# coordinates are x, y, z
dipoles = [
[0.057592, 0.000000, 0.867089],
[0.046593, 0.033852, 0.867089],
[0.017797, 0.054773, 0.867089],
[-0.017797, 0.054773, 0.867089],
[-0.046593, 0.033852, 0.867089],
[-0.057592, 0.000000, 0.867089],
[-0.046593, -0.033852, 0.867089],
[-0.017797, -0.054773, 0.867089],
[0.017797, -0.054773, 0.867089],
[0.046593, -0.033852, 0.867089],
[0.067555, 0.092981, 0.861366],
[0.035516, 0.109306, 0.861366],
[0.000000, 0.114931, 0.861366],
[-0.035516, 0.109306, 0.861366],
[-0.067555, 0.092981, 0.861366],
[-0.092981, 0.067555, 0.861366],
[-0.109306, 0.035516, 0.861366],
[-0.114931, 0.000000, 0.861366],
[-0.109306, -0.035516, 0.861366],
[-0.092981, -0.067555, 0.861366],
[-0.067555, -0.092981, 0.861366],
[-0.035516, -0.109306, 0.861366],
[-0.000000, -0.114931, 0.861366],
[0.035516, -0.109306, 0.861366],
[0.067555, -0.092981, 0.861366],
[0.092981, -0.067555, 0.861366],
[0.109306, -0.035516, 0.861366],
[0.114931, -0.000000, 0.861366],
[0.109306, 0.035516, 0.861366],
[0.092981, 0.067555, 0.861366],
[0.121456, 0.121456, 0.851856],
[0.094521, 0.143418, 0.851856],
[0.063716, 0.159509, 0.851856],
[0.030303, 0.169070, 0.851856],
[-0.004351, 0.171709, 0.851856],
[-0.038827, 0.167318, 0.851856],
[-0.071713, 0.156077, 0.851856],
[-0.101663, 0.138447, 0.851856],
[-0.127451, 0.115148, 0.851856],
[-0.148022, 0.087135, 0.851856],
[-0.162532, 0.055555, 0.851856],
[-0.170388, 0.021700, 0.851856],
[-0.171268, -0.013043, 0.851856],
[-0.165137, -0.047252, 0.851856],
[-0.152245, -0.079526, 0.851856],
[-0.133120, -0.108545, 0.851856],
[-0.108545, -0.133120, 0.851856],
[-0.079526, -0.152245, 0.851856],
[-0.047252, -0.165137, 0.851856],
[-0.013043, -0.171268, 0.851856],
[0.021700, -0.170388, 0.851856],
[0.055555, -0.162532, 0.851856],
[0.087135, -0.148022, 0.851856],
[0.115148, -0.127451, 0.851856],
[0.138447, -0.101663, 0.851856],
[0.156077, -0.071713, 0.851856],
[0.167318, -0.038827, 0.851856],
[0.171709, -0.004351, 0.851856],
[0.169070, 0.030303, 0.851856],
[0.159509, 0.063716, 0.851856],
[0.143418, 0.094521, 0.851856],
[0.172877, 0.148410, 0.838599],
[0.147532, 0.173627, 0.838599],
[0.118555, 0.194569, 0.838599],
[0.086658, 0.210719, 0.838599],
[0.052627, 0.221681, 0.838599],
[0.017301, 0.227185, 0.838599],
[-0.018452, 0.227094, 0.838599],
[-0.053750, 0.221412, 0.838599],
[-0.087725, 0.210277, 0.838599],
[-0.119539, 0.193965, 0.838599],
[-0.148410, 0.172877, 0.838599],
[-0.173627, 0.147532, 0.838599],
[-0.194569, 0.118555, 0.838599],
[-0.210719, 0.086658, 0.838599],
[-0.221681, 0.052627, 0.838599],
[-0.227185, 0.017301, 0.838599],
[-0.227094, -0.018452, 0.838599],
