積分過程（分子動力学シミュレーションの本体部分）

いよいよ分子動力学シミュレーションの本体を実装する段階に到達しました。分子動力学シミュレーションでは、仮定した力を受ける粒子の新しい位置・速度を計算するプロセスは言い換えれば時間の刻み$\Delta t$で積分をしていく過程です。ダフィング振動子のプログラムで利用したベルレのアルゴリズムを少し変形した「速度ベルレのアルゴリズム」を用いると、ある時間$t$から$\Delta t$後の位置$x(t+\Delta t)$と速度$v(t+\Delta t)$は次式で表されます。

$$x(t+\Delta t) = x(t) + v(t)\Delta t + \frac{F(t)}{2}\Delta t^2$$ (6)

$$v(t+\Delta t) = v(t) + \frac{F(t+ \Delta t) + F(t)}{2}\Delta t$$ (7)

これまでのプロセスで時間t = 0における $x(0), v(0), F(0)$は計算済みである。従って、こられの値から全ての粒子の新しい位置$x(0+\Delta t)$が計算される。新しい速度を計算するためには、$F(0+\Delta t)$が必要であるが、これは新しい位置$x(0+\Delta t)$を利用して計算することができる。よって、新しい速度$v(0+\Delta t)$も計算できる。この結果得られる新しい位置と速度 $x(\Delta t), v(\Delta t)$を初期配置と置き換えることにより続いて $x(2\Delta t), v(2\Delta t)$、さらには $x(3\Delta t), v(3\Delta t)$と積分を続けていくことが可能となる。

後は、必要な時間だけ積分を繰り返していけば良いが、以下に幾つかの注意事項をまとめる。

1. 位置を更新すると境界近傍にある粒子の座標値がマイナス、もしくは、格子定数よりも大きい領域に飛び出す可能性がある。従って、位置を更新した際にそのような状況になる場合は周期的境界条件を適用して適正な座標内に戻す必要がある。
2. 「速度ベルレのアルゴリズム」はテーラー展開から得られているものであり$\Delta t$を小さくとることにより良い積分となる。しかし、$\Delta t$を小さく取りすぎると一定の時間に関する計算を完了するたに必要な計算時間が膨大となる。そこで、 $\epsilon = 1, \sigma = 1, m = 1$としている今回の場合には $\Delta t = 0.004$とすると良い結果が得られる。
3. 計算の初期段階においては、乱数とリスケールにより与えた運動エネルギーが適正でないため、場合によっては粒子が遠くに飛んでいってしまう場合がある。そこで、2000ステップに達するまでは10回に一度速度のリスケールを行う。1000ステップ経過後には配置と速度がある程度適正化されているのでそれ以降は速度をリスケールする必要はない。
4. 計算ステップの総数は2500ステップとし、5回に一度粒子の配置$(x, y)$と速度$(v_x, v_y)$を出力すること。結果の出力例を以下に示す。

出力例（1行目は経過時間、2行目以降が座標・速度データ $(x, y, v_x, v_y)$の順）

0.000000
  3.325e-01   3.395e-01   1.675e+00   1.014e+00
  1.016e+00   1.009e+00   1.772e+00   1.567e-01
  3.410e-01   1.686e+00   9.483e-01   3.637e+00
  1.004e+00   2.360e+00   2.950e+00   9.871e+00
  3.435e-01   3.041e+00   5.361e+00   2.578e+01
  1.005e+00   3.710e+00   2.401e+00   1.173e+01
  3.364e-01   4.383e+00   6.150e-02   5.327e+00
  1.015e+00   5.062e+00   3.243e+00   1.740e+01
  3.338e-01   5.732e+00   7.395e-01   7.836e+00
  1.017e+00   6.409e+00   3.258e+00   1.503e+01
  3.397e-01   7.083e+00   1.279e+00   1.109e+00
  1.011e+00   7.756e+00   5.891e-01   1.797e+00
  3.371e-01   8.425e+00   4.400e-01   7.760e-01
  1.010e+00   9.101e+00   1.115e-01   2.049e+00
  3.380e-01   9.778e+00   3.074e-01   2.048e+00
  1.007e+00   1.045e+01   2.300e+00   8.854e+00
  3.370e-01   1.112e+01   1.913e+00   7.113e+00
  1.011e+00   1.179e+01   2.537e+00   2.435e+00
  3.435e-01   1.248e+01   4.561e+00   1.786e+01
  1.006e+00   1.314e+01   2.554e+00   2.090e+01
  1.692e+00   3.342e-01   3.319e+00   7.894e+00
  2.360e+00   1.009e+00   5.117e-01   5.092e+00
  1.686e+00   1.690e+00   1.188e+00   1.189e+00
  2.354e+00   2.364e+00   3.591e+00   7.857e+00
  1.685e+00   3.041e+00   3.005e+00   1.185e+01
  2.359e+00   3.702e+00   2.092e+00   4.565e+00
  1.685e+00   4.385e+00   4.716e-01   2.358e+00
  2.362e+00   5.055e+00   3.133e-01   9.172e-01
  1.681e+00   5.725e+00   3.662e+00   1.427e+01
  2.354e+00   6.407e+00   2.225e+00   5.514e+00
  1.683e+00   7.074e+00   1.906e+00   1.760e+01
  2.365e+00   7.751e+00   1.941e+00   3.151e+00
  1.680e+00   8.431e+00   2.245e+00   7.760e+00
  2.353e+00   9.101e+00   2.775e+00   4.237e+00
  1.691e+00   9.774e+00   2.358e+00   8.387e+00
  2.367e+00   1.045e+01   3.780e+00   6.834e+00
