+09 2.33642e+09 2.44197e+09 2.52736e+09 2.39406e+09 2.31638e+09 2.46015e+09 2.42267e+09 2.58441e+09 2.31764e+09 2.33733e+09 2.64607e+09 2.73452e+09 2.87486e+09 3.38732e+09
  5. I implemented a routine called cholesky that computes the cholesky factor for a matrix. I tested the output of several of these matrices using numpy and found that my algorithm achieved nearly identical results for small matrices. See my software manual entry. Interestingly, my routine sometimes fails when run on the output of my getRandomSPDArray for matrices larger than 100 x 100. I suspect the problem is that getRandomSPDArray is unstable for large matrices due to roundoff error in the matrix multiplication of the random cholesky factor. It is much more likely to succeed when I make the possible values for the random cholesky factor used to generate the SPD array have a larger span (e.g. [0, 1e4] instead of [0, 10]). Here is an example usage of the routine on the output of the 110 x 110 matrix in problem 4 above. See the code in problem 4 for the code used to generate SPD_large. 
     std::cout << "cholesky(SPD_large):  " << std::endl;
 cholesky(*SPD_large);
 SPD_large->print();

    Output from the code above:

     cholesky(SPD_large):  
 5796.18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 7774.04 6886.81 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4292.15 3251.02 9716.32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 9689.89 8022.39 9510.67 2649.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2451.51 3965.37 5670.06 2553.62 6509.97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 7725.85 4529.37 8642.46 1499.84 8397.43 4225.06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4478.34 4161.5 4471.03 8475.96 4398.53 7066.83 6782.91 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 5254.85 7497.55 8979.61 1338.42 2999.81 1414.3 3351.61 3550.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 6995.39 5496.61 3169.13 4395.68 4939.46 5157.61 7409.88 1829.89 7145.08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 725.156 3059.62 7881.43 676.524 8445.1 2371.37 3104.29 1310.59 5078.54 8422.35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4453.85 3925.5 7106.27 2008.48 8212.77 1958.65 1241.12 7431.66 8389.02 7339.92 4348.55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 3478.02 987.745 6607.69 7364.22 1884.14 9022.34 7093.34 4073.88 248.339 356.512 3894.6 135.79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
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 162.858 8889.55 9145.3 7120.44 2098.56 6288.83 2150.84 6684.35 6651.44 9534.54 6558.9 3617.14 2623.15 8656.48 399.597 7264.97 3401.48 9032.03 3524.18 5317.2 5170.53 5984.66 2367.9 9576 8983.44 2604.1 4693.14 1680.57 950.027 4619.98 6158.93 4425.32 5969.55 3333.43 633.791 2367.9 9316.75 6349.53 2564.81 5591.79 497.481 7898.97 8779.26 1065.56 2593.1 9646.02 7197.87 923.119 8928.03 6370.62 12179.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2991.05 904.187 2453.59 1069.04 4100.28 571.57 9655.88 4140.8 4076.92 3051.83 2561.77 9528.89 8285.77 3279.59 3714.9 5490.07 6887.87 8010.62 3682.46 4062.35 3076.25 9377.33 2931.69 8425.62 4475.66 1440.97 3119.18 9157.03 8367.23 2238.35 8695.76 5109.36 4092.06 2804 6429.24 5106.9 7248.72 -115.785 8578.52 5208.4 -593.697 4480.22 4442.81 6524.25 4376.66 5928.97 6193.6 5605.99 7354.76 4654 6930.91 3209.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 424.679 2712.72 6129.32 9733.13 8211.86 9371.73 9867.87 8153.19 8765.87 6092.42 2736.39 7085.2 3380.45 5065.61 1112.99 2027.86 794.887 3494.4 6711.69 5002.82 7514.27 6176.31 5944.31 9180.42 4780.75 4325.79 6503.74 878.544 7927.53 6581.97 2873.34 7044.6 9494.85 8453.53 2700.73 2452.65 522.561 3641.48 7383.28 6719.66 919.345 3255.56 6761.69 2682.74 2517.46 2731 2394.84 6136.66 8815.76 1654.78 10295.1 984.318 2619.98 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 1125.49 125.954 251.141 4936.59 8052.08 1654.44 1130.11 2924.45 9863.97 3378.91 3502.64 1569.35 7032.95 5036.46 2798.54 5920.61 3757.41 1173.33 8253.75 2231.33 1785.19 7832.27 5161.05 1412.04 9917.27 5577.83 5418.23 2597.69 5989.57 5560.21 3105.96 2487.96 3303.71 8711.3 920.056 2241.34 8849.3 5753.02 2601.6 8478.58 -2619.43 2476.76 3282.38 5126.02 -647.205 7843.1 9155.5 2408.06 8297.53 -421.363 8646.13 3700.67 4898.31 5883.88 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 6453.62 5600.54 6374.51 8723.13 2932.19 4639.72 7525.65 6500.44 5333.42 6508.46 2853.05 6879.24 4184.66 2219.69 3045.38 5347.18 8029.6 5763.14 3142.05 7075.95 9249.14 2079.49 9593.78 1637.89 8800.32 9775.31 1664.25 4856.51 6895.51 4441.59 7760.68 2746.73 8478.66 6225.68 1329.96 5671.2 6009.99 7118.21 5938.47 1438.65 2254.77 3722.96 6801.17 8630.93 1840.91 7059.64 8302.98 6952.74 8432.32 1102.48 10735.5 1050.23 4271.94 9125.33 6646.39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 9688.89 8450.04 1885.27 402.65 8819.8 5479.34 4899.14 2724 4833.97 1405.8 1734.76 3874.93 9986.49 2864.83 2017.34 2005.69 9594.87 4624.64 4776.27 1749.62 468.025 1546 3230.01 4405.46 1890.67 7806.17 8949.9 2573.46 5404.95 6225.48 3823.13 6805.98 4683.36 6290.86 1869.18 3232.34 2519.87 2384.22 877.478 1568.65 1187.48 10434.9 4326.79 5934.76 1951.16 8917.18 8864 3962.54 2081.09 7014.79 10090.8 5096.47 269.886 1290.83 8783.23 3652.79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2759.01 4817.1 72.6944 2054.76 6816.2 6286.56 9625.54 656.473 1061.58 5564.98 9215.23 8014.29 9742.14 6116.77 4255.69 3852.33 705.796 403.221 4167.21 4483.74 3554.36 6553.16 9191.03 7454.83 9440.83 3054.13 1210.66 677.216 8596.99 7351.76 6825.28 5781.93 5453.28 8903.84 1549.05 3386.03 79.7288 2812.51 729.418 3828.24 1813.89 8862.87 5869.96 4834.83 3602.02 3228.47 4395.45 2878.44 4682.53 710.141 8831.06 9320.94 -3424.49 2407.53 9357.74 7029.76 9768.62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2895.77 8911.88 9031.65 5106.64 7303.98 3837.68 5754.61 5716.89 4014.09 2229.95 6313.37 8753.12 6293.22 2301.36 7428.44 8308.84 2957.93 8070.17 8418.52 3935.46 1878.2 3347.73 5527.07 7685.13 3092.97 30.4119 6300.17 6449.35 6660.78 2904.75 8460.34 1094.09 5417.01 3167.06 4441.05 2047.71 6568.45 5032.74 5323.64 865.713 2598.84 3911.03 6264.65 -252.674 -1386.81 4360.77 5050.32 5219.32 3774.95 4123.89 4776.57 7673.53 1250.02 5903.62 11282.6 3990.79 3615.33 6452.45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4523.89 5592.92 4876.43 3135.9 7525.01 6112.23 5139.63 2027.77 2940.78 6636.26 1103.61 5986.34 4619.9 6732.87 9130.62 3608.9 1879.84 8054.98 6700.88 4169.97 8521.08 2928.22 8541.76 60.2916 5027.3 6099.96 6009.53 7492.45 354.717 8048.63 2375.86 1377.7 3897.64 7610.38 9232.14 9529.42 10337 5206.32 2558.53 8200.92 826.994 5060.86 2012.77 3403.68 2415.37 6148.23 4912.04 8348.65 4479.34 5893.82 11993.9 7265.97 1976.23 4687.23 5135.09 9523.3 7034.76 3788.55 2570.31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 7483.04 7666.26 5699.93 4517.69 2274.5 596.683 9732.11 2978.16 4089.17 4760.23 1410.84 6918.73 8817.96 2009.1 4761.66 7215.03 8485.19 5206.88 9319.51 492.964 4961.76 2615.34 6537.32 2865.59 6734.4 9508.65 4674.26 7914.95 2678.19 929.846 2055.81 6596.02 2889.59 5862.04 9234.16 3235.37 2712.77 6050.33 8426.85 7864.29 5345.09 10064.1 3499.73 5167.66 7778.13 4087.73 6075.67 5048.71 9424.13 -1412.71 7690.71 1002.92 -1980.71 1360.62 1443.9 88.6426 1981.92 1407.8 5440.98 9571.77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2887.78 5022.53 9881.2 4474.27 6872.02 1408.62 4709.06 7258.26 581.398 3910.93 1773.18 4305.85 5246.22 6429.53 388.591 4238.54 5723.44 655.154 4718.75 1341.75 4898.91 6736.39 2277.55 6161.23 8765.54 6987 8467.73 8628.79 9161.41 2832.77 6450.74 7176.77 1752.45 6178.65 545.91 629.518 562.73 465.087 5650.52 8928.77 -2129.18 11287.7 8787.94 4115.63 4542.66 9693.49 10186.4 6535.57 6053.04 3993.3 8107 9101.49 597.319 2492.88 2048.47 3093.34 3674.96 2943.89 1136.31 5910.73 10037.