[-0.221412, -0.053750, 0.838599],
[-0.210277, -0.087725, 0.838599],
[-0.193965, -0.119539, 0.838599],
[-0.172877, -0.148410, 0.838599],
[-0.147532, -0.173627, 0.838599],
[-0.118555, -0.194569, 0.838599],
[-0.086658, -0.210719, 0.838599],
[-0.052627, -0.221681, 0.838599],
[-0.017301, -0.227185, 0.838599],
[0.018452, -0.227094, 0.838599],
[0.053750, -0.221412, 0.838599],
[0.087725, -0.210277, 0.838599],
[0.119539, -0.193965, 0.838599],
[0.148410, -0.172877, 0.838599],
[0.173627, -0.147532, 0.838599],
[0.194569, -0.118555, 0.838599],
[0.210719, -0.086658, 0.838599],
[0.221681, -0.052627, 0.838599],
[0.227185, -0.017301, 0.838599],
[0.227094, 0.018452, 0.838599],
[0.221412, 0.053750, 0.838599],
[0.210277, 0.087725, 0.838599],
[0.193965, 0.119539, 0.838599],
[0.215133, 0.183741, 0.821656],
[0.190408, 0.209255, 0.821656],
[0.162680, 0.231470, 0.821656],
[0.132386, 0.250034, 0.821656],
[0.100005, 0.264655, 0.821656],
[0.066046, 0.275102, 0.821656],
[0.031046, 0.281210, 0.821656],
[-0.004444, 0.282884, 0.821656],
[-0.039864, 0.280096, 0.821656],
[-0.074655, 0.272891, 0.821656],
[-0.108268, 0.261383, 0.821656],
[-0.140175, 0.245752, 0.821656],
[-0.169870, 0.226246, 0.821656],
[-0.196887, 0.203171, 0.821656],
[-0.220798, 0.176893, 0.821656],
[-0.241228, 0.147825, 0.821656],
[-0.257853, 0.116425, 0.821656],
[-0.270412, 0.083190, 0.821656],
[-0.278706, 0.048642, 0.821656],
[-0.282605, 0.013327, 0.821656],
[-0.282047, -0.022198, 0.821656],
[-0.277040, -0.057372, 0.821656],
[-0.267665, -0.091642, 0.821656],
[-0.254069, -0.124467, 0.821656],
[-0.236466, -0.155329, 0.821656],
[-0.215133, -0.183741, 0.821656],
[-0.190408, -0.209255, 0.821656],
[-0.162680, -0.231470, 0.821656],
[-0.132386, -0.250034, 0.821656],
[-0.100005, -0.264655, 0.821656],
[-0.066046, -0.275102, 0.821656],
[-0.031046, -0.281210, 0.821656],
[0.004444, -0.282884, 0.821656],
[0.039864, -0.280096, 0.821656],
[0.074655, -0.272891, 0.821656],
[0.108268, -0.261383, 0.821656],
[0.140175, -0.245752, 0.821656],
[0.169870, -0.226246, 0.821656],
[0.196887, -0.203171, 0.821656],
[0.220798, -0.176893, 0.821656],
[0.241228, -0.147825, 0.821656],
[0.257853, -0.116425, 0.821656],
[0.270412, -0.083190, 0.821656],
[0.278706, -0.048642, 0.821656],
[0.282605, -0.013327, 0.821656],
[0.282047, 0.022198, 0.821656],
[0.277040, 0.057372, 0.821656],
[0.267665, 0.091642, 0.821656],
[0.254069, 0.124467, 0.821656],
[0.236466, 0.155329, 0.821656],
[0.259471, 0.214653, 0.801099],
[0.235612, 0.240599, 0.801099],
[0.209172, 0.263910, 0.801099],
[0.180440, 0.284328, 0.801099],
[0.149731, 0.301632, 0.801099],
[0.117382, 0.315631, 0.801099],
[0.083747, 0.326171, 0.801099],
