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@mikadou
Created December 16, 2015 15:24
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Visualize error in timestep calculation
{
"metadata": {
"name": "",
"signature": "sha256:33e7f9e3f731a2024eada8fab72f28df081b12087b950267d15a973a3c2925f3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 10000 # sample points\n",
"fps = np.linspace(5, 300, N) # frames per second\n",
"dt = 1.0 / fps # frame duration [s]\n",
"f = 2000 # physics update frequency [Hz]\n",
"\n",
"# Calculate fixed and jittered versions of timesteps\n",
"timestep_fixed = np.ones(N) / f\n",
"timestep_jitter = dt / np.trunc(f * dt)"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# plot results\n",
"plt.figure()\n",
"plt.plot(fps, timestep_fixed * 1000.0, 'g', label='fixed')\n",
"plt.plot(fps, timestep_jitter * 1000.0, 'r', label='jittered')\n",
"plt.ylim([0.49, 0.6])\n",
"plt.xlabel('Frames per Second')\n",
"plt.ylabel('Timestep [ms]')\n",
"plt.legend(loc='upper left')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 36,
"text": [
"<matplotlib.legend.Legend at 0x7fbd98bfdfd0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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wDsMojN694e67IdMMkMce64LK2SZCUnXC4efdR8nlP+64+PGGsWNdcPzQIRdE\njsvkyfDEE/G3C2PCBCd8773n6lKiEsWKEHFxjocecn26SoXvrip0FsJiMmsWPP+8S9Do37/coymY\njBaHiFzmPd8Q8ihSIrlhFJFsvZd693bPuVwYjY0uLffPf452zHwC5N26uXkr8m2PMXw47N0bzx2T\nSQS7dnXnkE/MJIqwzp7tMtryId8ivEqMc9TWwuLFbi7yYlCsAsU8yeaq8idr+mGGh2FUFi+8kPkz\n/x8tSouQOO6qfFxVED3OEXZnX1NTPe6q2bPhgQeS2XcmZsxwrsC33sq9binpQO6qbMKxDUBV14Q8\n1pZofIbh2L8f/v3fs6/z/PO591Ms4fBdWb7FEXeq1DgB8rC7y2K6q5IUjhkz3DhL2Sm3a1dXQ1Jq\nwcrFSSe5+TlKOa1uQmQTjmYR+ftAJtVXLKvKKBv33Qfnnpt9nWyuH1U45pjiWxyNje4Rt1q50NYj\nkyYVr/4iSeHo1s1ZZYW2cI9LJbqrhg+HXr2Sq5spIdmEoxMue6p7yMOyqozSMmCAe37vvczr5IoZ\njBxZfOGA/ALkhabkTppUPItj8mQ3f8aBA8XZXzpz5pT+7r8ShQM6jLsqm3D8WVVXZXqUbITG0cW+\nfeETFflNBzPVYjQ25p4wx8+sykWpUnI3b86/xmHiRHexL8akTt26uaynQoQsG+WIc8yZ46yobDca\nmUiy7qSD9K2KUsdhGKWjVy+46KLMn2eqCejb1z1nC4jGFY6oF5B8Mqv69HFzeuzcGW87n8ZGl9YZ\nR+CykaS7qhwWR/furp1KqVue5KK11fXvevvtco+kILIJx9KSjcIwgmQr3sqUOSXiUh6zZVYdc4yL\nReRyyfTu7QrJXn8991ghmqsqrC5k/HhnNeRLtQTIR450d/47diSz/0wsWgRr1pT2mLno3t3VdFT5\nrIAZhUNVd5dyIMZRhmrm7JJsrUGyVSEPH549zlFXBwMHZt5H0MIYNSpel9x8UnILFY5qCZCLFFbP\nkS+LF7ui0ErjlFPgppvKPYqCMFeVUR7mzoWPfjT8s2zCkc2iGDEid0puLneVbxXEiXOMGOHupuOm\nnBZDOKJYHFFcblOmOBEqRswkjHK4q+bPh4cfzi/OkWSB3cknw803V0Szwnwx4TDKwyOPwB/+0H75\ngAHh/1D+skIsDkgmQF5XFz3VN8iECZXjqurVy8VM8p0nJBdz5pTe4ujRw/2NS33cXIwd65I9CulX\nVmZMOIyDpaioAAAgAElEQVTk+eEP208WNHhw+LpDh2beT64YRjbh8IUnqnCMHp1dONJjFvkEyH2L\nI9udZ7bPjj3WxWHitnXPRNKFgBs2lH5Oikp0V4lUvbvKhMNIngsugDvvbLtsyJDwdf0GcGFun6FD\nnUsoU2wkl8UhklxKbj61HE1Nro17rqBxJrdJTU30FutRXC/TpsGjj+ZeD+K7Wbp3d3/TqIWAxXLj\ntLZWXoAcTDgMow07doRnLaVXVmcSDr9e4+WX239WXw89e4ZPAavqYg3lcFVBftPIQmVlVk2fHl04\nIH4coBzuqnnz3Dm9+25pj5uLxYvduHLVHlUoJhxGcRk6FFaF1IemC4dfCZ4pNTZTgPyYY7LXcrz/\nfvZ/xqjC0aePs2yidqAdOzY/4Sg0zlHMzKrp052rqiMFyLt3d3+jYs2+VywaGlyCyB13lHskeWHC\nYRRGmNsorEV3ugXhz0MR1r68oSGzcAwblr2WY/jw7HGQPn3chXHv3szr+PuKY3WMHZtfJfj48YVN\nA1vM1iNNTdCvX36pxVGIW0FerMymxYvNXVVkTDiM/Nm6NXwiorBq6ExNAMP8+0OH5mdxgBOObCm5\nScU5+vVzopGtaDDsQliMlNwnnyxex9Xjj3cprEkwerRLkojbELJQKjFADk44qjQt14TDyB8/Qyb9\nhx92Ych0sQiLZYQJh3+MbBYHlC8lVyRldYSR6eLgd8nN98Lfs6dz0T37bH7bp3P88S5VOgnKVQg4\ndy6sX98+s6/cjBrlrOu4FmMFCE3iwiEiy0Vki4hsFZGvhXzeKiL7RORx7/ENb/lQEblbRJ4SkSdF\n5EtJj9XIwauvujYOPvX17jk9HTQpi0MkmsWRr3Ckp9jGDZCPGwdbtkRfH1z9RM+ehc3LXUx31YwZ\nyQkHlCfO0dAAU6dWXpwDqtZdlahwiEgn4DJgOdACnCUi40JWXauqU73HJd6yA8Dfqep4YDbwhQzb\nGqVi27bwVtXBOEVTU/vgaqdO4S6cfv3aC4dqdldVpVockN3iyMaECYXFOYqZWTV1qgu2J9VivRyd\ncsGl5Vaqu8qEox0zgW2qul1VDwBXAytC1mvn/FXVP6vqeu/128BmYFCSgzVCEEldPPv0cc/pF5Wg\nheFnSwXxazPStxs8ONxVdcwx8WMcvvmeKSU3aN7HEY5MgeKwpoX5WBxQWT2rGhvd3zipquaZM53b\nqByFgJUYIF+0yH13uZI1KoykhWMwELwC7PCWBVFgrohsEJGbRKQlfSciMhyYCjyU0DgNn1dfhbVp\nMwP7rgu/xuK119p+HrQ4fJEIWh1hGVSqrpYjzFXVt6+bKnb//vaf9enjUm7D2qf7WVWZLA7/Qh9V\nOPr3d2IXJyU3H4sjm3BE8WfnclXF9YnPmJFcgLxHD9ctt9Sz4M2Z4/5GldbOvGtXN+nU7bfH2y7J\nXloR6Jzw/qP8Yh8DhqrqfhE5Gfg9cJz/oYh0B64FvuxZHm1YuXLlkdetra20trYWOOSjnG98A37x\ni7YXmzChGDw4tU5QEGprU9sMHJha3r+/i3MEW4oMGRJe9SziPnvpJVdYl/6Zb3WMH99+26Ymd7Hf\nt8/FDsIYNswJ1sGDrn16Jvw5xbduda2wczFihBPe/fudXz0q48fD5ZdnH0c2Ro1yx33zTWcxFIof\nIP/c5wrfVxi+u2rGjGT2H0Z9vatTue8+NwtfJeG7q/7iLxI7xJo1a1hTRIsraeF4GQg2HxqKszqO\noKpvBV7fLCI/FZEmVd0jIrXA74Bfq+rvww4QFA4jT665xl3szj475Y4K4guHLxTpldthtRg7d6aE\nQxUGDWrvlho82InJ4cMpa8bHj3OkCwek4hxhwhG0OiZPbv85QJcuTsheesld7LPh96CKIhydOrmL\n+NNPu1hBVFpanIvr0KHw9OYoxx0/3t1Rz58ff/t0ZsyAK68sfD+ZmDvXpaF+qcT5Ln5abi7hKHXW\n0sknu6LZsP+DIpF+U70qrEg3Bkm7qh4BRovIcBGpA84Erg+uICL9RdwtlYjMBMQTDQGuADap6qUJ\nj/PoY+fOVL3DF74Af/VX7nVzc/t104Ui/X0wxqHqfvzpWVS+SASpr3eui7DAeXqAPPjPnGRmVTpx\nmxfmE+fo0cP93XO1hM+G3xa9GEye7GIc2drEF3JxnTfP3fmXmkoNkI8Y4SzlqH28KoBEhUNVDwLn\nA7cCm4BrVHWziJwrIud6q50BbBSR9cClwMe95fOATwGLA6m6y5Mc71HFqae6iye0FQv/dS5XVbb3\ngwa1T8kNEw7IHOcoRWZVlNqHuM0Lk4hzRGHKlOwXnjg+8YYGV6yXK1MrXz/7yJHOnVhICnI+zJ7t\n/saV2B+qyrKrEq/jUNWbVXWMqo5S1e94y1ar6mrv9eWqOkFVp6jqXFV90Fv+J1Wt8Zb7qbq3JD3e\nDs22bTBxonsdNIn9+bohVZsRDD6nC0cuV9XAge2FI8xVBU44gst9wQoTDv9CFWZxBIUuSrPDkSNL\nb3Fku9AWKhxTp7pspWKRZIBcxFkd2aYIToKuXd15lfq4UTDhMCqO//f/3MX5qadS9QJhVkaQXbtS\nrzMJh6prIhcmElFcVf7yfNqOFGpxhNVohKXYjh7tguNRK7szWRy5XDuF1nJMmuTcS8Wqv0iyghxy\nu6uSijNETcstddbS/Pnu+4s6z32ZMeHoqBw44AKQAOedB//6r20ti+DrMOEIikW24Hhzs8tgCubl\nh1kc6TUb/r7CXFUiuV1VYW4O/589TDjSL0RRi/saG90jTPTCLi5jxrj9xu0wW6jF0a2bE9R83GRh\nlFs4kqK1Fe66q/THzUWXLrBkSep/tsIx4eho3HQT/OQn7q7qlFNSy3fvdhcXcHMTBLOnfBEJi2t0\n7do+9z3omqqpcRXgQaFJFw7V7DGOqP2qfAYPdmPIdHedyeIIXuhHjnQX+Ch3tmHuqkzbNTS4jK24\nge5x45xlc/BgvO2CFNNdNXGi+/sk1d9p6lS3/337ktl/JmbPdt9l1NqcUnLaaXDDDeUeRSRMODoK\na9e63PiLLnJpjuk1DHv2pC6cu3enhEPV3e1A26Ch76ry1/PvoJua2sc4BgxIiYmfepsuEr16uSyd\n4IVIJLOrqmdPt6+wC0ttbaouJIzevd14s02p2quXi+eETQqVTikyqxoanOAW0qxw6tTiZeZ06eKs\noGLGTYLU1TmrptQND+vqXDpwJVaRn3KKKwQsdVV9HphwVDsvvujuzFtb3aOpyS3v0cM9+z/C3btT\nd8m7d6eC4EFrYteu1Dq+BeHXFfi+1z59XOA8+OMeMKCthTFwoNs+GBcQCReUTFlVudxV2eIcIi5A\nnuuuP6q7asyYeMJRSGZVepwjjq8/V2ZVXJIMkENud1VScYYlS9pPZVwJ9O/vfmv33lvukeTEhKNa\neekleOghd5fZ0uLuED/4wN1tB/F74ARN82AA7vXXUxenTAHx7t1T72tqnGsr+HnQ4gB3V9fY2D7Q\nF9abyheOsAtkUDjSP88U5/CJUqcRVThKYXFA5tkAo15AfVdVsQLLHTXOsXRpZQoHVI27yoSj2ti5\n05m0Z5/t/LWHDzurwReMdOHwBWP37tSyoPURvLgHhSP4ul8/59Lxt+nfv+37gQPDaznSrYuwZY2N\n7sLou8mCF710iyN4AU23ONIvluUUjnJ1yW1udiKfKzEgKkkLx5w5sG5dcp14MzF5svvdh1m65eZD\nH3LCUQFzbmTDhKMaOHzYBU1F4Je/dJkXviuqVy/3nEk4fMFIFw6fMOHo2bOtRdG/f+q9iLMw/NiA\n/z49iypTZpUvHMF/jHyLAEtlcRx7rDtWVN+zb3HE/eefODG8d1cciumuamlx30tSAezevV0iQ6kb\nHtbUuLTcSrQ6Jk1yQpqPxVpCTDgqnV//Gj77WfcPBqm7SV8w0p/9GIfPnj0u8HrgQLiVESYczc1t\nhcO3OHz6929rYaQHx6GtcPj1EVGLAH3LIm71eNAiKaZw1NW5MUbNlOrb140lvf4ll8tpzBj3/b77\nbrTjhFHMzKrOnd3d+WOPFWd/YZi7qi0iVeGuMuGoRLZtc3ccN9wAn/40/O//pi6sfnZT9+7uOV0w\n/KC335J8z572jQuDFocfEK+vT73u1y8lIqptLQ5Iuap80l1VIm5ZLleVfyHNpwgwV5FflMpwXzh8\nsQsrAPSJ464SaR/niGJ91NW5gsNCajGKmVkFyc5BDq7wrRyV3EuWwB13VKZLyHdXVTAmHJXGTTe5\ni8e4cXD66e0/97Og/GynXLGNPXvaWyHBgLhvcTQ3t329a1cqKypdKIKuKv991H5VmSyOfPtVZfrH\nHzbMbesLbdh6TU3uIh8U0kyECUc2CyLfOMfEiYXN5jdlSvFbj6xb1355sS64vsVR6gv4yJEurbsS\nXUKLF7vfQJTfZZkw4agU3nwTfv9713wwneAFyvc3+8vShcP/BwxmU/nWid/t1P9BBjOfglZGly6u\nWNCvg/AtjmBwPH3ypp072/7zZ+pXFbcIMFPGVbduLs6TqQ6jS5f2U9OmX+hF3AUkarPDoHDkutDl\nm1k1aVJhcY4RI1y6dHpGW76prbNmhQtHIfsMku6CLRUilZuW27UrnHBC5iryCrCSTDjKzaxZ7kfc\nsyd85CO51/cv5n6g1p8wyC/i8/3jQYsjWPgHqYtK377trQyfoJAEYxwi7bOqund3/vBgAWE2V1X6\nDz+Tq6pbN/dPFLSQggwfnj3uEKUDbqVlVhUaIBcpboB81ChXtJl+E1As/IaHFudoS4W7q0w4Ss0H\nH7g7uP793T9Npru5TPgWhy8g773nnn3BSK/bSC/8a2xMCUiYcPjrBtuIpMc40rOqIBXn8LdPd1WJ\nOJGrr3djS8+q8i2OdIHINvdGsAtumLBUYy1Hoa4qKK67SsTNE/5QgrM2lyvOccIJroK8kDYvSXHq\nqXDbbaVPVY6ICUepUHUB