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2308.14 5133.14 9561.97 1224.87 6836.3 8661.38 7948.33 4204.7 9035.4 3829.79 8799.33 5514.13 6502.81 2123.27 6154.89 4050.61 603.842 4389.26 3140.67 1583.37 5843.4 2201.16 8432.71 9374.82 5828.6 9124.45 2008.56 8754.57 4457.46 816.623 5562.7 6986.51 8309.85 6908.66 6323.91 9536.78 6772.81 1923.56 6794.98 7904.64 -365.262 3358.71 5647.16 9438.92 932.248 4440.39 5959.45 2850.78 2140.64 1211.79 6863.15 8295.39 -1327.51 11380.4 10704.3 9958.46 7684.04 1957.59 5980.36 6025.06 7285.34 10034.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 8003.24 3524.19 8590.2 6258.06 1031.8 6432.2 1891.78 4203.62 3473.9 684.596 9907.46 4688.18 923.935 9990.62 9863.48 2954.03 8228.48 3812.8 8099.92 4977.74 6500.36 4539.9 547.656 6835.19 6203.6 3741.69 1387.08 814.45 7390.33 7244.51 8244.09 5943.83 4563.19 998.387 3420.5 3119.56 9802.35 4600.1 7291.18 1622.23 1737.53 3291.74 10048.3 87.356 4381.19 8871.09 3184.05 2929.63 6371.42 1117.63 6613.21 7723.6 5397.59 1878.09 5318.07 2170.78 6546.98 4366.41 5198.57 9354.29 2917.03 3102.15 4553.85 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 653.822 8020 3217.21 3740.04 7529.24 7507.88 6498.85 926.186 9472.83 4944.77 5020.06 3053.63 111.668 3524.54 7213.1 1132.89 1925 5443.09 5855.53 2435.48 9653 7207.26 2773.45 2593.22 3272.92 2535.73 7942.36 6813.05 5276.04 2592.9 6351.82 1481.73 3729.64 1143.14 8867.43 8281.22 2508.14 4279.04 7555.65 7867.16 4359.18 10539.7 4523.65 1694.9 7447.3 7118.42 3054.34 5425.15 4132.91 1437.06 4595.89 6904.59 -69.4729 9988.63 7039.26 3767.32 6209.52 3433.39 -1574.44 7107.2 7968.5 691.453 1475.19 9269.92 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4384.53 7924.38 3963.82 8168.98 7736.13 8603.34 8397.72 4540.35 4760.14 7527.95 4798.2 8067.25 2904.93 3702.05 6945.32 5598.85 5040.8 8668.27 9538.72 2089.74 4018.35 4263.73 5518.2 890.977 1979.59 6320.46 4752.88 8024.31 310.639 2456.91 5622.04 9791.75 9069.24 7028.4 6474.7 7667.22 538.827 4253.57 4805.71 7531.42 2254.37 9459.73 413.782 8539.11 55.7655 5092.57 7789.6 1708.31 868.443 2525.75 7059.71 5251.04 6476.83 8245.92 8903.79 2647.01 4249.84 6864.45 5167.43 2414.38 -712.147 7571.07 -148.32 3270.34 7288.36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 8213.34 7404.51 991.139 648.331 5077.64 2241.89 5084.56 4473.28 9074.44 4358.8 3966.78 634.766 5453.55 5547.04 7996.63 9273.93 2674.62 8895.58 9176.7 3793.61 3147.89 8170.22 7958.43 5901.11 7908.57 8846.21 4403.05 8325.77 7589.81 2285.38 1972.1 2521.17 4899.44 7683.82 4976.02 5652.81 3551.55 3838.01 1514.76 6963.69 1868.96 11633.9 4452.17 7199.75 3779.2 8657.94 9219.81 -179.391 6181.11 -94.0688 7943.03 1432.79 2917.98 5948.98 10073.9 7147.01 3008.33 4045.74 7139.32 5057.42 10293.5 5911.56 4631.41 5647.57 9741.48 6225.13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 871.38 4982.83 2223.27 5559.44 4696.42 2529.17 3122.49 3919.13 7939.45 7714.18 9155.31 9222.12 7277.18 5287.25 2268.03 2738.96 2912.63 5346.61 724.457 6755.39 8575.96 1260.68 9215.93 9258.6 9480.71 1703.9 4754.49 2212.77 7578.11 9080.66 3723.84 6882.26 6457.96 3974.45 426.217 2701.58 2428.78 7592.01 3605 6916.24 2424.33 3075.01 10470.7 3110.24 2441.4 8111.63 5619.15 -770.336 3541.32 4241.54 5031.4 7629.04 -3262.65 2269.2 1856.45 2519.2 7684.9 2016.36 532.216 2010.44 4502.74 7336.29 3166.73 1727.76 1143.13 7969.05 9966.96 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4186.77 5244.99 7008.14 6612.92 7033.4 2770.36 8227.99 4329.78 8667.5 8830.43 2094.69 6663.52 8920.35 3855.18 8204.6 1350.03 8446.53 9338.56 1241.66 4865.78 5135.67 8768.93 4338.14 3041.3 9641.62 4422.4 342.681 1601.63 8591.63 8374.54 6995.45 2899.17 3220.34 2077.28 3351.42 5369.35 8649.46 2243.37 1131.98 789.745 825.672 3801.67 6419.88 5600.4 1636.68 1622.61 6419.27 6029.06 8847 2103.13 10276.7 8673.55 -1494.33 8655.38 5594.98 4603.88 1714.62 4766.57 8920.86 7149.42 8052.73 4124.44 -747.815 8575.06 3061.7 8140.14 6799.23 4198 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2901.78 5446.33 7863.11 3514.56 3522.01 5118.4 5060.24 3844.91 3694.63 7956.37 6405.51 9068.02 4666.01 8435.46 3747.05 3255.82 8922.32 9377.57 1888.44 7665.02 8697.95 7524.67 5976.9 610.91 1224.21 3587.76 3230.96 6458.39 9726.05 4649.47 9465.36 4088.64 6386.14 5476.66 6634.13 1381.84 1833.77 6498.94 7904.2 7278.27 3273.01 8871.5 229.771 1714.25 3756.85 646.546 3803.68 8984.35 3548.81 223.287 1897.65 2325.06 -393.52 7488.88 4814.26 1656.14 1260.21 -24.8566 5068.46 1959.23 4180.66 7158.86 3426.23 9315.61 -364.783 8040.91 4952.71 4705.06 5711.41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 6343.78 9443.21 208.943 8717.26 4863.42 8964.76 3097.74 462.475 2045.99 9817.98 9516.21 7269.72 5485.71 4366.05 3096.43 7098.69 5197.53 5563.25 8703.09 5543.15 8423.18 2044.56 5868.71 8930.95 4224.04 320.115 5891.01 9502.31 3560 8956.84 5918.58 7201.52 2684.1 8001.72 1423.13 904.332 5189.84 9186.46 224.825 8279.52 826.304 3344.27 3844.44 862.286 2750.33 9152.84 5694.56 7625.78 2575.51 39.8063 8831.53 1160.93 807.623 6277.3 4907.72 7887.17 8510.79 4539.79 10283 4196.94 4016.65 5037.82 -587.18 6089.99 5819.83 2827.45 7619.25 5423.24 7348.73 5454.23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 984.392 8062.21 3221.6 9452.54 1270.12 2094.99 5468.13 5949.11 9719.94 5787.6 5608.96 9393.48 1700.85 6702.69 7081.1 6511.2 1139.73 7539.86 3812.72 1799.94 4061.15 4292.72 3062.74 1344.13 1407.83 9633.86 7902.29 7954.39 7215.3 8924.26 2587.71 3133.92 7569.01 500.25 5341.99 5318.06 7463.58 706.208 4214.6 7415.4 -1082.23 7853.88 1114.45 2501.08 5798.1 4653.69 3338.93 7154.96 5295.77 -1740.13 6378.11 195.227 329.096 4161.05 7690.78 1536.09 790.109 724.977 7250.13 6985.58 6602.99 4085.55 4312.31 11146 4648.01 556.653 9085.55 -1148.13 4513.33 -319.728 7936.66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 8315.37 6547.76 2616.52 7057.31 411.491 366.288 8140.21 4527.14 3393.36 9976.3 9312.11 6387.61 2385.97 4585.95 8041.95 318.684 9076.09 4334.84 3774.97 5295.09 815.572 7738.9 5863.75 8923.02 7041.5 1239.24 