In [1]: import numpy.random\n \n In [2]: rng = np.random.default_rng()\n \n In [3]: %timeit -n 1 rng.standard_normal(100000)\n ...: %timeit -n 1 numpy.random.standard_normal(100000)\n ...: \n-1.02 ms +- 53.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-2.57 ms +- 68.7 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+935 us +- 46.7 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.54 ms +- 43.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n In [4]: %timeit -n 1 rng.standard_exponential(100000)\n ...: %timeit -n 1 numpy.random.standard_exponential(100000)\n ...: \n-1 ms +- 15.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-1.88 ms +- 18.7 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+799 us +- 18.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.88 ms +- 14.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n In [5]: %timeit -n 1 rng.standard_gamma(3.0, 100000)\n ...: %timeit -n 1 numpy.random.standard_gamma(3.0, 100000)\n ...: \n-2.47 ms +- 22.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-7.95 ms +- 3.34 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.34 ms +- 29.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+4.47 ms +- 19.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n integers is now the canonical way to generate integer\n random numbers from a discrete uniform distribution. This replaces both\n randint and the deprecated random_integers.
The rand and randn methods are only available through the legacy\n@@ -586,21 +586,21 @@\n
Standard Exponentials (standard_exponential)
In [6]: rng = np.random.default_rng()\n \n In [7]: rng.random(3, dtype=np.float64)\n-Out[7]: array([0.26314191, 0.23305205, 0.21018643])\n+Out[7]: array([0.22978782, 0.08194945, 0.27917787])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.1394285 , 0.46245968, 0.24632704], dtype=float32)\n+Out[8]: array([0.0332737 , 0.40015244, 0.07163864], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([140, 155, 8], dtype=uint8)\n+Out[9]: array([ 42, 218, 66], dtype=uint8)\n Optional out argument that allows existing arrays to be filled for\n select distributions
Uniforms (random)
In [10]: rng = np.random.default_rng()\n \n In [11]: existing = np.zeros(4)\n \n In [12]: rng.random(out=existing[:2])\n-Out[12]: array([0.12454461, 0.18662093])\n+Out[12]: array([0.71719118, 0.0370398 ])\n \n In [13]: print(existing)\n-[0.12454461 0.18662093 0. 0. ]\n+[0.71719118 0.0370398 0. 0. ]\n Optional axis argument for methods like choice,\n permutation and shuffle that controls which\n axis an operation is performed over for multi-dimensional arrays.
Added a method to sample from the complex normal distribution\n (complex_normal)
With the legacy polynomial module, a linear fit (i.e. polynomial of degree 1)\n could be applied to these data with polyfit:
In [4]: np.polyfit(x, y, deg=1)\n-Out[4]: array([ 1.14016016, -1.11946821])\n+Out[4]: array([ 1.06730508, -0.0899841 ])\n With the new polynomial API, the fit\n class method is preferred:
In [5]: p_fitted = np.polynomial.Polynomial.fit(x, y, deg=1)\n \n In [6]: p_fitted\n-Out[6]: Polynomial([4.01125252, 5.13072073], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.71288877, 4.80287287], domain=[0., 9.], window=[-1., 1.], symbol='x')\n Note that the coefficients are given in the scaled domain defined by the\n linear mapping between the window and domain.\n convert can be used to get the\n coefficients in the unscaled data domain.