  1.686e+00   1.112e+01   3.928e-02   3.145e+00
  2.365e+00   1.180e+01   1.700e+00   4.932e+00
  1.689e+00   1.247e+01   1.302e+00   3.424e+00
  2.357e+00   1.315e+01   4.472e-01   6.101e+00
  3.031e+00   3.410e-01   1.360e+00   1.176e+01
  3.705e+00   1.006e+00   2.555e+00   8.245e+00
  3.030e+00   1.686e+00   8.525e-01   6.895e-01
  3.711e+00   2.359e+00   5.841e-01   5.703e-01
  3.040e+00   3.041e+00   5.268e+00   4.274e+00
  3.713e+00   3.715e+00   4.603e+00   5.558e+00
  3.029e+00   4.378e+00   2.266e+00   6.536e-01
  3.712e+00   5.050e+00   3.276e+00   7.428e+00
  3.037e+00   5.731e+00   4.319e-01   2.122e-01
  3.714e+00   6.400e+00   3.562e+00   8.629e+00
  3.040e+00   7.078e+00   2.589e+00   2.351e+00
  3.705e+00   7.760e+00   3.364e+00   7.418e+00
  3.036e+00   8.435e+00   3.674e+00   9.641e+00
  3.706e+00   9.096e+00   2.202e+00   1.580e+01
  3.028e+00   9.770e+00   4.507e+00   1.320e+01
  3.713e+00   1.046e+01   4.296e+00   1.093e+01
  3.039e+00   1.113e+01   1.526e+00   8.923e-01
  3.714e+00   1.180e+01   2.332e+00   6.975e+00
  3.034e+00   1.247e+01   1.166e+00   4.626e+00
  3.712e+00   1.314e+01   1.607e+00   9.696e+00
  4.379e+00   3.402e-01   1.298e+00   1.997e+00
  5.051e+00   1.014e+00   2.101e+00   6.262e+00
  4.383e+00   1.683e+00   3.689e-01   2.550e+00
  5.050e+00   2.365e+00   4.120e+00   2.714e+01
  4.388e+00   3.032e+00   2.477e+00   1.742e+01
  5.057e+00   3.705e+00   7.902e-01   4.888e+00
  4.378e+00   4.383e+00   1.227e+00   1.743e+01
  5.052e+00   5.061e+00   2.700e+00   3.288e+00
  4.380e+00   5.736e+00   2.030e+00   6.529e+00
  5.052e+00   6.409e+00   2.197e+00   1.990e+01
  4.389e+00   7.076e+00   3.587e+00   2.333e+01
  5.052e+00   7.756e+00   2.100e+00   5.475e+00
  4.389e+00   8.429e+00   2.735e+00   5.540e+00
  5.055e+00   9.103e+00   2.512e-01   2.734e-01
  4.386e+00   9.778e+00   1.365e+00   3.057e+00
  5.064e+00   1.045e+01   3.137e+00   5.725e+00
  4.382e+00   1.113e+01   3.204e+00   1.531e+01
  5.052e+00   1.180e+01   1.164e+00   6.390e+00
  4.378e+00   1.247e+01   9.754e-01   2.108e+00
  5.051e+00   1.315e+01   1.838e+00   2.041e+00
  5.732e+00   3.381e-01   1.307e-01   1.157e+00
  6.407e+00   1.017e+00   2.414e+00   1.233e+01
  5.736e+00   1.682e+00   2.417e+00   2.141e+01
  6.398e+00   2.354e+00   4.911e+00   1.394e+01
  5.736e+00   3.041e+00   5.230e+00   1.570e+01
  6.400e+00   3.708e+00   1.387e+00   1.029e+01
  5.733e+00   4.382e+00   2.258e-01   5.902e+00
  6.403e+00   5.057e+00   3.073e-01   3.609e+00
  5.731e+00   5.725e+00   1.876e+00   8.600e+00
  6.403e+00   6.405e+00   2.567e-01   1.591e+00
  5.723e+00   7.074e+00   5.077e+00   9.117e+00
  6.403e+00   7.755e+00   4.042e-01   1.020e+00
  5.726e+00   8.426e+00   1.762e+00   5.149e+00
  6.409e+00   9.107e+00   2.480e+00   1.530e+01
  5.730e+00   9.771e+00   1.492e+00   8.055e-01
  6.398e+00   1.045e+01   4.188e+00   5.731e+00
  5.726e+00   1.113e+01   1.836e+00   3.805e+00
  6.410e+00   1.180e+01   2.354e+00   2.922e-01
  5.736e+00   1.247e+01   1.787e+00   5.911e+00
  6.403e+00   1.315e+01   4.055e-01   2.304e+00
  7.083e+00   3.306e-01   3.396e+00   3.063e+00
  7.751e+00   1.015e+00   1.524e+00   1.404e+00