1612.48 7220.85 2427.84 7015.04 8772.5 9106.47 4805.15 9010.88 5361.89 984.524 6393.01 2363.74 2399.51 7751.87 -1246.1 5846.31 3201.63 50.5834 890.056 5037.86 3097.6 5480.33 6493.32 3873.48 8175.95 5380.25 3267.84 4121.03 5769.94 7679.01 381.035 3670.63 6643.7 8385.57 7087.85 2598.71 -3860.49 2530.08 2011.73 313.455 1680.71 4392.35 6975.53 -2736.57 9667.81 4275.11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 6270.03 7829.09 5300.88 3883.56 3243.18 7359.01 4314.11 4437.48 4541.56 9261.7 4225.66 5094.09 9757.08 7543.06 5207.05 2104.51 5701.39 1794.4 4126.27 2611.46 4737.82 8256.83 1500.74 826.143 3404.04 363.956 3887.67 68.7637 1976.23 1382.82 3865.91 4815.53 3502.2 8695.82 8286.82 4105.59 3014.86 185.839 7564.21 3778.29 1926.19 10310.5 5725.64 1901.86 8172.72 7174.34 4702.41 6064.7 5150.82 5899.08 1550.54 213.351 -181.784 4192.01 8479.81 1515.64 10249.6 5288.81 9479.54 2581.28 7158.82 2390.29 3510.41 4379.35 223.746 4253.07 6730.94 1003.98 4128.51 -2878.69 5567.04 3504.91 8599.05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 1260.04 1867.17 6042.74 9656.38 7390.98 441.965 9801.62 1642.3 1020.72 3101.29 3017.82 2259.22 2648.4 7148.37 5418.98 6921.68 7623.55 895.707 9046.32 6667.18 2594.71 9258.28 9216.68 137.555 6536.87 9863.38 3752.19 5024.96 6996.1 8563.49 5231.6 2551.91 3492.93 7701.67 2321 9247.58 1433.29 1514.64 8237.96 5357.15 -726.451 6080.35 7354.54 5794.78 4326.94 8800.39 8298.94 7322.3 7560.23 407.86 5597.79 6673.66 5229.53 5535.75 8571.12 4580.9 5966.67 6151.94 3493.56 4819.89 8032.18 4216.08 3250.33 4273.22 4984.98 6432.74 9460.81 3726.41 6411.13 3089.99 1694.38 2885.64 627.712 9129.61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 7590.66 7089.97 4254.67 2508.8 1847.4 2109.87 5285.56 9858.69 2382.72 2994.45 4309.54 8742.95 4120.05 927.213 7892.43 4503.15 3613.17 7380.57 5732 810.061 4795.84 2874.08 9663.52 6814.43 8401.67 1281.34 8393.68 5366.19 2508.03 6772.29 710.166 4025.83 6752.63 2247.79 3569.65 5882.42 1515.9 3005 138.903 10036.9 244.967 7653.59 7196.13 3034.26 1903.36 8850.89 8008.09 1920.21 1884.34 5673.34 3543.74 4605.04 -3021.48 2743.1 1983.98 4983.19 2313.01 5573.17 5594.97 -893.765 2981.42 3342.08 1934.58 3410.34 7701.31 5760.58 8797.23 -1518.53 8921.39 4419.91 10142.5 6024.62 7625.62 4466.9 7551.68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4703.27 9456.19 3292 6604.83 155.324 5072.47 140.428 7251.07 1099.69 2816.72 4458.4 7151.77 5930.08 5508.76 5839.3 477.257 7894.72 1934.78 4374.57 7006.65 131.329 713.065 404.73 812.843 7631.7 1477.03 448.458 8315.08 851.265 1634.77 4810.34 5286.66 6088.89 8928.74 395.701 6843.11 6901.42 5901.26 2816.84 5340.01 -1078.8 3209.38 976.352 5203.08 6626.79 6979.03 9237.49 5631.62 7213.3 -2218.01 9140.02 211.345 100.968 5122.57 7717.58 1860.65 5669.11 -1508.53 4552.78 5996.11 1941.9 2625.77 744.089 2678 4583.11 2331.37 2414.94 3462.29 10172.4 -1192.09 10298 6336.41 6912.33 3773.36 3641.99 9061.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4184.3 4459.15 3932.67 5892.91 5476.54 8979.99 7198.47 8552.5 2173.53 5337.27 8090.53 3824.63 6782.12 1844.16 4040.64 3470.52 755.299 161.417 8877.24 5199.51 7403.53 8403.43 538.855 2484.29 3959.76 6335.19 2314.86 7567.75 6259.87 7602.92 7520.04 9397.06 7978.63 5486.68 8501.53 6993.23 3982.41 2815.47 5637.29 1497.3 3477.25 2396.25 1930.74 4577.33 88.473 5058.66 1795.86 5291.61 5287.63 6301.72 8976.31 9341.06 1356.9 11000.1 1398.36 6999.71 5058.89 4755.1 8088.13 2579.83 11595.5 1426.08 7035.39 3962.51 5135.19 774.818 6146.01 6324.32 6024.05 -6352.43 3588.45 2259.53 2346.85 4524.03 6666.38 8675.08 5386.79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 991.793 1457.35 6914.04 982.455 8448.76 1998.48 1295.06 2803.82 7598.82 4920.16 6399.68 5019.83 4903.78 7011.08 2720.83 2857.31 1765.64 280.401 7920.96 8584.52 1448.81 5524.89 5633.08 148.783 6648.91 7938.07 7162.48 1236.94 2179.58 1511.18 7735.25 5198.06 8172.23 3425.02 7617.46 5851.86 6364.24 6856.64 4164.58 3941.33 4169.91 2220.75 2825.34 5550.99 8242.86 9466.13 3647.73 5675.39 2029.33 3376.79 4491.96 6144.46 898.127 3845.37 661.61 1972.94 1543.41 3927.52 5771.58 10145.4 3004.47 6582.51 220.705 1340.55 6140.23 4816.21 3671.31 3298.23 12730.8 -650.021 7074.03 7413.25 1719.74 4470.03 6713.23 2739.5 -983.727 7744.05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4850.76 4294.05 3499.41 1989.55 393.717 1740.18 57.7798 6064.74 8050.38 2088.43 7897.65 1401.98 6928.69 7239.4 889.059 9232.05 9223.9 5208.3 9728.4 7605.97 1610.36 4209.11 1838.95 391.885 5830 5067.18 5893.4 7472.35 1786.54 7290.7 1037.28 4237.33 1925.94 3291.33 2524.33 9682.88 2989.32 1995.28 1582.73 5328.14 435.422 7781.24 8138.28 4208.17 1547.18 1726.69 5853.9 1196.09 127.397 6900.56 9139.5 6972.49 4000.47 5814.76 2135.04 9279.04 3303.12 6687.12 4859.64 505.903 3550.12 -164.849 6585.98 7498.34 8299.87 7713.21 937.177 3807.77 6616.05 21.8347 2631.85 4125.83 10968 10253.1 651.676 4284.83 737.107 10508.8 4856.81 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4087.51 8021.95 3372.47 5420.8 6832.26 5749.81 4225.38 8962.46 8498.98 8122.91 6002.11 5506.64 690.482 822.407 7048.08 7446.38 6679.11 2016.09 8513.77 5317.88 3687.13 1859.49 9903.34 7601.05 4502.6 6090.74 3224.09 1473.84 1464.9 4634.13 8533.72 5641.72 818.008 7550.49 6627.87 4993.53 4100.31 72.6383 2517.99 7628.99 -504.698 3465.35 5757.42 1002.82 2416.54 9561.36 6788.64 3883.24 9968.33 2209.57 6831.01 -511.679 -3133.94 9912.38 7719.63 -375.456 9415.3 1476.88 7186.61 5065.36 4026.54 4257.35 2656.13 12571.8 3614.42 4220.02 3706.8 372.272 5595.75 3608.47 10450.4 5980.2 10710.5 8742.55 7268.03 3288.27 3498.42 10573.3 8262.91 3082.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 853.67 2247.64 2655.47 6808.9 7092.67 8517.77 2376.11 6058.9 8005.52 7676.82 6149.4 5838.79 6651.93 9422.36 7015.13 6144.14 30.498 3064.83 2357.93 8346.86 9359 3094.89 4485.45 8589.6 1920.8 4613.48 9158.16 2735.42 944.824 957.749 8222.29 6347.05 1585.13 1649.67 8952.59 4500.96 10144.5 5581.88 2577.29 9525.2 1698.83 2331.01 2465.9 4645.07 6629.01 9395.82 2359.67 270.507 2583.31 725.161 4224.19 1558.18 4099.4 6332.18 698.774 4764.6 4299.97 5981.77 6504.27 172.171 6875.15 8436.05 7010.14 4746.26 7789.29 2992.44 1227.98 6699.89 9269.59 4049.77 4789.88 6059.76 603.773 8556.34 41.5982 472.07 3338.36 2945.87 5382.41 7491.19 6450.68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 5013.62 3183.6 2644.7 9109.98 2492.27 8029.01 2208.62 2749.09 4701.82 1622.97 4456.56 5019.12 9551.84 5895.88 1288.66 6497.02 2625.38 4240.32 3252.58 2923.17 6780.88 193.767 4206.84 9967.9 4813.45 7671.28 586.594 9152.87 2736.64 1910.72 7196.2 8662.49 7895.44 6621.12 3174.97 2051.5 2616.19 7225.64 4143.59 2134.13 4003.8 2427.42 4983.76 5354.88 4264.03 1364.75 3829.99 4649.96 8969.71 5486.43 9444.43 1858.27 2602.24 9930.8 10129.5 5601.2 4172.3 6502.7 7556.06 9967.26 3084.91 3423.94 4931.66 4549.26 7533.74 262.351 8688.19 3505.25 8155.92 -2039.54 2655.52 2689.56 7038.26 1773.24 1124.25 4510.27 2790.42 6679.83 10861.2 5743.68 3958.04 11187.