[0.049194, 0.333138, 0.801099],
[0.014102, 0.336456, 0.801099],
[-0.021145, 0.336087, 0.801099],
[-0.056160, 0.332035, 0.801099],
[-0.090559, 0.324346, 0.801099],
[-0.123966, 0.313103, 0.801099],
[-0.156015, 0.298430, 0.801099],
[-0.186355, 0.280487, 0.801099],
[-0.214653, 0.259471, 0.801099],
[-0.240599, 0.235612, 0.801099],
[-0.263910, 0.209172, 0.801099],
[-0.284328, 0.180440, 0.801099],
[-0.301632, 0.149731, 0.801099],
[-0.315631, 0.117382, 0.801099],
[-0.326171, 0.083747, 0.801099],
[-0.333138, 0.049194, 0.801099],
[-0.336456, 0.014102, 0.801099],
[-0.336087, -0.021145, 0.801099],
[-0.332035, -0.056160, 0.801099],
[-0.324346, -0.090559, 0.801099],
[-0.313103, -0.123966, 0.801099],
[-0.298430, -0.156015, 0.801099],
[-0.280487, -0.186355, 0.801099],
[-0.259471, -0.214653, 0.801099],
[-0.235612, -0.240599, 0.801099],
[-0.209172, -0.263910, 0.801099],
[-0.180440, -0.284328, 0.801099],
[-0.149731, -0.301632, 0.801099],
[-0.117382, -0.315631, 0.801099],
[-0.083747, -0.326171, 0.801099],
[-0.049194, -0.333138, 0.801099],
[-0.014102, -0.336456, 0.801099],
[0.021145, -0.336087, 0.801099],
[0.056160, -0.332035, 0.801099],
[0.090559, -0.324346, 0.801099],
[0.123966, -0.313103, 0.801099],
[0.156015, -0.298430, 0.801099],
[0.186355, -0.280487, 0.801099],
[0.214653, -0.259471, 0.801099],
[0.240599, -0.235612, 0.801099],
[0.263910, -0.209172, 0.801099],
[0.284328, -0.180440, 0.801099],
[0.301632, -0.149731, 0.801099],
[0.315631, -0.117382, 0.801099],
[0.326171, -0.083747, 0.801099],
[0.333138, -0.049194, 0.801099],
[0.336456, -0.014102, 0.801099],
[0.336087, 0.021145, 0.801099],
[0.332035, 0.056160, 0.801099],
[0.324346, 0.090559, 0.801099],
[0.313103, 0.123966, 0.801099],
[0.298430, 0.156015, 0.801099],
[0.280487, 0.186355, 0.801099],
[0.302390, 0.244870, 0.777020],
[0.278869, 0.271353, 0.777020],
[0.253039, 0.295588, 0.777020],
[0.225111, 0.317374, 0.777020],
[0.195318, 0.336529, 0.777020],
[0.163906, 0.352896, 0.777020],
[0.131137, 0.366339, 0.777020],
[0.097281, 0.376746, 0.777020],
[0.062618, 0.384031, 0.777020],
[0.027437, 0.388134, 0.777020],
[-0.007972, 0.389021, 0.777020],
[-0.043314, 0.386684, 0.777020],
[-0.078298, 0.381143, 0.777020],
[-0.112633, 0.372444, 0.777020],
[-0.146034, 0.360659, 0.777020],
[-0.178226, 0.345885, 0.777020],
[-0.208940, 0.328245, 0.777020],
[-0.237923, 0.307885, 0.777020],
[-0.264935, 0.284974, 0.777020],
[-0.289752, 0.259702, 0.777020],
[-0.312167, 0.232277, 0.777020],
[-0.331996, 0.202928, 0.777020],
[-0.349073, 0.171897, 0.777020],
[-0.363259, 0.139442, 0.777020],
[-0.374434, 0.105831, 0.777020],
[-0.382506, 0.071344, 0.777020],
[-0.387409, 0.036265, 0.777020],