  7.078e+00   1.691e+00   1.961e+00   5.607e-01
  7.747e+00   2.365e+00   3.726e+00   1.038e+01
  7.082e+00   3.034e+00   6.613e-01   1.354e+01
  7.748e+00   3.714e+00   3.809e+00   1.058e+01
  7.079e+00   4.379e+00   6.120e-01   7.106e+00
  7.753e+00   5.058e+00   1.010e-01   2.985e+00
  7.082e+00   5.726e+00   1.813e+00   4.665e+00
  7.753e+00   6.406e+00   4.338e-02   1.725e+00
  7.079e+00   7.085e+00   1.962e+00   9.196e-01
  7.755e+00   7.759e+00   2.112e+00   1.482e+00
  7.086e+00   8.425e+00   3.627e+00   1.171e+01
  7.750e+00   9.102e+00   6.856e-01   4.037e+00
  7.081e+00   9.771e+00   1.671e+00   1.458e+01
  7.749e+00   1.045e+01   1.898e+00   5.218e+00
  7.080e+00   1.112e+01   2.735e+00   3.181e+00
  7.753e+00   1.179e+01   2.439e+00   2.099e+00
  7.080e+00   1.248e+01   3.869e+00   7.089e+00
  7.758e+00   1.314e+01   1.846e+00   5.724e-01
  8.425e+00   3.306e-01   3.024e+00   7.942e+00
  9.098e+00   1.011e+00   7.472e-01   1.103e+00
  8.429e+00   1.688e+00   4.313e-01   2.251e+00
  9.107e+00   2.361e+00   1.553e+00   3.989e+00
  8.428e+00   3.034e+00   1.293e-02   2.031e+00
  9.098e+00   3.706e+00   1.147e+00   4.799e+00
  8.422e+00   4.381e+00   1.709e+00   7.672e+00
  9.106e+00   5.063e+00   3.726e+00   6.542e+00
  8.425e+00   5.728e+00   1.058e+00   2.714e+00
  9.099e+00   6.408e+00   1.035e+00   2.512e+00
  8.420e+00   7.080e+00   3.475e+00   3.540e+00
  9.102e+00   7.754e+00   2.999e-02   4.514e+00
  8.431e+00   8.430e+00   1.272e+00   2.330e+00
  9.100e+00   9.099e+00   7.998e-01   4.631e+00
  8.423e+00   9.776e+00   1.433e+00   9.919e-02
  9.099e+00   1.045e+01   8.316e-01   4.699e+00
  8.432e+00   1.112e+01   2.530e+00   2.352e+00
  9.106e+00   1.180e+01   1.117e+00   5.010e-01
  8.433e+00   1.247e+01   2.548e+00   1.181e+00
  9.101e+00   1.315e+01   2.077e-01   1.224e+00
  9.776e+00   3.339e-01   6.196e-01   2.092e+00
  1.045e+01   1.006e+00   2.537e+00   2.935e+00
  9.772e+00   1.690e+00   1.866e+00   1.196e+01
  1.045e+01   2.364e+00   1.387e+00   5.186e+00
  9.782e+00   3.033e+00   2.402e+00   8.716e+00
  1.046e+01   3.703e+00   3.027e+00   5.976e+00
  9.781e+00   4.382e+00   1.758e+00   2.779e+00
  1.045e+01   5.056e+00   6.675e-01   2.265e+00
  9.777e+00   5.737e+00   2.759e+00   1.573e+00
  1.045e+01   6.405e+00   2.210e-01   7.967e-01
  9.775e+00   7.075e+00   1.286e+00   3.504e+00
  1.045e+01   7.751e+00   1.597e+00   3.512e+00
  9.775e+00   8.421e+00   2.766e+00   6.221e+00
  1.046e+01   9.100e+00   2.108e+00   7.215e+00
  9.780e+00   9.772e+00   1.634e+00   1.176e+00
  1.045e+01   1.045e+01   2.371e+00   1.068e+01
  9.773e+00   1.112e+01   2.083e+00   2.138e+00
  1.045e+01   1.180e+01   5.224e-01   6.930e+00
  9.781e+00   1.248e+01   3.424e+00   7.591e+00
  1.045e+01   1.315e+01   3.204e-01   5.622e+00
  1.113e+01   3.316e-01   2.702e+00   4.050e+00
  1.180e+01   1.010e+00   4.245e-02   6.772e-01
  1.112e+01   1.690e+00   2.539e+00   3.349e+00
  1.179e+01   2.355e+00   2.400e+00   3.077e+00
  1.112e+01   3.030e+00   3.196e+00   1.828e+01
  1.180e+01   3.713e+00   3.379e+00   6.679e+00
  1.113e+01   4.381e+00   3.003e+00   4.679e+00
  1.180e+01   5.052e+00   2.023e+00   5.191e+00