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 7078.56 8926.14 5826.06 6489.84 932.544 6321.38 3881.26 3103.26 2575.89 1174.75 8563.88 5035.52 8976.25 4101.99 762.978 2936.45 3566.98 26.7114 2196.23 9380.23 6763.39 1236.82 2835.04 6026.68 8978.23 7531.72 6343.23 630.905 9832.06 6872.45 7229.49 751.245 4910.14 392.4 3455.27 52.5073 980.954 105.841 1097.05 3253.76 1711.53 7730.2 9879.21 7444.18 6666.79 5528.59 4077.74 4967.62 7032.8 2005.63 4143.98 4363.26 6026.5 4755.41 5424.4 2969.46 7872.34 4211.11 3359.71 7219.86 9191.44 1349.99 3334.54 6566.48 2500.07 7007.13 2103.21 -463.795 7313.01 -4939.24 4390.54 5338.59 6503.69 9383.81 4822.49 4104.64 3287.03 5876.12 6356.94 8827.83 9738.96 4140.45 9951.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 1278.35 4960.36 8784.8 6542.03 5304.53 7889.5 2243.98 4212.09 6771.4 3769.24 8885.79 2923.99 32.374 4487.97 8128.12 8171.99 825.385 6559.23 9069.62 3349.68 6873.27 9271.19 429.759 7770.06 6701.5 8939.27 5661.85 3613.97 8872.34 7539.71 1095.63 3391.74 1080.03 139.821 2057.39 6904.01 255.883 534.35 9969.45 5183.6 1100.51 5702.89 9400.97 7372.58 9214.75 2129.1 4872.62 6598.02 1396.89 2349.07 7775.17 1161.17 -447.621 7121.56 3716.56 9373.53 9924.61 3597.81 10397 5014.01 1866.06 7558.75 251.63 1195.26 5090.54 3045.29 3617.35 1018.73 2670.93 -132.776 5780.54 -66.4937 9407.43 6757.57 2663.16 -151.982 4712.34 7819.82 6150.69 5330.27 4464.26 1522.97 10782.3 3002.54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 6139.11 3309.56 2895.84 4046.57 544.349 9683.46 3338.73 5673.54 4565.79 5001.89 7959.2 6588.47 6584.79 932.336 4087.2 2417.63 6382.79 5413.66 1506.34 5154.5 8566.08 8026.04 9367.9 1379.96 4730.7 3249.12 6004.81 1750.58 8726.16 7470.9 302.16 1150.6 1199.22 5370.52 3768.14 4306.53 1936.58 2639.9 6748.28 10066.9 -214.231 5026.71 8448.77 696.197 4205.96 9099.01 2968.66 8304.13 7229.33 5556.51 10537.1 4317.73 -478.843 3357.33 893.982 918.88 2948.86 1471.85 2290.11 8013.41 7421.15 6217.92 4428.54 9134.72 1601.76 6682.46 4509.2 3250.12 3404.71 -363.561 1761.34 5103.06 6850.35 543.769 436.273 3736.8 5163.35 2870.95 606.797 6459.08 7631.15 8812.63 8892.6 5661.14 7028.54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 3532.18 4526.67 2200.57 5212.97 3864.74 961.096 1406.91 9603.7 7909.31 7683.2 1416.92 1914.76 3160.91 6321.68 3808.36 8283.63 1596.58 5789.85 5338.29 6456.18 6012.52 3316.32 2428.82 7664.57 7778.56 7307.03 8007.5 5487.39 6727.62 1314.07 4990.16 3497.85 3388.76 6615.78 4795.88 5723.26 6984.73 7235.66 7035.56 4685.16 1869.42 7921.27 3251.3 5938.29 -1030.63 2438.94 11458.2 2864.68 5328.41 5043.33 5088.83 4559.56 4328.49 1314.86 1250.33 3529.59 7957.42 4971.86 11892.5 5979.15 6181.33 5541.51 961.417 720.502 2216.92 9854.62 9533.06 244.686 5497.85 -2799.51 2443.91 3065.13 4698.09 4031.09 9960.45 7224.37 6910.64 1664.44 8952.13 7767.03 6854.53 121.515 4489.55 4386.16 7571.09 6843.19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 967.243 3410.4 670.064 6944.68 4124.33 3368.84 7143.13 6936.1 1605.37 5175.04 620.549 6798.92 18.8636 7352.79 145.462 177.68 420.256 1183.87 3845.9 5099.3 7341.3 817.196 3659.78 2175.55 8592.14 6745.44 4611.72 6187.43 4277.31 3765.22 4918.76 197.671 5763.39 6430.9 3925.54 137.811 2815.99 2843.33 846.68 6793.58 333.444 3270.23 2368.11 3704.87 2442.48 746.436 2510.93 2288.3 3310.44 2774.79 4138.37 6085.27 -1072.05 8460.69 2722.22 5308.22 2267.99 7787.88 5671.11 9507.38 1903.14 2544.53 5926.65 3267.19 967.849 9555.41 5118.72 1467.93 9492.26 1834.51 1721.36 8186.17 6312.07 1120.42 1441.84 2177.58 2297.25 6245.63 4867.5 6078.8 5233.1 4042.89 2030.18 -3834.83 4759.28 8674.59 5420.84 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 8898.12 8126.65 2968.54 6101.33 7360.55 5970.02 2964.26 6330.01 5627.36 566.866 7174.43 4602.76 6326.93 7049.11 8342.89 6269.96 7088.58 5816.88 5673.54 9638.24 2120.44 4579.2 8558.93 8834.76 4171.55 6303.24 7215.53 2427.75 7323.22 4822.71 7127.42 6932.35 6652.44 4302.24 5037.64 7704.26 2179.46 5147.33 7476.62 4600.78 3181.21 10075.8 469.408 5117.55 7177.42 2458.87 8368.63 5240.65 1669.69 705.702 4047.51 3918.64 -1518.28 5636.04 10182.9 7782.58 2835.37 5251.01 7357.66 5095.46 7835.3 326.92 3868.07 5335.81 5951.63 7663.12 3442.87 2557.73 9706.09 3707.48 5042.92 1502.92 1420.81 7351.01 213.507 3943.87 7606.23 6727.9 8083.05 6235.87 4105.43 3744.19 8629.89 7206.8 5220.99 6265.63 6512.07 3509.68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 6427.95 3438.56 1232.22 319.606 1168.71 4798.77 7161.52 5320.59 1923.4 9913.15 7730.29 667.888 9454.13 8623.03 1236.8 6592.47 4554.51 3860.03 3756.81 391.644 7890.72 6664.04 7955.89 5349.77 871.489 7337.45 4307.65 1936.75 3388.39 4218.83 3450.5 4591.93 8805.77 9782.62 9237.96 7770.93 3832.89 2287.52 2363.55 4775.82 2198.37 2681.46 3696.38 7345.5 113.94 6332.02 4028.13 5349.4 9195.98 7813.67 5170.72 673.508 -1580.93 7605.13 2935.98 8977.97 1321.71 5592.69 1867.18 3056.92 1106.89 1854.74 656.866 1583.22 5056.05 5351.34 7370.69 1849.01 11223.4 -2201.69 6133.34 7509.43 1976.84 3465.63 2736.72 2512.09 470.452 9933.77 6935.59 4744.2 2510.15 3075.02 5208.06 4327.38 6604.83 9006.87 -235.002 5096.02 5394.24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 5491.14 9003.32 5546.5 80.5722 1649.34 9481.07 2282.75 8963.87 4546.15 1811.3 1724.16 2785.26 4638.77 4085.66 9276.09 3786.58 2300.1 9238.85 546.784 9269.26 5862.38 3745.42 2201.55 2235.79 3619.47 2845.39 621.36 3679.8 4632.11 1813.9 7294.6 1575.21 9660.98 4069.67 3599.94 9616.04 2719.59 8320.87 3406.16 5340.18 3763.3 8131.59 4083.52 7031.77 4740.75 6916.3 7571.5 3311.87 7590.17 2548.38 1678.27 3481.19 971.473 9635.94 5982.03 1564.25 9717.39 2382.57 3937.85 9166.71 3950.7 8736.55 242.548 5036.4 8304.26 6491.01 6987.29 613.276 9178.1 -2051.45 8839.31 8313.46 9267 9857.68 4750.04 3721.34 5348.81 8208.04 6050.52 5064.75 7171.46 2650.6 6099.02 7406.38 5648.77 8888.2 3727.21 12206.4 8235.44 7916.73 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 6381.16 5792.91 8668.47 619.024 9635.06 6566.7 2696.37 9308.17 9716.53 5327.09 8585.27 1521.49 5144.89 9058.2 3104.55 3484.99 5573.77 1023.76 4993.05 131.198 7082.2 7194.55 5096.24 1700.39 905.925 5811.89 1889.78 342.702 1.41891 5752.57 9183.23 3528.38 9542.06 198.344 4687.71 890.959 4233.49 3510.91 5915.9 10257 -16.1842 7777.16 1526.7 -177.309 4920.52 6474.19 4677.56 4374.5 850.723 2782.85 6330.74 5857.69 1358.15 6734.35 1683.42 8492.13 4676.2 7469.83 6781.89 1915.48 9250.61 8806.17 2766.5 5437.46 4437 4341.51 6504.39 456.2 3700.7 -4019.02 8474.19 1900.77 11713.1 6164.61 8841.77 2647.33 1815.76 6534.69 9539.5 3069.63 9943.9 8031.08 3882.29 2298.96 619.482 9398.88 4710.69 5867.16 4507.18 1944.09 7414.37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 9315.72 8461.09 1113.42 4793.87 8040.73 6207.39 1870.58 2578.85 2504.8 3824.08 9503.47 4973.74 4700.34 5052.56 1625.39 831.002 277.95 4515.18 8475.56 1733.39 2789.63 3400.44 233.445 1511 9637.01 4324.45 2775.37 565.54 2549.8 7051.61 