[-0.389102, 0.000886, 0.777020],
[-0.387570, -0.034501, 0.777020],
[-0.382827, -0.069601, 0.777020],
[-0.374912, -0.104125, 0.777020],
[-0.363890, -0.137787, 0.777020],
[-0.349852, -0.170306, 0.777020],
[-0.332916, -0.201414, 0.777020],
[-0.313221, -0.230853, 0.777020],
[-0.290931, -0.258380, 0.777020],
[-0.266230, -0.283765, 0.777020],
[-0.239323, -0.306799, 0.777020],
[-0.210433, -0.327290, 0.777020],
[-0.179799, -0.345070, 0.777020],
[-0.147675, -0.359990, 0.777020],
[-0.114327, -0.371928, 0.777020],
[-0.080032, -0.380783, 0.777020],
[-0.045074, -0.386483, 0.777020],
[-0.009743, -0.388981, 0.777020],
[0.025670, -0.388255, 0.777020],
[0.060869, -0.384312, 0.777020],
[0.095564, -0.377185, 0.777020],
[0.129468, -0.366932, 0.777020],
[0.162298, -0.353639, 0.777020],
[0.193784, -0.337415, 0.777020],
[0.223664, -0.318395, 0.777020],
[0.251690, -0.296737, 0.777020],
[0.277631, -0.272620, 0.777020],
[0.301272, -0.246244, 0.777020],
[0.322416, -0.217828, 0.777020],
[0.340888, -0.187607, 0.777020],
[0.356536, -0.155831, 0.777020],
[0.369229, -0.122764, 0.777020],
[0.378863, -0.088679, 0.777020],
[0.385357, -0.053860, 0.777020],
[0.388658, -0.018595, 0.777020],
[0.388739, 0.016825, 0.777020],
[0.385598, 0.052105, 0.777020],
[0.379262, 0.086954, 0.777020],
[0.369784, 0.121081, 0.777020],
[0.357241, 0.154206, 0.777020],
[0.341739, 0.186053, 0.777020],
[0.323404, 0.216358, 0.777020],
[0.341114, 0.277517, 0.749524],
[0.317677, 0.304065, 0.749524],
[0.292180, 0.328641, 0.749524],
[0.264788, 0.351086, 0.749524],
[0.235678, 0.371255, 0.749524],
[0.205040, 0.389015, 0.749524],
[0.173073, 0.404252, 0.749524],
[0.139983, 0.416868, 0.749524],
[0.105985, 0.426780, 0.749524],
[0.071300, 0.433925, 0.749524],
[0.036152, 0.438255, 0.749524],
[0.000770, 0.439743, 0.749524],
[-0.034617, 0.438379, 0.749524],
[-0.069780, 0.434172, 0.749524],
[-0.104490, 0.427149, 0.749524],
[-0.138522, 0.417356, 0.749524],
[-0.171656, 0.404856, 0.749524],
[-0.203677, 0.389731, 0.749524],
[-0.234377, 0.372078, 0.749524],
[-0.263556, 0.352012, 0.749524],
[-0.291027, 0.329663, 0.749524],
[-0.316610, 0.305176, 0.749524],
[-0.340140, 0.278710, 0.749524],
[-0.361464, 0.250436, 0.749524],
[-0.380443, 0.220538, 0.749524],
[-0.396956, 0.189210, 0.749524],
[-0.410893, 0.156655, 0.749524],
[-0.422167, 0.123084, 0.749524],
[-0.430702, 0.088714, 0.749524],
[-0.436444, 0.053770, 0.749524],
[-0.439355, 0.018476, 0.749524],
[-0.439417, -0.016937, 0.749524],
[-0.436629, -0.052241, 0.749524],
[-0.431010, -0.087205, 0.749524],
[-0.422595, -0.121604, 0.749524],
[-0.411440, -0.155215, 0.749524],
[-0.397616, -0.187819, 0.749524],