  1.112e+01   5.726e+00   3.085e+00   7.845e+00
  1.180e+01   6.401e+00   1.268e+00   6.039e+00
  1.112e+01   7.075e+00   2.193e+00   1.030e+01
  1.181e+01   7.755e+00   3.062e+00   1.127e+01
  1.112e+01   8.430e+00   3.760e+00   1.662e+01
  1.179e+01   9.102e+00   1.201e+00   5.656e+00
  1.113e+01   9.774e+00   3.253e+00   1.466e+01
  1.180e+01   1.045e+01   8.057e-01   4.568e+00
  1.112e+01   1.112e+01   2.364e+00   1.264e+01
  1.180e+01   1.180e+01   3.003e+00   7.371e+00
  1.112e+01   1.247e+01   1.354e+00   1.474e+00
  1.179e+01   1.315e+01   1.144e+00   7.405e+00
  1.248e+01   3.380e-01   2.867e+00   1.077e+01
  1.314e+01   1.014e+00   7.992e-01   3.454e+00
  1.247e+01   1.681e+00   1.790e+00   5.417e+00
  1.314e+01   2.354e+00   2.221e+00   9.034e+00
  1.247e+01   3.034e+00   1.129e+00   2.228e+00
  1.314e+01   3.713e+00   3.115e+00   5.057e+00
  1.248e+01   4.386e+00   1.509e+00   2.186e-01
  1.314e+01   5.062e+00   4.139e+00   3.644e+00
  1.247e+01   5.731e+00   2.093e+00   2.464e+00
  1.315e+01   6.400e+00   2.797e+00   8.912e+00
  1.247e+01   7.080e+00   1.166e-01   3.546e+00
  1.315e+01   7.757e+00   6.459e-01   1.112e+00
  1.247e+01   8.430e+00   6.245e-01   1.322e+00
  1.315e+01   9.102e+00   9.460e-01   5.642e-01
  1.247e+01   9.775e+00   3.786e-01   2.119e+00
  1.315e+01   1.045e+01   1.306e-02   2.296e+00
  1.247e+01   1.112e+01   1.755e+00   3.740e+00
  1.314e+01   1.181e+01   4.826e+00   1.178e+01
  1.247e+01   1.247e+01   1.573e-01   4.955e+00
  1.314e+01   1.315e+01   2.941e+00   1.141e+01
0.020000
  3.101e-01   3.515e-01   1.517e+00   2.971e+01
  1.041e+00   9.998e-01   1.750e+00   3.423e+00
  3.598e-01   1.687e+00   7.854e-01   1.808e+02
  9.717e-01   2.364e+00   2.338e+00   3.087e+02
  3.727e-01   3.073e+00   3.916e+00   1.083e+03
  9.770e-01   3.718e+00   1.864e+00   8.638e+02
  3.324e-01   4.387e+00   1.445e-01   1.319e+02
  1.034e+00   5.090e+00   2.026e+00   1.595e+03
  3.191e-01   5.737e+00   4.073e-01   4.267e+02
  1.045e+00   6.428e+00   2.195e+00   9.750e+02
  3.521e-01   7.101e+00   1.127e+00   3.339e+01
  1.013e+00   7.771e+00   4.834e-01   6.642e+01
  3.375e-01   8.412e+00   3.576e-01   3.502e+01
  1.005e+00   9.097e+00   1.017e-01   9.076e+01
  3.416e-01   9.788e+00   1.893e-01   1.482e+02
  9.885e-01   1.042e+01   1.777e+00   3.742e+02
  3.359e-01   1.109e+01   1.565e+00   1.314e+02
  1.008e+00   1.176e+01   2.231e+00   7.416e+01
  3.734e-01   1.251e+01   3.007e+00   1.648e+03
  9.816e-01   1.313e+01   1.411e+00   1.734e+03
  1.724e+00   3.199e-01   2.684e+00   2.921e+02
  2.363e+00   9.956e-01   3.096e-01   2.234e+02
  1.689e+00   1.711e+00   1.029e+00   5.130e+01
  2.325e+00   2.388e+00   3.262e+00   1.833e+02
  1.683e+00   3.075e+00   2.606e+00   5.083e+02
  2.354e+00   3.675e+00   1.638e+00   2.341e+02
  1.685e+00   4.398e+00   3.532e-01   5.168e+01
  2.371e+00   5.049e+00   2.680e-01   3.136e+01
  1.659e+00   5.696e+00   2.390e+00   1.486e+03
  2.327e+00   6.416e+00   1.787e+00   2.091e+02
  1.669e+00   7.053e+00   1.078e+00   1.119e+03
  2.390e+00   7.742e+00   1.700e+00   3.946e+01
  1.656e+00   8.446e+00   1.768e+00   1.955e+02
  2.321e+00   9.099e+00   2.412e+00   3.351e+02