9901.24 1768.72 558.249 5996.42 194.807 8350.57 3700.15 4053.1 8018.65 3407.33 789.07 4589.15 6323.18 3200.97 7570.71 5502.03 1453.35 1131.67 5169.8 3864.5 8439.2 789.179 3671.56 6338.25 2976.87 7224.07 6098.04 2205.22 7966.61 6739.73 3407.15 8260.77 11358.8 2041.7 8791.91 8154.05 2265.87 3738.23 6652.62 6349.85 9509.77 2007.63 4932.87 7991.82 1438.41 6153.57 8666.22 9206.54 8163.85 5377.28 5018.5 -1756.92 9861.54 5154.91 3767.15 2313.57 8.11861 9128.64 3105.68 2633.89 4525.77 2192.47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 7799.27 4136.46 5108.46 1305.44 8485.64 8142.45 231.084 3168.57 3581.55 5641.09 523.483 8299.39 1141.57 6208.93 5430.98 7837.2 2903.94 3628.11 3687.45 852.637 1705.77 5946.58 634.247 1610.67 9448.02 1969.85 2629.83 2434.45 9089.47 2630.47 2857.32 8561.91 7970.89 1015.98 323.151 9104.85 8843.36 2539.55 213.512 1563.15 63.4034 11745.9 10111.6 6737.2 6340.24 1248.32 3619.78 7579.47 9682.82 4461.45 7454.77 2141.24 929.1 8058.62 5656.68 781.429 7322.3 4330.59 4544.72 2151.28 1940.23 8174.72 5216.06 11564.6 5321.89 8205.21 4938.27 814.517 5794.56 5092.26 5880.88 2497.43 5569.35 11053.8 2624.55 7834.78 3148.07 4956.68 6015.59 8344.8 3519.73 6290.89 9029.53 -3023.24 6450.43 9718.65 1322.11 6249.9 8774.11 9533.02 2828.49 4435.82 6064.45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 4384.4 9317.1 7258.67 6877.09 666.854 2998.91 4588.15 3511.79 3190.43 6011.69 8492.73 6209.67 6068.82 9048.82 2968.03 6439.02 3802.25 4836.56 3092.97 5108.93 3582.56 1734.44 5643.91 8535.55 7109.54 9553.58 3276.89 1157.13 7391.77 2997.1 7427.31 9472.15 4105.23 1196.03 8111.49 4010.39 4314.24 7051.13 3203.37 3050.71 6742.81 10684 2836.72 816.303 1093.3 4950.28 5252.2 3087.77 7364.95 1813.49 9385.72 1824.97 -2963.84 5629 5408.44 6816.54 2177.3 -923.293 10472 4836.53 8510.13 3643.05 -248.917 7625.49 2452.72 6663.55 3012.06 5004.76 6130.6 -626.519 8266.73 8885.24 7724.92 2716.13 4895.81 1565.49 1224.6 7934.32 8850.84 5095.84 7077.26 924.095 3654.28 9402.94 3547.76 1788.3 1954.87 4627.4 6969.66 2682.29 5120.11 8745.84 1052.35 10663.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 9969.55 6481.09 4330.63 8533.91 5569.97 3715.28 8369.43 3505.03 1977.63 8768.85 4523.53 8027.37 4812.01 8577.11 8838.49 1963.9 2202.95 9958.27 4331.09 4168.87 2442.63 607.696 3006.91 4104.18 2909.96 6860.17 717.823 7378.5 7825.94 9644.56 6253.04 3250.3 4287.84 7135.64 9080.37 6632.46 6237.34 -640.75 5582.21 9869.8 -1041.32 2585.85 8135.59 4195.8 4359.9 2678.04 5005.52 7361.24 9275.47 5699.73 5626.15 6427.54 -4507.14 3876.54 9060.72 8684.57 2911.86 1700.22 9479.46 5350.67 8706.98 283.855 1663.76 8207.57 8641.8 7780.04 7207.79 -584.188 4737.03 1300.27 7260.6 8284.16 9472.89 3683.48 4384.2 245.734 3256.2 2690.62 9334 3101.28 612.789 3424.79 460.533 5587.75 5439.4 7566.64 7429.46 3229.72 6427.36 8945.69 8014.91 3544.82 5153.56 9800.54 4651.01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2183.8 2060.85 9072.28 9474.42 6221.77 6745.79 8628.81 7708.93 8341.69 3169.05 5321.68 6366.63 4046.5 9910.98 2376.3 3436.04 7944.74 2296.38 3226.18 2942.37 5724.12 210.307 6152.45 2501.62 1427.63 8290.3 7382.76 458.732 9400.11 5087.38 8479.35 8353.69 7040.16 8047.42 6783.78 6774.08 9430.04 6703.64 5018.91 9150.47 405.844 8334.73 -839.1 5672.58 7261.13 6181.05 10312 7514.66 615.604 5984.21 9276.61 5750.19 -2653.4 3959.52 3857.94 2216.5 1927.67 1876.55 5506.27 6453.66 323.138 6358.43 1778.15 8260.85 1435.86 8227.23 8509.66 7364.98 10358.9 1530.79 7457.85 5401.33 10484.8 8430.07 8333.78 2189.7 3467.49 10387.4 9047.83 9506.95 4822.15 1448.52 5270.59 7452.79 9433.45 8976.71 248.58 3687.72 9336.69 4722.07 276.672 6916.75 3904.22 9991.16 4240.76 7531.16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
 2597.74 6721.62 8249.81 7525.42 5744.49 5240.79 9672.71 7985.07 2264.87 370.49 2459.5 6844.44 1522.37 4595.86 964.663 5712.96 6476.87 3732.14 2269.67 8902.53 6730.45 9904.67 3602.34 4436.66 5018.09 8399.79 7679.93 9482.9 4981.6 5282.5 9399.4 1993.33 9004.7 8881.2 3805.37 9600.47 6991.19 3606.04 4731.96 7559.84 -652.593 10010.6 4928.93 7406.69 3943.2 3794.81 6585.93 7597.4 3391.53 3915.02 7134.7 2473.67 -4114.08 11797.7 5796.28 6466.45 4289.21 1465.43 2018.64 1440.81 7309.05 9610.76 -970.12 7990.9 3455.45 3455.77 5436.72 -5124.88 5607.98 3906.78 3066.44 3497.98 8127.86 9146.19 975.145 2349.18 3444.36 3964.48 2483.53 7573.39 6922.3 2890.72 7485.14 6496.13 2889.97 2317.58 2599 1470.03 100.278 7031.33 6798.08 1010.6 3736.14 4927.77 -2613.71 5198.61 7532.94 0 0 0 0 0 0 0 0 0 0 0 0 0 
 840.926 1463.92 6553.9 4093.35 266.393 6244.45 1491.92 7424.16 9917.08 6483.03 3678.84 7249.49 2089.19 3864.36 1106.52 4702.86 5115.59 5304.88 5055.55 924.269 1018.59 1868.38 2222.84 3362.84 2390.62 8564.08 5472.26 9591.3 5404.04 8725.23 9976.88 132.58 745.826 1145.06 9194.18 9347.11 8848.46 6610.31 9186 7514.11 3030.19 1842 4749.48 6890.63 6167.79 921.604 2363.4 10673.7 2682.79 2799.4 4578.55 5285.51 -461.023 5751.02 903.042 2914.52 -39.5164 6909.8 7508.53 8484.76 3865.88 6799.53 7960.33 8763.53 10032.7 5867.15 6972.94 -694.739 10266.3 967.297 8810.59 3782.33 7310.18 8244.24 1447.32 9726.49 5391.7 5161.96 9938.95 2313.74 7628.07 7359.65 5033.01 8463.45 5479.56 4193.63 6615.99 8562.02 887.684 6589 7088.92 -1557.09 1926.27 6482.46 -1572.45 6357.47 4715.3 6224.05 0 0 0 0 0 0 0 0 0 0 0 0 
 6370.57 7305.84 6080.43 6087.34 3255.16 9516.15 6856.8 2038.71 7009.18 1999.48 7416.38 3030.16 2966.85 3766.16 580.896 4786.07 6391.27 1634.94 4467.83 7808.15 859.794 8979.24 490.598 5542.89 1069.27 2712.7 7725.49 2060.32 7991.8 3461.97 5474.79 1252.75 260.484 156.583 561.234 2094.34 7695.17 9126.4 6151.52 9828.15 903.317 2836.74 7703.96 1989.36 660.626 7399.09 4684.14 3944.09 9340.03 841.26 6843.81 4251.69 -4108.02 12612.8 9451.78 6817.61 3642.92 6639.5 9048.96 7675.07 2412 8284.43 4276.91 8334.24 6295.17 7085.37 3766.87 2185.9 8098.78 -1846.89 9730.11 6909.8 901.754 6688.17 1945.33 7187.77 6397.51 1651.3 1598.77 9088.39 8845.6 1665.64 6650.17 2870.52 11150 6395.88 3816.9 5542.45 8339.63 7425.6 4925.6 1149.44 7008.63 7409.33 3550.69 1897.7 4535.95 1047.17 10353 0 0 0 0 0 0 0 0 0 0 0 
 5499.52 2167.95 6112.92 1039.97 9266.51 359.197 4732.95 1829.99 5959.49 8326.86 8865.02 5912.45 6188.38 3031.32 4711.71 8968.78 5399.2 3109.71 4158.11 6567.56 5428.4 7429.33 9579.23 5047.6 6242.29 1987.55 910.9 5941.28 4707.66 9931.99 8864.75 6081.92 5390.83 4389.93 864.681 933.257 8160.82 2428.33 2648.62 3138.8 -765.88 9816.82 7631.25 -72.4806 9190.91 4165.92 8498.57 5961.09 6852.34 5424.25 7039.8 5143.67 -2717.84 9809.98 1439.65 10608.8 4984.52 4687.94 4541.5 4542.75 2136.74 6196.49 3689.19 9039.14 2129.93 1146.91 1232.67 5851.88 2929.61 -1553.2 5296.92 4389.25 8067.09 3054.98 6377.08 587.148 685.705 2000.92 8352.06 5582.03 7248.22 1386.14 2198.86 2355.27 2736.5 9174.17 248.086 6999.14 5890.76 7665.62 4233.09 5150.09 -220.478 8240.87 4782.3 1486.78 2667.76 5525.34 3561.18 9803.91 0 0 0 0 0 0 0 0 0 0 