[-0.381213, -0.219204, 0.749524],
[-0.362339, -0.249169, 0.749524],
[-0.341114, -0.277517, 0.749524],
[-0.317677, -0.304065, 0.749524],
[-0.292180, -0.328641, 0.749524],
[-0.264788, -0.351086, 0.749524],
[-0.235678, -0.371255, 0.749524],
[-0.205040, -0.389015, 0.749524],
[-0.173073, -0.404252, 0.749524],
[-0.139983, -0.416868, 0.749524],
[-0.105985, -0.426780, 0.749524],
[-0.071300, -0.433925, 0.749524],
[-0.036152, -0.438255, 0.749524],
[-0.000770, -0.439743, 0.749524],
[0.034617, -0.438379, 0.749524],
[0.069780, -0.434172, 0.749524],
[0.104490, -0.427149, 0.749524],
[0.138522, -0.417356, 0.749524],
[0.171656, -0.404856, 0.749524],
[0.203677, -0.389731, 0.749524],
[0.234377, -0.372078, 0.749524],
[0.263556, -0.352012, 0.749524],
[0.291027, -0.329663, 0.749524],
[0.316610, -0.305176, 0.749524],
[0.340140, -0.278710, 0.749524],
[0.361464, -0.250436, 0.749524],
[0.380443, -0.220538, 0.749524],
[0.396956, -0.189210, 0.749524],
[0.410893, -0.156655, 0.749524],
[0.422167, -0.123084, 0.749524],
[0.430702, -0.088714, 0.749524],
[0.436444, -0.053770, 0.749524],
[0.439355, -0.018476, 0.749524],
[0.439417, 0.016937, 0.749524],
[0.436629, 0.052241, 0.749524],
[0.431010, 0.087205, 0.749524],
[0.422595, 0.121604, 0.749524],
[0.411440, 0.155215, 0.749524],
[0.397616, 0.187819, 0.749524],
[0.381213, 0.219204, 0.749524],
[0.362339, 0.249169, 0.749524],
[0.378356, 0.308918, 0.718733],
[0.354797, 0.335712, 0.718733],
[0.329345, 0.360715, 0.718733],
[0.302136, 0.383794, 0.718733],
[0.273315, 0.404824, 0.718733],
[0.243036, 0.423695, 0.718733],
[0.211459, 0.440305, 0.718733],
[0.178755, 0.454566, 0.718733],
[0.145097, 0.466402, 0.718733],
[0.110665, 0.475749, 0.718733],
[0.075642, 0.482558, 0.718733],
[0.040216, 0.486792, 0.718733],
[0.004575, 0.488429, 0.718733],
[-0.031090, 0.487460, 0.718733],
[-0.066589, 0.483890, 0.718733],
[-0.101734, 0.477739, 0.718733],
[-0.136335, 0.469038, 0.718733],
[-0.170209, 0.457835, 0.718733],
[-0.203174, 0.444189, 0.718733],
[-0.235056, 0.428173, 0.718733],
[-0.265684, 0.409873, 0.718733],
[-0.294894, 0.389386, 0.718733],
[-0.322530, 0.366821, 0.718733],
[-0.348446, 0.342300, 0.718733],
[-0.372503, 0.315952, 0.718733],
[-0.394572, 0.287918, 0.718733],
[-0.414536, 0.258348, 0.718733],
[-0.432289, 0.227399, 0.718733],
[-0.447734, 0.195238, 0.718733],
[-0.460791, 0.162034, 0.718733],
[-0.471390, 0.127966, 0.718733],
[-0.479473, 0.093216, 0.718733],
[-0.484999, 0.057968, 0.718733],
[-0.487936, 0.022410, 0.718733],
[-0.488270, -0.013266, 0.718733],
[-0.485999, -0.048872, 0.718733],
[-0.481135, -0.084218, 0.718733],
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