  1.719e+00   9.764e+00   1.722e+00   4.776e+02
  2.400e+00   1.043e+01   3.171e+00   2.672e+02
  1.690e+00   1.112e+01   9.141e-02   7.627e+01
  2.389e+00   1.181e+01   1.378e+00   2.408e+02
  1.704e+00   1.245e+01   1.128e+00   8.692e+01
  2.346e+00   1.314e+01   3.019e-01   2.780e+02
  3.019e+00   3.588e-01   9.204e-01   4.204e+02
  3.688e+00   9.800e-01   1.995e+00   3.311e+02
  3.012e+00   1.686e+00   8.006e-01   1.764e+01
  3.725e+00   2.354e+00   5.139e-01   1.481e+01
  3.070e+00   3.075e+00   4.880e+00   8.085e+01
  3.739e+00   3.748e+00   3.737e+00   4.754e+02
  3.007e+00   4.359e+00   2.124e+00   2.382e+01
  3.727e+00   5.019e+00   2.523e+00   4.846e+02
  3.049e+00   5.731e+00   3.979e-01   4.088e+00
  3.744e+00   6.380e+00   2.591e+00   8.609e+02
  3.072e+00   7.074e+00   2.530e+00   4.558e+01
  3.690e+00   7.792e+00   3.001e+00   1.057e+02
  3.043e+00   8.471e+00   3.001e+00   7.371e+02
  3.696e+00   9.070e+00   1.433e+00   8.754e+02
  2.998e+00   9.741e+00   3.907e+00   3.006e+02
  3.740e+00   1.049e+01   3.638e+00   1.675e+02
  3.062e+00   1.113e+01   1.372e+00   3.396e+01
  3.741e+00   1.179e+01   1.674e+00   5.364e+02
  3.034e+00   1.245e+01   9.138e-01   2.336e+02
  3.732e+00   1.313e+01   1.112e+00   3.336e+02
  4.363e+00   3.552e-01   1.060e+00   9.716e+01
  5.027e+00   1.026e+00   1.588e+00   2.870e+02
  4.387e+00   1.672e+00   2.753e-01   1.415e+02
  5.022e+00   2.390e+00   2.642e+00   1.464e+03
  4.415e+00   3.022e+00   1.467e+00   1.346e+03
  5.061e+00   3.688e+00   5.535e-01   1.430e+02
  4.358e+00   4.384e+00   5.647e-01   1.173e+03
  5.028e+00   5.082e+00   2.456e+00   7.153e+01
  4.369e+00   5.760e+00   1.361e+00   7.196e+02
  5.030e+00   6.425e+00   1.327e+00   1.254e+03
  4.421e+00   7.061e+00   2.343e+00   1.174e+03
  5.028e+00   7.771e+00   1.609e+00   2.957e+02
  4.419e+00   8.439e+00   2.194e+00   3.228e+02
  5.048e+00   9.110e+00   2.236e-01   1.394e+01
  4.406e+00   9.790e+00   1.166e+00   5.634e+01
  5.098e+00   1.045e+01   2.633e+00   1.472e+02
  4.380e+00   1.117e+01   2.342e+00   7.695e+02
  5.032e+00   1.180e+01   9.928e-01   2.557e+02
  4.359e+00   1.247e+01   7.694e-01   1.357e+02
  5.026e+00   1.314e+01   1.608e+00   4.963e+01
  5.737e+00   3.433e-01   1.236e-01   2.457e+01
  6.418e+00   1.045e+00   1.950e+00   4.600e+02
  5.760e+00   1.666e+00   1.638e+00   8.773e+02
  6.366e+00   2.326e+00   3.847e+00   5.943e+02
  5.763e+00   3.076e+00   3.865e+00   9.289e+02
  6.379e+00   3.711e+00   8.529e-01   7.539e+02
  5.741e+00   4.380e+00   1.061e-01   1.630e+02
  6.394e+00   5.062e+00   1.760e-01   1.473e+02
  5.734e+00   5.699e+00   1.428e+00   2.375e+02
  6.393e+00   6.404e+00   1.937e-01   2.600e+01
  5.687e+00   7.049e+00   4.216e+00   3.550e+02
  6.394e+00   7.764e+00   4.341e-01   1.223e+01
  5.701e+00   8.420e+00   1.478e+00   9.688e+01
  6.426e+00   9.131e+00   1.767e+00   4.803e+02
  5.724e+00   9.748e+00   1.345e+00   3.476e+01
  6.362e+00   1.047e+01   3.786e+00   9.146e+01
  5.702e+00   1.114e+01   1.803e+00   1.777e+02
  6.436e+00   1.178e+01   2.263e+00   1.051e+01
  5.761e+00   1.248e+01   1.415e+00   2.241e+02
  6.392e+00   1.314e+01   3.064e-01   1.283e+02