In [7]: p_fitted.convert()\n-Out[7]: Polynomial([-1.11946821, 1.14016016], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([-0.0899841 , 1.06730508], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n polynomial package#In addition to standard power series polynomials, the polynomial package\n", "details": [{"source1": "html2text {}", "source2": "html2text {}", "unified_diff": "@@ -150,26 +150,26 @@\n \n In [2]: x = np.arange(10)\n \n In [3]: y = np.arange(10) + rng.standard_normal(10)\n With the legacy polynomial module, a linear fit (i.e. polynomial of degree 1)\n could be applied to these data with _\bp_\bo_\bl_\by_\bf_\bi_\bt:\n In [4]: np.polyfit(x, y, deg=1)\n-Out[4]: array([ 1.14016016, -1.11946821])\n+Out[4]: array([ 1.06730508, -0.0899841 ])\n With the new polynomial API, the _\bf_\bi_\bt class method is preferred:\n In [5]: p_fitted = np.polynomial.Polynomial.fit(x, y, deg=1)\n \n In [6]: p_fitted\n-Out[6]: Polynomial([4.01125252, 5.13072073], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.71288877, 4.80287287], domain=[0., 9.], window=[-1.,\n 1.], symbol='x')\n Note that the coefficients are given i\bin\bn t\bth\bhe\be s\bsc\bca\bal\ble\bed\bd d\bdo\bom\bma\bai\bin\bn defined by the linear\n mapping between the window and domain. _\bc_\bo_\bn_\bv_\be_\br_\bt can be used to get the\n coefficients in the unscaled data domain.\n In [7]: p_fitted.convert()\n-Out[7]: Polynomial([-1.11946821, 1.14016016], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([-0.0899841 , 1.06730508], domain=[-1., 1.], window=[-1.,\n 1.], symbol='x')\n *\b**\b**\b**\b**\b* D\bDo\boc\bcu\bum\bme\ben\bnt\bta\bat\bti\bio\bon\bn f\bfo\bor\br t\bth\bhe\be _\bp\bp_\bo\bo_\bl\bl_\by\by_\bn\bn_\bo\bo_\bm\bm_\bi\bi_\ba\ba_\bl\bl p\bpa\bac\bck\bka\bag\bge\be_\b#\b# *\b**\b**\b**\b**\b*\n In addition to standard power series polynomials, the polynomial package\n provides several additional kinds of polynomials including Chebyshev, Hermite\n (two subtypes), Laguerre, and Legendre polynomials. Each of these has an\n associated c\bco\bon\bnv\bve\ben\bni\bie\ben\bnc\bce\be c\bcl\bla\bas\bss\bs available from the _\bn_\bu_\bm_\bp_\by_\b._\bp_\bo_\bl_\by_\bn_\bo_\bm_\bi_\ba_\bl namespace that\n provides a consistent interface for working with polynomials regardless of\n"}]}, {"source1": "./usr/share/doc/python-numpy/html/searchindex.js", "source2": "./usr/share/doc/python-numpy/html/searchindex.js", "unified_diff": null, "details": [{"source1": "js-beautify {}", "source2": "js-beautify {}", "unified_diff": "@@ -32337,29 +32337,28 @@\n \"009a87ff44bf\": 42,\n \"00j\": [514, 642, 2167],\n \"01\": [41, 42, 45, 54, 55, 62, 147, 162, 163, 164, 335, 361, 410, 514, 547, 557, 566, 669, 897, 1088, 1094, 1586, 1594, 1601, 1658, 1715, 1772, 1829, 