6/p6Z2WkZ9xkI8xVlS4g/nPQ0gg+iziR6NMndQfvxzVUnYgELY6gkITV\ncaTHNIIpuX5w3BeS4EU9WxFgGMG023TXSK4AeTGFY8gQ9zeOOmf1sGHu7xc2N3qu47z/fvvGknEo\ndoB81qxkhaNcFseAAe73mJ41VgGuIAYMcDcrFVpFbsJRCvbtc/MJd+sWvT13kOAP2RcM37LwBcN/\nn/7sC0efPu51z57OOvngg7YB8e7dXSDZz8YKWhzdurlAon8RbGoKbzsSFJOuXZ2FkR7gC4tz9O3r\nLsi+1RQUiGyTNqULR7qwFFM4amrculu35l4XXPLCmDHxrQ6R9u6quLGEahOOyZPd9+j/ZqF0F+9K\njXNAdndVqdu+p2HCkTQiLmX22mvz30cwr99vEpguGL5ABN/7biFwwrF7t7sANjWlsq327nViJpKy\nMkTad7wNxjkydcSNklkVrOXwf/zZajyyuaqixDiKJRwQ313V0uLmWIhLoQHyceOc2Bars+2MGa6C\nPG6r+KjU1rpjPPBAMvvPxtKlLi23EvHrOSrBAkrDhCMJ9u51F8Ni3RWEVSxnc1V17pwSBj+e0NTU\nPrbRubPLTPLHGwyQpwfL/YC4f05hRYBxq8eDZEq9zWZx5JrpL4pw9O/vhDlbJ12fuNPIps+xEfX3\nUGico7bWiUehVeg+ffu6G4UkU1fnzy+Pu2rRImdNFVJ0mRSTJzu3ZZzfXIkw4SgW+/e7C4VI+7qJ\nJEgXjKCl4QtGY6O76zxwoG0g3I9zQNvYRlAswiyObEWAYbUcUYoAfTIJRzaLw49/ZHL/NTe75IF9\n+zLftYk4q8PPvsp2ca8WiwPauquKccdaijhHOQLkjY1OqO+/v+3yMruCjoyhQrOrTDgK5f33YdUq\nFwfI5yKRL2Euq+7d3bMvHDU1rr5j796UqwpSwiGSOSXXbzsSzLIKE4pMWVWQclUFK7IzFQH6whHW\nBTdToV99vXMDpguWj4izOnx3VqaLQXoFeSaCwpGtytwnaHHEuXhPmOB+S4W4hopdCJi0cMyZA48+\nmqo1KiV+FXklctppcOON5R5FO0w48uXpp92Fo2tXWLmyfOM4dMgJhN9S/e23U7ELSImILxy+WGRL\nyYW2dRzB2g2fbP2qgmKSqXo8/UKayeLo18/Vh/hB+3T8OEemC3MSKblRRWDECPc3iRtr6NHDnXel\nTOoEyQtHY6NLJgh24y3VXX8l13MsXuxuACqsityEIw6q7qJ3ww2uwKtSSK8eb2pK+Wz79MlscUAq\nsypqcDwY40i3QMJiHFEnbsokHDU1qc/CLiRR4hzFKgLs08dlS0VNpe7c2YlNPoWAhbqrJk921k6x\nahSmTHEZZUlNJQuwcGF50k/nzHHfUZQ4V6mpr3f1JjfdVO6RtMGEIyobN7qL2JAh4T2kykF6o8Og\ncPg0NTnB69MnVSzYt28qtTYY4wi+9tN3fXdJrkaHzc1OoIIFS2FZVf36ufXSXRJB4UgXiKgpuWHC\nUuzMqrFj4wfI83FhFhog797d/VYLaZgYpEsX50Lzax6SyPRZsADuuaf4+81Fly5OPO6+u/THjsKK\nFfCHP5R7FG0w4cjFypXugjRpUrlHksJvM5JJMPzlwUB9sEOu/9p3W/kX++bmlEuoc2e3Hz+dN1OM\nw6dTp/ZFhGGB8E6dUtZJ8EKfa5rYbCm5pSoCBOdOiSMc5QyQT5+eutAXw+2TXkFebFfSggUuSJ1U\n2m82Kjkt90MfcnOR+zd+FYAJRybWr3f/GKtWlXskbamrc0V8kHkSp06dUuukC4dIWxHp2zf1urm5\n7bH69UulAvfv37ZAy49xBC8e6e6qYHA8SJi7qqnJWSFhlda5UnKz1XJEaa8+aJDLvIpSFT52bLy0\n1PSU3KgUo/XItGku4Fwsko5zNDc792ah550Py5a5i3Ml0revcxVWUBzGhCOdTZvcxXDq1HKPpC3+\nBbpXr8yC4YtE0NLwn+vqUq6toFhkEw7/vR/zCNK/f/sxDhjgAtn+WOvrnXUUbLQI4cIh4iyLTCm5\nUavH0/FTdrPdxdbURIuFQHzhyNfiGD3aWWtRW5yEEbQ4ikHSwgHli3NMmuRuHkrdpTcqFeauMuEA\nZwL6BXvjx5d7NO3xu+eCE426OndBTp/9Lzgnh/86zEUVZnH4wXH/NbQVC39/vlvLF6RgrGLgwPZj\nHzSofaO2wYPburR8hg4NT9XNZnH4YpNJGLp2deeRyQ3mE9VdFbeNyMiRTgAyZYVlonNnJ1JPPpm/\nS2jqVDcta7FcP0l3ygUnHOWIc9TUOHdVpVodK1bA9dfn17IoAY5u4bj7bvdP6c+aV6n07JkSjuBz\nuqXRtat7BJcFrRBfMDJZHL16pSaIgrbCUeP9VPwAefp7CBeOwYPbLxsypP0ycMIRlgU0bFjmZoFd\nu7rzyjQvB6TiHNkuwL5w5LpIH3usEzf/ZiMXnTs762HLlvgCUGiL9V69nGUYp2gxG36n3LgdneOw\nYIGzOMrRZmPZMteRthIZOdLd2CVt8UXk6BOO/ftdhaqIS3OrZHxBa2wMn2O8vt5ZH42NKYupd++U\nqyq9it1f1qtXav2ge6qmJrvrqlOntimL9fVt76QHDWp/DmHLsglHGP76mS68I0Zkv6s+9ti2c4WE\nMWpUNDdFba07XtRgOpQ3QF5tcY5jjnG/q2KJXRyWLoW77ipPcD4KFeSuOnqE45133IWnWzd3V1Pp\npFsZQVdV8OLfq5e74PufZ4p7QMri6NQptbxnz7ZWRlAs0uMa6e8HDGj7PqrF4S9LFwJfONKXd+kS\nvm8ffxa5TMJy7LGZt/UZPTq6G2DMmFSvsCiMHx9PaHyKESCvxjiHb3WUmsGD3e+smEJbTFascLOE\nVgAdXzhuvtm1NPcDw5WOb2X06BEuHOnPuQLlYcIRfO2n5PoEX+crHMELuG9xpAfHw8hkcYC7E82E\nLxyZiCIcxx2Xex2fuMWfLS353cVOmuRcdIW4baZNK14tB6Q65SbpSipXnAMqO7tq+nSXLFEBTQ8T\nFQ4RWS4iW0Rkq4h8LeTzVhHZJyKPe49vRN02J48/DuefD6ecAr/9bYFnUiJqa5310L27cz81Nrrl\nPXumBCJdMDIFyLNZHOmv+/ZNXdibm9u+hvBgObQXjjC3VJjFEbYeZBeOYcMyf1YM4Rg8OBUfykVc\n4cg34cLPXCskGD1tWnEDqn37tndhFpsFC0rb9y3IiSdWbj1HTY0rPq4Ad1ViwiEinYDLgOVAC3CW\niIwLWXWtqk71HpfE3LY9zz/vLnTTpsHllxfjVEqDH6uAlLURFI4wwQi6rPzYRnqMo2dP94Pzg+O+\nCATFIlNcI1cKbrr7yBeS4IUqTCTq6sLTefMVjhEjMn8G0YTDn6gpCmPGRFvPZ+RId1MQF//7y9TE\nMQp9+mT/2+XDrFnF3V86Y8YkL06ZWLgw2bYqhbJiRXF7kOVJkhbHTGCbqm5X1QPA1cCKkPXCHNNR\nt21PlItEJdKjh3uIpKyNoFuqSxd3wfW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"text": [
"<matplotlib.figure.Figure at 0x7fbd9988d290>"
]
}
],
"prompt_number": 36
}
],
"metadata": {}
}
]
}
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