  7.099e+00   2.987e-01   3.049e+00   5.087e+01
  7.737e+00   1.035e+00   1.363e+00   2.563e+01
  7.070e+00   1.718e+00   1.827e+00   2.354e+01
  7.719e+00   2.388e+00   2.811e+00   5.539e+02
  7.097e+00   3.033e+00   3.123e-01   5.765e+02
  7.721e+00   3.740e+00   2.911e+00   5.081e+02
  7.077e+00   4.365e+00   4.054e-01   4.314e+02
  7.754e+00   5.063e+00   3.608e-02   1.325e+02
  7.094e+00   5.703e+00   1.433e+00   1.650e+02
  7.752e+00   6.409e+00   3.696e-02   6.737e+01
  7.081e+00   7.112e+00   1.806e+00   2.124e+01
  7.766e+00   7.785e+00   1.943e+00   1.566e+02
  7.119e+00   8.410e+00   2.705e+00   5.556e+02
  7.734e+00   9.100e+00   4.778e-01   1.833e+02
  7.087e+00   9.748e+00   1.073e+00   5.293e+02
  7.729e+00   1.047e+01   1.365e+00   4.342e+02
  7.081e+00   1.109e+01   2.319e+00   3.184e+02
  7.750e+00   1.176e+01   2.199e+00   3.389e+01
  7.083e+00   1.252e+01   3.232e+00   1.944e+02
  7.780e+00   1.313e+01   1.954e+00   3.908e+01
  8.412e+00   2.997e-01   2.397e+00   3.088e+02
  9.081e+00   1.009e+00   6.917e-01   2.629e+01
  8.435e+00   1.700e+00   4.792e-01   4.404e+01
  9.130e+00   2.367e+00   1.320e+00   2.294e+02
  8.429e+00   3.033e+00   3.409e-03   5.954e+01
  9.080e+00   3.696e+00   8.694e-01   1.249e+02
  8.398e+00   4.375e+00   1.326e+00   1.606e+02
  9.125e+00   5.096e+00   3.241e+00   1.078e+02
  8.411e+00   5.713e+00   8.425e-01   9.695e+01
  9.084e+00   6.422e+00   1.086e+00   7.907e+01
  8.384e+00   7.087e+00   3.056e+00   1.175e+02
  9.105e+00   7.754e+00   6.301e-03   1.698e+02
  8.450e+00   8.441e+00   1.002e+00   1.464e+02
  9.090e+00   9.085e+00   5.246e-01   2.479e+02
  8.399e+00   9.778e+00   1.401e+00   2.011e+00
  9.087e+00   1.043e+01   8.982e-01   1.883e+02
  8.454e+00   1.110e+01   2.166e+00   1.182e+02
  9.126e+00   1.179e+01   1.150e+00   9.481e+00
  8.458e+00   1.245e+01   2.394e+00   2.896e+01
  9.100e+00   1.316e+01   1.399e-01   5.064e+01
  9.775e+00   3.189e-01   4.777e-01   6.522e+01
  1.047e+01   9.815e-01   2.281e+00   3.402e+01
  9.757e+00   1.710e+00   1.286e+00   3.869e+02
  1.044e+01   2.383e+00   1.007e+00   4.065e+02
  9.811e+00   3.028e+00   1.801e+00   4.806e+02
  1.048e+01   3.680e+00   2.484e+00   3.048e+02
  9.807e+00   4.380e+00   1.554e+00   5.916e+01
  1.047e+01   5.052e+00   5.344e-01   1.599e+02
  9.784e+00   5.769e+00   2.466e+00   6.871e+01
  1.044e+01   6.406e+00   1.578e-01   4.663e+01
  9.769e+00   7.054e+00   1.016e+00   1.097e+02
  1.047e+01   7.737e+00   1.371e+00   1.103e+02
  9.770e+00   8.389e+00   2.308e+00   1.963e+02
  1.048e+01   9.091e+00   1.467e+00   6.321e+02
  9.797e+00   9.754e+00   1.519e+00   2.597e+01
  1.042e+01   1.047e+01   1.805e+00   2.886e+02
  9.756e+00   1.110e+01   1.854e+00   8.077e+01
  1.046e+01   1.179e+01   3.331e-01   2.853e+02
  9.804e+00   1.250e+01   2.644e+00   4.374e+02
  1.044e+01   1.314e+01   1.355e-01   3.700e+02
  1.115e+01   3.053e-01   2.118e+00   3.741e+02
  1.180e+01   1.007e+00   3.948e-02   1.523e+01
  1.110e+01   1.711e+00   2.317e+00   1.237e+02
  1.178e+01   2.331e+00   2.040e+00   1.299e+02
  1.109e+01   3.010e+00   2.334e+00   6.254e+02
  1.183e+01   3.737e+00   2.936e+00   9.127e+01