1885, 2104, 2160, 2323, 2329, 2367, 2373, 2414, 2420, 2525, 2657],\n \"010\": [653, 1602, 1659, 1716, 1773, 1830, 1886],\n \"0100\": 1519,\n \"01041667\": 1585,\n \"011\": [1602, 1659, 1716, 1773, 1830, 1886],\n- \"01125252\": 2488,\n \"012\": [1602, 1659, 1716, 1773, 1830, 1886],\n \"0123456789\": [303, 2132],\n \"01280782\": [2335, 2378, 2425],\n \"016\": [648, 653],\n \"01652764\": 2634,\n \"01666667\": 1544,\n \"016j\": 2105,\n \"01831564\": 1660,\n \"018318\": [2353, 2400, 2450],\n \"01j\": 514,\n \"01t00\": [55, 62, 361, 2525],\n \"01t08\": 2525,\n \"01t12\": 55,\n- \"02\": [54, 55, 147, 162, 163, 410, 547, 566, 669, 1335, 1586, 1601, 1658, 1715, 1772, 1816, 1829, 1885, 2104, 2461],\n+ \"02\": [54, 55, 147, 162, 163, 410, 547, 566, 669, 1335, 1586, 1601, 1658, 1715, 1772, 1816, 1829, 1885, 2104],\n \"020995\": 57,\n \"02284196\": 1697,\n \"02294967\": 1640,\n \"023\": 2643,\n \"02332573e\": 54,\n \"0253\": 2651,\n \"02654825\": 1891,\n@@ -32367,16 +32366,18 @@\n \"02755911\": 2665,\n \"027559113243068367\": 2665,\n \"02785049\": 1867,\n \"02i\": [513, 2643],\n \"03\": [55, 67, 163, 566, 669, 1335, 1586, 1816, 2657],\n \"03125\": [1585, 2491],\n \"0326911\": [2335, 2378, 2425],\n+ \"0332737\": 2461,\n \"0361\": 2607,\n \"03703704\": 1809,\n+ \"0370398\": 2461,\n \"03943254e\": 2104,\n \"03968254\": [1113, 1543],\n \"0396842\": 680,\n \"03t13\": 55,\n \"04\": [54, 55, 164, 410, 547, 1586, 2463, 2594, 2658],\n \"0400\": 360,\n \"04097352\": 2634,\n@@ -32394,33 +32395,37 @@\n \"0596779\": 1153,\n \"06\": [55, 566, 2083, 2508],\n \"0614962j\": [439, 453],\n \"0625\": [418, 624, 1645],\n \"06369197489564249\": 2458,\n \"06381726\": 349,\n \"0660\": [302, 2131],\n+ \"06730508\": 2488,\n \"06959433e\": [420, 947],\n \"07\": [55, 164, 547, 896, 897, 1335, 2170, 2508],\n \"07106781e\": 514,\n+ \"07163864\": 2461,\n \"07407407\": 1809,\n \"07779185\": 2458,\n \"07937323\": 524,\n \"07944154\": [657, 2654],\n \"08\": [55, 91, 147, 410, 523, 548, 896, 1095, 2322, 2366, 2413, 2525, 2658],\n \"0800\": 2525,\n \"08187135\": 54,\n+ \"08194945\": 2461,\n \"08333333\": [1645, 1871],\n \"08405657\": 1867,\n \"0855\": 2641,\n \"08553692\": 38,\n \"085537\": 2641,\n \"0856306\": 1154,\n \"08618131\": 1526,\n \"08703704\": [1113, 1543],\n \"087300000000000003\": [2346, 2392, 2441],\n+ \"0899841\": 2488,\n \"09\": [55, 2171, 2252, 2323, 2367, 2414],\n \"090097550553843\": 2641,\n \"09417735\": [349, 2457, 2638],\n \"0943951\": 1911,\n \"09640474436813\": 675,\n \"09861229\": [657, 2654],\n \"0999755859375\": 62,\n@@ -32655,15 +32660,14 @@\n \"1179\": 2463,\n \"118\": 2463,\n \"1180339887498949\": 2115,\n \"11803399\": 1228,\n \"11885628817151628\": 2458,\n \"119\": 2616,\n \"11902\": 2544,\n- \"11946821\": 2488,\n \"11981\": 2544,\n \"11982\": 2544,\n \"11985\": 2541,\n \"11986\": 2541,\n \"11987\": 2541,\n \"11992\": 2544,\n \"11995\": 2541,\n@@ -32714,15 +32718,14 @@\n \"123456789a12\": 25,\n \"123456789a123456789b\": 25,\n \"1234567e\": 2172,\n \"12346\": 2462,\n \"1235\": 2091,\n \"123abc\": [302, 305, 2131, 2134],\n \"124\": [98, 905],\n- \"12454461\": 2461,\n \"125\": [470, 660, 1114, 1142, 1645, 1651, 1899, 1900, 2239, 2339, 2382, 2429, 2460, 2491, 2658, 2665],\n \"12589991e\": 645,\n \"126\": [863, 1048, 1116, 1904],\n \"1261\": 2612,\n \"12658\": 2560,\n \"12697628\": 2634,\n \"127\": [62, 66, 514, 863, 1048, 1102, 1116, 1904, 2301, 2302, 2462, 2463, 2464, 2583, 2638],\n@@ -32745,15 +32748,14 @@\n \"130\": 409,\n \"1300000\": 2634,\n \"13020\": 2549,\n \"13026\": 2549,\n \"13028\": 2549,\n \"13038\": 2549,\n \"13041\": 2549,\n- \"13072073\": 2488,\n \"13090\": [186, 827, 999, 1172, 1259, 1414, 1933],\n \"131\": [527, 2463],\n \"1312\": 485,\n \"13182611e\": [420, 947],\n \"132\": [527, 2330, 2374, 2421, 2463, 2636],\n \"1324274851176597e\": 1867,\n \"133\": [527, 2330, 2374, 2421],\n@@ -32799,22 +32801,20 @@\n \"13845\": 2552,\n \"13867\": 2552,\n \"1387\": 2612,\n \"13899\": 2560,\n \"139\": 655,\n \"13905\": 2552,\n \"13933\": 2552,\n- \"1394285\": 2461,\n \"13984\": 2552,\n \"13994\": 2552,\n \"13d7934\": 13,\n \"13j\": 1915,\n \"14\": [9, 47, 54, 55, 56, 57, 58, 59, 98, 107, 108, 114, 140, 141, 142, 270, 366, 367, 375, 460, 476, 486, 530, 542, 544, 546, 566, 645, 661, 880, 893, 905, 963, 968, 969, 1069, 1083, 1143, 1229, 1247, 1312, 1466, 1577, 1695, 1704, 1711, 1758, 1764, 1867, 1873, 1986, 2086, 2089, 2115, 2168, 2205, 2206, 2208, 2209, 2210, 2222, 2224, 2225, 2237, 2240, 2246, 2333, 2342, 2377, 2385, 2424, 2432, 2457, 2461, 2463, 2490, 2513, 2519, 2531, 2542, 2543, 2544, 2545, 2546, 2547, 2553, 2554, 2559, 2560, 2561, 2566, 2572, 2576, 2583, 2584, 2585, 2586, 2588, 2591, 2596, 2599, 2600, 2622, 2627, 2634, 2637, 2640, 2644, 2652, 2656, 2658, 2665],\n- \"140\": [2238, 2461, 2576],\n- \"14016016\": 2488,\n+ \"140\": [2238, 2576],\n \"14022471\": [2387, 2434],\n \"14036\": 2560,\n \"14039\": 2560,\n \"14042\": 2552,\n \"14043\": 2552,\n \"14044\": 2552,\n \"14045\": 2552,\n@@ -33023,15 +33023,15 @@\n \"15302337\": 523,\n \"1534\": 485,\n \"15355\": 2566,\n \"15385\": 2566,\n \"154\": [2463, 2665],\n \"15427\": 2566,\n \"15463\": 2566,\n- \"155\": [2461, 2463, 2636],\n+ \"155\": [2463, 2636],\n \"15534\": 2566,\n \"15648\": 2566,\n \"15666\": 2572,\n \"15675\": 2562,\n \"15676\": 2562,\n \"15677\": 2562,\n \"15679\": 2562,\n@@ -33317,15 +33317,14 @@\n \"18629\": 2576,\n \"1863\": 2611,\n \"18636\": 2574,\n \"18638\": 2574,\n \"18657\": 2576,\n \"18658\": 2576,\n \"18661\": 2574,\n- \"18662093\": 2461,\n \"18666\": 2576,\n \"1867\": 