 7184.71 907.131 6762.84 2810.61 5129.81 5209.21 4589.66 7886.64 1963.07 6301 3195.05 4519.21 7574.91 8230.41 4202.95 1801.55 313.12 868.131 3758.64 6467.41 9441.77 3912.94 8091.56 2293.81 6614.63 8884.19 1363.25 9093.62 8964.01 7682.06 5895.46 7334.13 3429.94 9147.45 1338.39 190.004 3481.77 7379.61 9420.67 4562.55 1841.5 5340.71 8824.11 7812.36 -581.714 9903.15 6881.91 8834.09 5131.17 4696.99 10531.5 6944.78 2932.24 11888.7 5736.2 10621.7 8512.18 4404.23 6422.71 2332.47 6102.02 2806.93 -2416.22 3426.75 5704.21 8693.89 4705.24 6209.67 9700.24 380.952 3314.37 5296.67 6969.04 6772.28 2319.1 4152.51 -511.897 5209.11 865.731 4081.01 2713.32 5163.85 3867.38 5964.07 2650.53 6789.12 8214.88 3075.55 7877.05 3308.39 2159.02 4442.88 1349.04 6033.5 4400.81 2593.26 3761.39 687.1 196.398 1644.91 5478.32 0 0 0 0 0 0 0 0 0 
 7354.96 5368.05 9302.02 5539.88 4525.28 1611.14 2324.93 7987.81 6729.12 7787.08 3025.33 2423.63 4667.69 468.849 7661.99 1297.27 7531.01 9174.8 8280.56 9608.09 4920.94 3271.96 3553.34 6887.02 2477.1 2346.56 5627.81 14.6892 5207.13 2386.26 8062.48 4386.55 7829.46 653.81 5917.23 7411.82 5430.88 -134.111 370.519 6974.76 624.35 10629.1 8726.65 4466.74 6422.59 2074.35 8273.62 3938.83 4434.88 1974.56 8769.59 5217.7 -1319.08 3752.68 6079 6270.09 4906.45 -2167.28 6879.4 3436.48 7653.85 3168.6 -548.108 7809.39 846.468 7661.3 2920.82 670.922 6273.42 5555.31 7593.95 7077.35 8459.33 6135.95 8096.2 -43.0784 5617.81 3554.63 10222.4 9175.56 2475.94 8215.43 8177.53 1525.06 3247.49 5573.41 1532.35 8104.85 2229.15 -25.7552 7592.9 -493.551 2879.87 9245.28 -199.165 7741.55 2679.68 4623.33 2245.36 1392.37 3584.64 4933.25 0 0 0 0 0 0 0 0 
 3814.89 8715.71 8729.44 8097.28 9678 725.484 2873.16 6357.13 9352.85 8303.16 8177.13 2300.06 8574.34 7617.27 2753.66 9287.47 4475.29 7444.55 7933.08 1862.65 6243.97 5168.24 5442.97 3970.68 3283.75 3226.78 2523.33 3162.19 7135.43 6946.99 7637.26 5188.54 196.051 3439.06 5898.95 1931.49 5025.34 3371.07 5043.12 2293.4 3686.7 5901.54 4102.95 1402.93 2663.39 8647.78 7778.93 -2291.62 3367.37 -119.624 5870.57 -230.574 -3971.59 10666.9 5466.64 5340 5707.61 6392.25 7345.6 6309.64 3591.76 6461.81 3589.98 2874.85 5980.01 2171.99 1323.67 -1740.38 4718.28 2028.96 4923.63 9078.93 7453 6867.05 5708.15 137.202 1106.55 8595.94 5863.98 2956.49 6015.89 2352.43 5993.41 9605.84 5538.83 51.8168 42.3843 3469.83 7090.94 6133.4 6776.72 8998.9 5579.27 9623.52 -1354.67 4159.67 7789.76 5028.29 2717.62 897.891 6348.67 7343.05 8595.99 0 0 0 0 0 0 0 
 3454.74 8736.22 2063.72 6694.17 8372.99 2568.22 8903.77 2324.12 6504.63 5562.7 7420.71 9613.3 7331.99 5773.47 9410 3906.07 6014.51 2662.53 7884.91 9078.87 4179.59 2169.76 9592.3 3119.94 18.6919 9248.15 5250.97 9162.35 940.296 9064.92 9761.36 2149.58 6932.13 7875.13 9327.17 4308.07 6670.56 7240.19 6983.75 8538.35 4346.16 6282.03 8404.77 1458.22 921.003 6398.27 7023.56 -35.6475 344.392 584.046 10450.2 7440.62 2676.79 3196.39 3225.51 1490.62 8661.15 2996.84 4259.76 1797.76 5949.11 3548.23 7383.58 5451.38 6425.83 3161.83 1018.08 3655.01 7806.51 4838.69 8715.54 5107.31 3359.39 3234.39 6413.56 1138.87 4339.14 6938.2 6086.52 2775.19 3290.1 3770.3 11986.4 9571.09 1395.44 243.343 819.556 3407.63 362.052 8856.73 3260.59 2620.77 8365.7 6684.53 1319.49 10477.2 1725.36 4558.33 4218.83 9160.84 3536.45 5274.76 2050.15 7762.39 0 0 0 0 0 0 
 8615 7235.22 5344.76 5196.26 1916.26 2053.11 2126.55 9630.12 7749.84 888.37 6043.16 4682.86 7316.09 7617.22 3080.97 8218.95 5154.56 70.5051 7326.88 6275.27 7515.64 2530.24 2770.02 7024.57 9013.98 2209.95 9380 5039.65 2203.25 949.781 3294.07 6938.37 1322.37 8354.21 8244.15 6660.57 6900.35 1312.87 8608.24 2889.26 1045.1 3604.06 4367.18 567.547 1886.57 600.685 5523.86 3274.85 1822.18 4846.98 3756.6 1355.97 2065.01 9388.1 4899.99 3199.13 92.0227 8010.41 7217.19 9672.98 6201.78 6621.31 475.29 5630.2 7195.75 4644.3 1214.3 -2521.54 5602.53 20.9478 8042.56 1590.24 9708.36 5791.94 4130.62 1954.57 2755.68 8606.08 9371.16 7833.02 3748.27 5688.26 5884.27 2662.1 5812.39 1052.46 5722.9 2194.82 2659.65 7650.95 7679.03 2717.3 4165.9 11852.2 1511.06 8245.09 2503.75 5103.06 -638.632 5357.55 6758.85 1450.99 -169.21 5050.83 9075.22 0 0 0 0 0 
 1405.55 5805.68 2984.11 606.081 1525.4 2835.35 8158.72 6215.82 1735.57 1297.61 2486.67 1043.01 2694.39 8544.49 646.09 3790.62 8088.46 4825.12 3665.09 2672.71 1039.81 8042.31 5106.5 785.106 1685.41 4508.12 917.043 8528.34 9643.52 3719.32 8347.41 9214.25 6948.65 5683.92 206.324 7750.35 5655.04 8033.2 5187.86 1810.25 1923.47 10016.5 6024.46 3075.23 2489.72 7897.31 9356.75 6669.93 5013.22 1.59622 871.999 5853.3 679.846 3615.63 7913.43 11440.6 7766.72 6614.79 5624.29 8700.13 4998.99 689.353 1194.44 7906.37 3482.92 7912.48 277.244 -1493.66 5696.67 -1126.61 3898.4 5366.65 3318.34 674.521 3051.14 -890.952 3068.81 8827.22 -574.846 2654.82 4871.38 -1027.75 10297.7 4103.32 4956.56 8176.78 7585.46 7602.99 8922.35 3186.54 8338.22 2579.94 6423.42 8729.45 3134.86 8087.59 5280.49 8015.06 220.441 7604.71 7273.03 2117.56 4974.71 2921.7 5480.8 1388.5 0 0 0 0 
 8158.02 8192.41 5355.73 3299 8528.31 7640.69 9044.2 9575.19 7604.32 8379.42 1879.11 6765.08 3262.07 1282.23 5249.3 4383.32 3909.23 4597.32 2259.49 6085.52 4310.92 2882.83 9997.02 3932.8 7650.38 725.181 5699.41 7477.46 1791.52 699.664 4571.7 7436.3 3021.04 6838.38 9412.58 1165.6 4073.03 2746.68 9803.46 3882.61 4870.29 9368.55 9198 6614.01 7475.68 3405.52 7287.69 963.071 7266.9 2615.77 6213.37 7418.89 1568.46 8384.27 1174.61 4394.57 4173.36 1925.76 8469.63 7947.81 7817.23 6204.07 2874.5 2809.98 2278.06 6041.19 2208.86 -2469.1 4786.26 2466.3 7701.24 3314.55 10875 7370.62 10232.4 3051.18 -40.5307 5388.12 3894.84 3667.98 7869.74 1921.25 7430.64 -1836.7 4236.84 3003.58 -457.256 7840.96 8662.68 8762.68 6343.06 1905.28 5863.77 3304.26 2178.82 4172.79 11425 2500.97 774.646 8751.31 83.3888 5518.26 5978.3 8155.19 3477.91 5843.86 11610.9 0 0 0 
 2799.3 1694.37 9277.43 1089.17 7392.8 1033.1 9325.02 8182.62 9923.37 6225.64 4133.68 8507.49 4098.21 9461.38 7121.61 1689.48 5909.86 231.921 6204.12 1474.78 4919.18 933.668 3308.88 9508.85 2973.75 8545.13 1694.94 2607.34 8463.17 8552.72 814.105 6335.42 9301.02 3874.26 7164.83 3605 10222.1 5363.67 4249.89 3609.24 2245.81 6174.79 6558 5212.04 2077.46 5640.42 7189.82 8356.56 7116.92 2007.39 2959.99 16.5791 -715.479 7723.39 5228.4 7615.48 5737.89 2580.98 11778.3 6725.69 4900.2 8675.26 5115.95 10489.3 2285.75 5458.34 7272.71 1672.82 5462.7 1177.5 1563 4083.49 12037.9 10305.5 829.099 2785.78 -2623.13 6074.35 4517.81 3532.53 6850.26 -789.104 1895.29 5110.97 2613.15 2787.85 2738.32 3481.87 8265.01 7641.09 6487.95 1159.06 7057.9 7771.02 1252.79 4931.36 3480.47 9774.69 5160.12 10310.8 2514.12 1400.09 676.831 2556.84 5534.9 3484.47 4318.13 6539.96 0 0 