  1.116e+01   4.374e+00   2.482e+00   1.943e+02
  1.182e+01   5.031e+00   1.590e+00   1.959e+02
  1.109e+01   5.706e+00   2.386e+00   3.708e+02
  1.181e+01   6.382e+00   8.950e-01   3.383e+02
  1.110e+01   7.054e+00   1.761e+00   2.553e+02
  1.184e+01   7.766e+00   2.469e+00   2.029e+02
  1.108e+01   8.443e+00   2.646e+00   9.398e+02
  1.177e+01   9.101e+00   9.351e-01   3.470e+02
  1.116e+01   9.765e+00   2.447e+00   5.154e+02
  1.182e+01   1.044e+01   5.814e-01   1.273e+02
  1.109e+01   1.113e+01   1.705e+00   3.816e+02
  1.183e+01   1.182e+01   2.538e+00   1.810e+02
  1.112e+01   1.245e+01   1.171e+00   4.615e+01
  1.178e+01   1.316e+01   7.056e-01   5.070e+02
  1.251e+01   3.430e-01   2.131e+00   5.950e+02
  1.314e+01   1.029e+00   6.454e-01   2.075e+02
  1.248e+01   1.657e+00   1.405e+00   2.982e+02
  1.313e+01   2.329e+00   1.773e+00   1.357e+02
  1.245e+01   3.036e+00   1.003e+00   6.322e+01
  1.312e+01   3.736e+00   2.600e+00   1.816e+02
  1.249e+01   4.407e+00   1.416e+00   1.295e+01
  1.311e+01   5.088e+00   3.701e+00   1.164e+02
  1.244e+01   5.733e+00   1.746e+00   1.376e+02
  1.318e+01   6.380e+00   2.058e+00   4.838e+02
  1.248e+01   7.085e+00   9.648e-02   8.671e+01
  1.314e+01   7.772e+00   5.339e-01   4.432e+01
  1.249e+01   8.442e+00   7.024e-01   4.326e+01
  1.317e+01   9.101e+00   8.868e-01   1.356e+01
  1.246e+01   9.770e+00   3.229e-01   7.045e+01
  1.315e+01   1.045e+01   1.861e-05   9.438e+01
  1.248e+01   1.109e+01   1.411e+00   1.577e+02
  1.312e+01   1.184e+01   3.910e+00   3.595e+02
  1.247e+01   1.248e+01   2.866e-01   2.555e+02
  1.311e+01   1.317e+01   2.088e+00   6.361e+02
0.040000
  2.898e-01   3.630e-01   1.186e+00   8.929e+01
  1.065e+00   9.898e-01   1.690e+00   7.673e+00
  3.755e-01   1.684e+00   5.636e-01   5.639e+02
  9.454e-01   2.370e+00   1.318e+00   7.837e+02
  3.903e-01   3.100e+00   1.241e+00   3.672e+03
  9.585e-01   3.734e+00   1.489e+00   3.411e+03
  3.267e-01   4.396e+00   4.500e-01   3.042e+02
  1.040e+00   5.107e+00   1.962e-01   6.793e+03
  3.117e-01   5.738e+00   2.314e-02   1.592e+03
  1.064e+00   6.438e+00   3.153e-01   3.811e+03
  3.631e-01   7.118e+00   8.267e-01   8.942e+01
  1.016e+00   7.783e+00   2.913e-01   1.958e+02
  3.382e-01   8.402e+00   1.886e-01   1.136e+02
  9.981e-01   9.096e+00   1.899e-01   2.789e+02
  3.420e-01   9.793e+00   3.323e-02   5.969e+02
  9.770e-01   1.040e+01   8.054e-01   1.248e+03
  3.332e-01   1.107e+01   9.892e-01   2.553e+02
  1.005e+00   1.173e+01   1.660e+00   1.721e+02
  3.911e-01   1.252e+01   1.983e-01   6.758e+03
  9.694e-01   1.312e+01   1.099e-01   6.938e+03
  1.750e+00   3.066e-01   1.378e+00   9.022e+02
  2.363e+00   9.879e-01   5.295e-02   7.001e+02
  1.691e+00   1.729e+00   7.082e-01   1.494e+02
  2.301e+00   2.413e+00   2.776e+00   3.887e+02
  1.673e+00   3.103e+00   2.192e+00   1.708e+03
  2.351e+00   3.654e+00   7.387e-01   7.935e+02
  1.684e+00   4.408e+00   1.806e-01   8.737e+01
  2.379e+00   5.045e+00   1.956e-01   7.770e+01
  1.649e+00   5.679e+00   1.671e-01   6.513e+03
  2.304e+00   6.422e+00   9.613e-01   6.202e+02
  1.660e+00   7.045e+00   4.698e-02   4.305e+03
  2.414e+00   7.734e+00   1.372e+00   4.687e+01