1643,\n \"18671\": 2574,\n \"18695\": 2576,\n \"18697\": 2576,\n \"187\": [2332, 2376, 2423],\n \"1870\": 2611,\n@@ -33669,15 +33668,14 @@\n \"20993\": 2588,\n \"20_ver\": 0,\n \"20count\": 141,\n \"20d03bcfd\": 0,\n \"21\": [21, 26, 28, 30, 31, 40, 47, 54, 55, 58, 74, 98, 162, 163, 270, 336, 357, 359, 377, 388, 396, 403, 476, 477, 628, 661, 669, 880, 905, 944, 1069, 1229, 1312, 1466, 1869, 1881, 1986, 2091, 2168, 2172, 2208, 2225, 2230, 2237, 2238, 2342, 2343, 2463, 2513, 2515, 2517, 2519, 2567, 2568, 2572, 2583, 2585, 2588, 2594, 2627, 2628, 2632, 2634, 2636, 2640, 2641, 2648, 2653, 2656, 2664, 2665, 2667],\n \"210\": 363,\n \"21001\": 2588,\n- \"21018643\": 2461,\n \"21029\": 2588,\n \"210306068529402873165736369884012333109\": [2275, 2280],\n \"21048\": 2586,\n \"211\": 2491,\n \"21106\": 2586,\n \"21120\": 2599,\n \"21130\": 2588,\n@@ -33735,30 +33733,30 @@\n \"21595\": 2594,\n \"216\": 2665,\n \"21623\": [2588, 2594],\n \"21627\": 2594,\n \"21645\": 2594,\n \"21663\": 2588,\n \"21760\": 2622,\n- \"218\": [566, 2463],\n+ \"218\": [566, 2461, 2463],\n \"21807\": 2594,\n \"2184\": 2225,\n \"21866\": 2589,\n \"21867\": 2589,\n \"21868\": 2589,\n \"21869\": 2589,\n \"21870\": 2589,\n \"219\": 2463,\n \"21925\": 2594,\n \"21949\": 2589,\n \"21951\": 2589,\n \"21952\": 2589,\n \"21976\": 2594,\n \"21995\": 2594,\n- \"22\": [21, 22, 29, 30, 40, 47, 52, 54, 55, 58, 59, 98, 107, 108, 109, 163, 270, 336, 378, 425, 485, 628, 658, 669, 880, 905, 1045, 1069, 1113, 1211, 1229, 1294, 1312, 1336, 1337, 1340, 1341, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1358, 1448, 1466, 1514, 1521, 1522, 1543, 1591, 1905, 1908, 1913, 1968, 1986, 2091, 2208, 2236, 2237, 2342, 2461, 2513, 2517, 2519, 2534, 2588, 2634, 2636, 2640, 2656, 2665],\n+ \"22\": [21, 22, 29, 30, 40, 47, 52, 54, 55, 58, 59, 98, 107, 108, 109, 163, 270, 336, 378, 425, 485, 628, 658, 669, 880, 905, 1045, 1069, 1113, 1211, 1229, 1294, 1312, 1336, 1337, 1340, 1341, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1358, 1448, 1466, 1514, 1521, 1522, 1543, 1591, 1905, 1908, 1913, 1968, 1986, 2091, 2208, 2236, 2237, 2342, 2513, 2517, 2519, 2534, 2588, 2634, 2636, 2640, 2656, 2665],\n \"220\": [2238, 2576],\n \"22004\": 2594,\n \"22014\": 2594,\n \"22030\": 2590,\n \"22031\": 2590,\n \"22032\": 2590,\n \"22033\": 2590,\n@@ -33893,14 +33891,15 @@\n \"22967\": 2596,\n \"22968\": 2596,\n \"22969\": 2596,\n \"22970\": 2596,\n \"22971\": 2596,\n \"22972\": 2596,\n \"22976\": 2596,\n+ \"22978782\": 2461,\n \"22982\": 2599,\n \"22989\": 2596,\n \"22997\": 2599,\n \"22998\": 2599,\n \"22e\": 457,\n \"23\": [1, 8, 10, 18, 32, 43, 47, 54, 55, 58, 62, 63, 75, 79, 98, 135, 139, 163, 270, 287, 329, 336, 483, 513, 628, 669, 880, 905, 917, 1029, 1069, 1104, 1229, 1241, 1312, 1324, 