 2397.35 7263.03 9898.15 1588.54 9974.16 4833.84 9453.78 9019.64 9334.39 6217.78 8886.34 6062.84 7598.17 5555.57 3366.92 6647.93 9854.1 5105.52 1586.05 1257.22 2488.62 3567.21 739.581 933.881 8334.33 2446.19 8079.53 9765.28 1823.11 5230.51 6082.65 4412.31 5120.9 9110.95 7814.5 3604.02 2344.65 4823.59 9356.48 5035.53 3996.25 3073.12 3010.48 449.151 4182.94 6661.98 8291.06 -2835.82 7109.02 2407.01 6869.09 1913.74 535.115 4008.97 6731.78 8963.06 10321.4 4729.16 10571.8 3762.8 8491.77 7072.81 2174.36 8962.66 9683.25 2774.1 3797.56 -741.221 4536.8 -2106.56 9539.15 3146.81 5752.94 5574.55 9973.96 3203.17 416.102 8014.02 3058.13 3904.15 9332.55 7156.51 1492.6 3832.43 3390.93 4937.38 1277.06 10281.5 1844.9 3713.31 4175.89 4419.71 360.974 3175 168.154 5919 8628.73 8183.9 3484.66 9276.41 6422.78 8136.92 3530.69 8226.99 8068.93 2239.68 5628.95 4131.07 9088.76 0 
 3008.77 2486.46 8855.13 5288.55 8922.03 9380.87 9101.98 5639.93 5654.7 467.858 9776.76 8167.05 190.767 8521.63 6138.36 3615.38 3133.13 9805.61 1987.89 3691.49 5921.28 7091.94 1835.98 4324.67 3480.39 5792.36 1592.88 4949.75 3578.11 7990.39 5608.97 1673.59 4946.99 162.628 2358.15 799.587 6400.5 5979.57 1390.56 8432.02 949.373 4466.27 6251.01 1290.56 407.48 4797.51 1574.14 899.731 7436.95 -144.47 6384.9 3571.59 708.511 1573.23 2260.55 2401.12 7437.89 2024.54 6983.22 4192.05 6668.98 7954.51 2155.44 13043.3 144.037 3665.29 3295.55 2319.55 3537.08 -3612.87 10471 5787.93 9482.75 6603.38 499.509 5091.59 3461.87 6065.51 9393.78 975.717 3165.61 9951.66 9008.86 -1636.56 1967.56 5185.22 550.013 7386.57 9792.29 3711.99 5711.51 -2437.42 3654.64 10193.4 4695.32 3047.84 6158 7238.78 3217.49 3211.18 3217.89 1957.53 5854.56 5410.15 6059.16 -443.003 5233.14 5059.37 6126.72 7994.14
  6. I wrote a routine called solveNormalEquation that computes the approximate solution of the least squares problem using the normal equation. My routine utilizes my cholesky. See my software manual entry.
  7. I wrote a routine called squareClassicalGramSchmidt which uses the Gram-Schmidt algorithm to compute the QR factorization of a matrix. See my software manual entry.
  8. I tested the squareClassicalGramSchmidt routine on Hilbert matrices for n = 4, 6, 8, 10. After each factorization, I computed matmul(Q, transpose(Q)) to verify how close to orthonormal Q was. The larger the Hilbert matrices, the further the result of matmul(Q, transpose(Q)) was from the identity, indicating that my factorization was less accurate. Below is my code and results: 
     std::cout << "Hilbert 4" << std::endl;
 DenseArray<double>* hil4 = new DenseArray<double>(4);
 hil4->makeHilbert();
 hil4->print();
 DenseArray<double>* Q_hil4 = new DenseArray<double>(4, 4, true);
 DenseArray<double>* R_hil4 = new DenseArray<double>(4, 4, true);
 squareClassicalGramSchmidt(*hil4, *Q_hil4, *R_hil4);
 std::cout << "Q_hil4 from Classical Gram Schmidt" << std::endl;
 Q_hil4->print();
 std::cout << "R_hil4 from Classical Gram Schmidt" << std::endl;
 R_hil4->print();
 std::cout << "Q_hil4 * transpose(Q_hil4)" << std::endl;
 Array<double>* QQThil4 = matmul(Q_hil4, transpose(Q_hil4));
 QQThil4->print();

 std::cout << "Hilbert 6" << std::endl;
 DenseArray<double>* hil6 = new DenseArray<double>(6);
 hil6->makeHilbert();
 hil6->print();
 DenseArray<double>* Q_hil6 = new DenseArray<double>(6, 6, true);
 DenseArray<double>* R_hil6 = new DenseArray<double>(6, 6, true);
 squareClassicalGramSchmidt(*hil6, *Q_hil6, *R_hil6);
 std::cout << "Q_hil6 from Classical Gram Schmidt" << std::endl;
 Q_hil6->print();
 std::cout << "R_hil6 from Classical Gram Schmidt" << std::endl;
 R_hil6->print();
 std::cout << "Q_hil6 * transpose(Q_hil6)" << std::endl;
 Array<double>* QQThil6 = matmul(Q_hil6, transpose(Q_hil6));
 QQThil6->print();

 std::cout << "Hilbert 8" << std::endl;
 DenseArray<double>* hil8 = new DenseArray<double>(8);
 hil8->makeHilbert();
 hil8->print();
 DenseArray<double>* Q_hil8 = new DenseArray<double>(8, 8, true);
 DenseArray<double>* R_hil8 = new DenseArray<double>(8, 8, true);
 squareClassicalGramSchmidt(*hil8, *Q_hil8, *R_hil8);
 std::cout << "Q_hil8 from Classical Gram Schmidt" << std::endl;
 Q_hil8->print();
 std::cout << "R_hil8 from Classical Gram Schmidt" << std::endl;
 R_hil8->print();
 std::cout << "Q_hil8 * transpose(Q_hil8)" << std::endl;
 Array<double>* QQThil8 = matmul(Q_hil8, transpose(Q_hil8));
 QQThil8->print();

 std::cout << "Hilbert 10" << std::endl;
 DenseArray<double>* hil10 = new DenseArray<double>(10);
 hil10->makeHilbert();
 hil10->print();
 DenseArray<double>* Q_hil10 = new DenseArray<double>(10, 10, true);
 DenseArray<double>* R_hil10 = new DenseArray<double>(10, 10, true);
 squareClassicalGramSchmidt(*hil10, *Q_hil10, *R_hil10);
 std::cout << "Q_hil10 from Classical Gram Schmidt" << std::endl;
 Q_hil10->print();
 std::cout << "R_hil10 from Classical Gram Schmidt" << std::endl;
 R_hil10->print();
 std::cout << "Q_hil10 * transpose(Q_hil10)" << std::endl;
 Array<double>* QQThil10 = matmul(Q_hil10, transpose(Q_hil10));
 QQThil10->print();

    Output from the code above:

     Hilbert 4
 1 0.5 0.333333 0.25 
 0.5 0.333333 0.25 0.2 
 0.333333 0.25 0.2 0.166667 
 0.25 0.2 0.166667 0.142857 
 Q_hil4 from Classical Gram Schmidt
 0.838116 -0.522648 0.153973 -0.0263067 
 0.419058 0.441713 -0.727754 0.31568 
 0.279372 0.528821 0.139506 -0.7892 
 0.209529 0.502072 0.653609 0.526134 
 R_hil4 from Classical Gram Schmidt
 1.19315 0.670493 0.474933 0.369835 
 0 0.118533 0.125655 0.117542 
 0 0 0.00622177 0.00956609 
 0 0 0 0.000187905 
 Q_hil4 * transpose(Q_hil4)
 1 2.30978e-12 -4.26429e-12 2.11242e-12 
 2.30978e-12 1 2.2206e-11 -5.93509e-12 
 -4.26429e-12 2.2206e-11 1 -1.61937e-11 
 2.11242e-12 -5.93509e-12 -1.61937e-11 1 
 Hilbert 6
 1 0.5 0.333333 0.25 0.2 0.166667 
 0.5 0.333333 0.25 0.2 0.166667 0.142857 
 0.333333 0.25 0.2 0.166667 0.142857 0.125 
 0.25 0.2 0.166667 0.142857 0.125 0.111111 
 0.2 0.166667 0.142857 0.125 0.111111 0.1 
 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 
 Q_hil6 from Classical Gram Schmidt
 0.81885 -0.539681 0.189261 -0.0482361 0.00902961 -0.00110541 
 0.409425 0.331988 -0.702417 0.448926 -0.161653 0.0331574 
 0.27295 0.421935 -0.152933 -0.572323 0.58539 -0.232076 
 0.204713 0.406725 0.201513 -0.38664 -0.468685 0.618816 
 0.16377 0.373526 0.396261 0.0915169 -0.428541 -0.69612 
 0.136475 0.339931 0.499772 0.557422 0.477276 0.278432 
 R_hil6 from Classical Gram Schmidt
 1.22122 0.701872 0.50447 0.396969 0.328434 0.280613 
 0 0.138467 0.15113 0.144364 0.134008 0.123669 
 0 0 0.00956161 0.0151932 0.0181303 0.0195317 
 0 0 0 0.000480282 0.000994238 0.0014191 
 0 0 0 0 1.7339e-05 4.40307e-05 
 0 0 0 0 0 3.98624e-07 
 Q_hil6 * transpose(Q_hil6)
 1 -2.25328e-08 1.29756e-07 -2.87325e-07 2.70119e-07 -9.0616e-08 
 -2.25328e-08 1 -2.77994e-06 5.6402e-06 -4.74311e-06 1.37215e-06 
 1.29756e-07 -2.77994e-06 1.00001 -2.35596e-05 1.5268e-05 -2.42751e-06 
 -2.87325e-07 5.6402e-06 -2.35596e-05 1.00003 -3.30938e-06 -8.48711e-06 
 2.70119e-07 -4.74311e-06 1.5268e-05 -3.30938e-06 0.99997 2.30261e-05 
 -9.0616e-08 1.37215e-06 -2.42751e-06 -8.48711e-06 2.30261e-05 0.999986 
 Hilbert 8
 1 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 
 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111 
 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1 