  1.636e+00   8.458e+00   9.683e-01   4.671e+02
  2.293e+00   9.092e+00   1.742e+00   1.319e+03
  1.740e+00   9.761e+00   5.952e-01   1.755e+03
  2.430e+00   1.042e+01   2.024e+00   7.417e+02
  1.696e+00   1.112e+01   2.667e-01   1.534e+02
  2.410e+00   1.181e+01   7.849e-01   8.244e+02
  1.716e+00   1.244e+01   8.724e-01   1.858e+02
  2.340e+00   1.313e+01   2.953e-01   9.416e+02
  3.007e+00   3.685e-01   3.788e-01   1.220e+03
  3.673e+00   9.614e-01   9.888e-01   1.005e+03
  2.995e+00   1.688e+00   7.078e-01   4.364e+01
  3.738e+00   2.349e+00   3.767e-01   4.229e+01
  3.100e+00   3.105e+00   4.288e+00   1.620e+02
  3.759e+00   3.773e+00   1.478e+00   2.340e+03
  2.986e+00   4.340e+00   1.821e+00   8.587e+01
  3.737e+00   4.995e+00   9.541e-01   1.901e+03
  3.062e+00   5.730e+00   3.388e-01   8.186e+00
  3.765e+00   6.368e+00   4.980e-01   4.300e+03
  3.103e+00   7.068e+00   2.438e+00   5.872e+01
  3.678e+00   7.824e+00   2.518e+00   1.537e+02
  3.040e+00   8.502e+00   1.849e+00   2.861e+03
  3.695e+00   9.053e+00   3.977e-01   3.148e+03
  2.975e+00   9.711e+00   3.324e+00   7.346e+02
  3.764e+00   1.051e+01   2.649e+00   3.514e+02
  3.084e+00   1.114e+01   1.038e+00   1.021e+02
  3.760e+00   1.178e+01   3.709e-01   2.232e+03
  3.038e+00   1.243e+01   5.326e-01   8.117e+02
  3.745e+00   1.312e+01   2.958e-01   1.027e+03
  4.349e+00   3.673e-01   5.575e-01   3.262e+02
  5.008e+00   1.036e+00   5.938e-01   9.989e+02
  4.387e+00   1.664e+00   1.371e-01   5.573e+02
  5.005e+00   2.405e+00   2.123e-01   5.389e+03
  4.430e+00   3.020e+00   1.585e-01   5.292e+03
  5.065e+00   3.677e+00   1.934e-01   3.468e+02
  4.353e+00   4.385e+00   1.234e-01   5.024e+03
  5.004e+00   5.101e+00   2.038e+00   1.691e+02
  4.364e+00   5.775e+00   9.884e-02   3.672e+03
  5.015e+00   6.429e+00   4.063e-01   4.750e+03
  4.442e+00   7.054e+00   3.640e-01   4.139e+03
  5.009e+00   7.780e+00   6.414e-01   1.082e+03
  4.442e+00   8.450e+00   1.146e+00   1.203e+03
  5.042e+00   9.117e+00   1.799e-01   4.813e+01
  4.423e+00   9.801e+00   8.904e-01   1.185e+02
  5.127e+00   1.045e+01   1.737e+00   3.642e+02
  4.384e+00   1.119e+01   8.712e-01   2.881e+03
  5.015e+00   1.181e+01   8.371e-01   8.917e+02
  4.345e+00   1.247e+01   3.534e-01   5.075e+02
  5.003e+00   1.313e+01   1.186e+00   1.186e+02
  5.740e+00   3.496e-01   1.387e-01   5.017e+01
  6.433e+00   1.065e+00   1.391e+00   1.312e+03
  5.772e+00   1.648e+00   8.667e-01   2.799e+03
  6.339e+00   2.306e+00   1.821e+00   1.926e+03
  5.782e+00   3.100e+00   1.065e+00   3.726e+03
  6.367e+00   3.718e+00   3.442e-01   3.144e+03
  5.745e+00   4.381e+00   1.502e-02   3.917e+02
  6.388e+00   5.063e+00   1.808e-02   4.160e+02
  5.733e+00   5.679e+00   7.091e-01   5.762e+02
  6.386e+00   6.403e+00   1.103e-01   3.649e+01
  5.656e+00   7.030e+00   2.397e+00   1.211e+03
  6.383e+00   7.772e+00   5.010e-01   1.535e+01
  5.678e+00   8.417e+00   1.029e+00   1.924e+02
  6.441e+00   9.146e+00   5.875e-01   1.356e+03
  5.720e+00   9.726e+00   1.005e+00   1.338e+02
  6.328e+00   1.049e+01   3.216e+00   1.534e+02
  5.681e+00   1.116e+01   1.915e+00   5.585e+02
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