1466, 1478, 1545, 1707, 1748, 1777, 1903, 1913, 1986, 1998, 2154, 2208, 2235, 2237, 2256, 2321, 2340, 2342, 2365, 2383, 2412, 2430, 2513, 2519, 2542, 2552, 2595, 2622, 2627, 2634, 2636, 2640, 2644, 2647, 2656, 2665],\n \"230\": 409,\n@@ -33935,15 +33934,14 @@\n \"23226\": 2597,\n \"23229\": 2599,\n \"23240\": 2599,\n \"23275\": 2599,\n \"23297648\": 349,\n \"233\": [28, 2463],\n \"23302\": 2599,\n- \"23305205\": 2461,\n \"23314\": 2599,\n \"23322\": 2599,\n \"23341\": 2597,\n \"23342\": 2597,\n \"23343\": 2597,\n \"23344\": 2597,\n \"23345\": 2597,\n@@ -34109,15 +34107,14 @@\n \"24614\": 2602,\n \"24615\": 2602,\n \"24616\": 2602,\n \"24617\": 2602,\n \"24622\": 2602,\n \"24629\": 2602,\n \"24630\": 2602,\n- \"24632704\": 2461,\n \"24634\": 2622,\n \"24637\": 2602,\n \"24638\": 2602,\n \"24647\": 2602,\n \"24648\": 2602,\n \"24653\": 2602,\n \"24659\": 2602,\n@@ -34345,15 +34342,14 @@\n \"26137788e\": 2104,\n \"26157\": 2625,\n \"262\": 2665,\n \"26268\": 2625,\n \"26285\": 2625,\n \"26292\": 2625,\n \"26313\": 2625,\n- \"26314191\": 2461,\n \"26388\": 2625,\n \"26393\": 2622,\n \"26452\": 2625,\n \"26501\": 2625,\n \"26579\": 2625,\n \"26580\": 2625,\n \"26590556\": 2634,\n@@ -34493,14 +34489,15 @@\n \"27735\": 2629,\n \"27736\": 2629,\n \"27807\": 2629,\n \"27808\": 2629,\n \"27896\": 2629,\n \"278dd2a\": 13,\n \"2791\": 2615,\n+ \"27917787\": 2461,\n \"27935\": 2630,\n \"2794155\": 2665,\n \"27950\": 2630,\n \"27955\": 2630,\n \"27958\": 2630,\n \"2795853\": 533,\n \"27959\": 2630,\n@@ -34577,15 +34574,15 @@\n \"28657\": 28,\n \"28790332\": 2665,\n \"2883\": [1643, 1655],\n \"28853036\": 1867,\n \"28904982231052\": 675,\n \"2892\": 2615,\n \"28mathematical_const\": 76,\n- \"29\": [10, 21, 45, 54, 55, 76, 144, 163, 1638, 1647, 2208, 2328, 2463, 2464, 2513, 2547, 2548, 2549, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2587, 2602, 2622, 2640, 2656, 2665],\n+ \"29\": [10, 21, 45, 54, 55, 76, 144, 163, 1638, 1647, 2208, 2328, 2461, 2463, 2464, 2513, 2547, 2548, 2549, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2587, 2602, 2622, 2640, 2656, 2665],\n \"290\": 2300,\n \"29001ed\": 13,\n \"290301\": 55,\n \"292\": 55,\n \"29229249\": 524,\n \"29239766\": 54,\n \"2925464970228\": 657,\n@@ -34818,14 +34815,15 @@\n \"3x4x5\": 2664,\n \"3x8000\": [2350, 2397, 2447],\n \"4\": [4, 5, 9, 12, 14, 25, 29, 30, 32, 37, 38, 39, 40, 47, 50, 54, 55, 56, 57, 58, 59, 61, 63, 65, 66, 67, 68, 69, 76, 78, 89, 90, 95, 96, 97, 98, 99, 104, 105, 107, 108, 109, 110, 111, 113, 115, 118, 120, 121, 127, 129, 130, 132, 134, 135, 136, 138, 140, 141, 144, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 167, 171, 176, 177, 185, 194, 213, 214, 215, 234, 239, 262, 264, 270, 280, 284, 287, 290, 295, 302, 305, 336, 337, 338, 339, 340, 