 0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 
 0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 
 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 
 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 
 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 
 Q_hil8 from Classical Gram Schmidt
 0.809134 -0.546655 0.206392 -0.0604753 0.0144143 -0.00277652 8.32896e-05 -6.14669e-05 
 0.404567 0.28253 -0.67657 0.493355 -0.223607 0.0713523 -0.007408 0.0068354 
 0.269711 0.373639 -0.24129 -0.427368 0.613506 -0.385459 0.0959512 -0.0927811 
 0.202284 0.363608 0.0543266 -0.451867 -0.110896 0.592018 -0.398529 0.393427 
 0.161827 0.335355 0.222629 -0.212438 -0.448134 0.0757814 0.58027 -0.580522 
 0.134856 0.305932 0.316135 0.0579406 -0.335968 -0.442761 -0.00552749 0.00950489 
 0.115591 0.279243 0.366918 0.293215 0.0291512 -0.331778 -0.611583 0.613348 
 0.101142 0.255918 0.392873 0.481305 0.496545 0.428929 0.348044 -0.351095 
 R_hil8 from Classical Gram Schmidt
 1.23589 0.71923 0.521442 0.413013 0.343473 0.294696 0.258423 0.230313 
 0 0.149919 0.166512 0.161161 0.151153 0.140662 0.13084 0.121966 
 0 0 0.0118284 0.0191923 0.0232833 0.0254209 0.0264065 0.0267049 
 0 0 0 0.000731517 0.00154947 0.00225333 0.00280789 0.00322702 
 0 0 0 0 3.61918e-05 9.41426e-05 0.000159206 0.000222793 
 0 0 0 0 0 1.41303e-06 4.33923e-06 8.35336e-06 
 0 0 0 0 0 0 4.18719e-08 1.58146e-06 
 0 0 0 0 0 0 0 1.43472e-06 
 Q_hil8 * transpose(Q_hil8)
 1 5.67991e-06 -4.70417e-05 0.000146183 -0.000173575 6.56806e-06 0.000128109 -6.58116e-05 
 5.67991e-06 0.999837 0.00105358 -0.00243879 0.00213228 -0.000670323 0.000603913 -0.000532657 
 -4.70417e-05 0.00105358 0.995997 -0.00055469 0.0114152 0.012774 -0.0481504 0.027679 
 0.000146183 -0.00243879 -0.00055469 1.05666 -0.102327 -0.0894116 0.297747 -0.160596 
 -0.000173575 0.00213228 0.0114152 -0.102327 1.11363 0.290771 -0.617404 0.303173 
 6.56806e-06 -0.000670323 0.012774 -0.0894116 0.290771 0.524112 0.380317 -0.117976 
 0.000128109 0.000603913 -0.0481504 0.297747 -0.617404 0.380317 1.1731 -0.187603 
 -6.58116e-05 -0.000532657 0.027679 -0.160596 0.303173 -0.117976 -0.187603 1.13667 
 Hilbert 10
 1 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1 
 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 
 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 
 0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 
 0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 
 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 
 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 0.0625 
 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 0.0625 0.0588235 
 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 0.0625 0.0588235 0.0555556 
 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 0.0625 0.0588235 0.0555556 0.0526316 
 Q_hil10 from Classical Gram Schmidt
 0.80328 -0.55033 0.216481 -0.0682831 0.0182675 -0.00418892 0.00102396 0.000979483 0.000950891 0.000921123 
 0.40164 0.254417 -0.657679 0.51362 -0.259222 0.0976859 -0.0336862 -0.0326299 -0.0319398 -0.0312132 
 0.26776 0.346139 -0.280854 -0.339936 0.59766 -0.449889 0.242857 0.23785 0.23447 0.230825 
 0.20082 0.339042 -0.0158501 -0.441101 0.057403 0.471067 -0.572405 -0.566515 -0.562022 -0.556763 
 0.160656 0.3136 0.138397 -0.297418 -0.315083 0.309612 0.269661 0.271463 0.271461 0.270486 
 0.13388 0.286551 0.226325 -0.108015 -0.386287 -0.128836 0.416236 0.415534 0.415375 0.415434 
 0.114754 0.261827 0.275879 0.0658122 -0.263812 -0.376578 -0.00674839 -0.00958886 -0.0105234 -0.0107279 
 0.10041 0.240132 0.302857 0.209404 -0.0460717 -0.328878 -0.378704 -0.382817 -0.38561 -0.388608 
 0.0892533 0.221296 0.31625 0.322969 0.205626 -0.0274597 -0.300742 -0.302687 -0.304931 -0.308106 
 0.080328 0.204944 0.321313 0.41084 0.457693 0.450501 0.363812 0.369867 0.374323 0.379409 
 R_hil10 from Classical Gram Schmidt
 1.2449 0.730254 0.532477 0.423641 0.353591 0.304294 0.267524 0.23895 0.216054 0.197267 
 0 0.157357 0.176816 0.172683 0.16314 0.152733 0.142791 0.133686 0.125472 0.118095 
 0 0 0.0134548 0.022149 0.0271856 0.0299697 0.0313865 0.0319636 0.0320187 0.0317474 
 0 0 0 0.000938887 0.00202152 0.00298003 0.00375637 0.00435984 0.00481744 0.00515741 
 0 0 0 0 5.49241e-05 0.000145408 0.000249603 0.000353809 0.000450912 0.000537824 
 0 0 0 0 0 2.69847e-06 8.45658e-06 1.653e-05 2.5999e-05 3.60845e-05 
 0 0 0 0 0 0 1.10345e-07 -8.07566e-07 -9.20326e-07 -8.96876e-07 
 0 0 0 0 0 0 0 1.20503e-06 -5.93595e-07 -4.51496e-07 
 0 0 0 0 0 0 0 0 2.38436e-06 -1.53066e-07 
 0 0 0 0 0 0 0 0 0 3.00489e-06 
 Q_hil10 * transpose(Q_hil10)
 1 -0.000101151 0.000727124 -0.00169472 0.000733702 0.00130976 3.90465e-05 -0.00118185 -0.000988761 0.00115789 
 -0.000101151 1.00332 -0.0237896 0.0550142 -0.0226034 -0.0439185 -0.00212349 0.0393043 0.0334207 -0.03866 
 0.000727124 -0.0237896 1.16935 -0.386146 0.142337 0.328488 0.024387 -0.288953 -0.25051 0.285086 
 -0.00169472 0.0550142 -0.386146 1.84974 -0.215961 -0.853177 -0.0929421 0.71357 0.630889 -0.701612 
 0.000733702 -0.0226034 0.142337 -0.215961 0.720166 0.706814 0.0755002 -0.432071 -0.371224 0.397473 
 0.00130976 -0.0439185 0.328488 -0.853177 0.706814 1.01978 0.280522 -0.449972 -0.469456 0.481212 
 3.90465e-05 -0.00212349 0.024387 -0.0929421 0.0755002 0.280522 0.373933 0.322184 0.144226 -0.125845 
 -0.00118185 0.0393043 -0.288953 0.71357 -0.432071 -0.449972 0.322184 0.903278 0.692152 -0.499776 
 -0.000988761 0.0334207 -0.25051 0.630889 -0.371224 -0.469456 0.144226 0.692152 0.674275 -0.0838388 
 0.00115789 -0.03866 0.285086 -0.701612 0.397473 0.481212 -0.125845 -0.499776 -0.0838388 1.28615
  9. I implemented a method called makeRandomDD on my DenseArray class template that makes the class instance from which it is called a square diagonally dominant matrix. See my software manual entry.
    • I read an article from a scientific computing company called COMSOL at https://www.comsol.com/blogs/solutions-linear-systems-equations-direct-iterative-solvers/. The article discusses the differences between their direct and iterative solvers for linear systems of equations and some of their advantages and disadvantages. One of the disadvantages of their direct solvers that they list is that if the problem does not have an exact solution, the method will fail. Interestingly, they state that their iterative methods take much more RAM and are generally more robust.
    • I read an article from SimScale, a scientific and engineering simulation software company, at https://www.simscale.com/blog/2016/08/how-to-choose-solvers-for-fem/. The website discusses iterative versus direct methods for finite element analysis (FEA). The article states that direct methods will typically fail when the matrices being dealt with become too large. For example, it discusses how matrices with dimensions in the millions could require ExaFlops of computation when direct methods are used. Another disadvantage of direct methods that it states is that they do not efficiently handle sparse matrices.