341, 342, 345, 348, 352, 353, 354, 355, 356, 357, 358, 359, 360, 364, 365, 366, 367, 368, 369, 370, 371, 372, 374, 375, 376, 385, 396, 401, 404, 408, 409, 410, 411, 412, 413, 415, 416, 417, 418, 419, 421, 422, 432, 435, 439, 440, 442, 443, 444, 445, 446, 447, 448, 450, 453, 454, 455, 456, 461, 464, 466, 467, 470, 472, 473, 474, 477, 478, 482, 483, 489, 513, 514, 520, 521, 522, 523, 524, 526, 527, 528, 529, 530, 531, 532, 533, 538, 540, 541, 542, 543, 544, 545, 549, 553, 554, 560, 565, 566, 567, 569, 572, 573, 574, 575, 582, 584, 608, 617, 618, 619, 621, 622, 623, 624, 625, 628, 638, 639, 640, 645, 647, 648, 649, 650, 651, 653, 657, 660, 661, 662, 663, 664, 666, 667, 668, 669, 673, 676, 680, 751, 823, 826, 830, 831, 834, 844, 847, 855, 859, 860, 863, 864, 865, 868, 873, 874, 877, 880, 881, 883, 884, 886, 887, 888, 891, 893, 897, 903, 904, 905, 906, 908, 911, 912, 913, 914, 916, 917, 919, 922, 924, 925, 926, 928, 929, 932, 936, 942, 943, 944, 945, 946, 948, 950, 952, 953, 957, 958, 959, 960, 961, 963, 964, 967, 968, 969, 976, 978, 988, 993, 997, 1002, 1003, 1006, 1011, 1020, 1023, 1027, 1029, 1038, 1042, 1044, 1045, 1048, 1049, 1050, 1052, 1054, 1061, 1063, 1066, 1069, 1070, 1072, 1074, 1076, 1077, 1078, 1081, 1083, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1094, 1096, 1097, 1100, 1103, 1104, 1105, 1106, 1107, 1110, 1113, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1133, 1135, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1147, 1148, 1153, 1154, 1155, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1166, 1167, 1171, 1178, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1203, 1204, 1205, 1206, 1208, 1211, 1212, 1213, 1224, 1226, 1227, 1228, 1229, 1230, 1236, 1239, 1240, 1241, 1242, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1258, 1265, 1278, 1279, 1281, 1286, 1291, 1294, 1307, 1309, 1312, 1319, 1322, 1324, 1326, 1327, 1328, 1329, 1331, 1333, 1334, 1336, 1337, 1339, 1341, 1342, 1344, 1346, 1347, 1349, 1351, 1413, 1420, 1433, 1434, 1435, 1440, 1445, 1448, 1461, 1463, 1466, 1473, 1476, 1478, 1479, 1480, 1483, 1510, 1512, 1513, 1515, 1517, 1520, 1521, 1522, 1523, 1526, 1527, 1540, 1541, 1542, 1543, 1544, 1545, 1554, 1557, 1574, 1575, 1577, 1578, 1579, 1586, 1588, 1590, 1591, 1596, 1604, 1605, 1606, 1615, 1618, 1635, 1639, 1643, 1644, 1649, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1661, 1662, 1663, 1672, 1675, 1692, 1694, 1696, 1706, 1709, 1710, 1711, 1718, 1719, 1720, 1729, 1732, 1749, 1750, 1751, 1753, 1757, 1758, 1759, 1763, 1765, 1766, 1767, 1768, 1769, 1770, 1775, 1776, 1777, 1786, 1789, 1805, 1806, 1808, 1809, 1810, 1812, 1816, 1818, 1820, 1822, 1824, 1832, 1833, 1834, 1843, 1846, 1862, 1864, 1865, 1866, 1867, 1869, 1870, 1875, 1876, 1879, 1880, 1881, 1882, 1883, 1884, 1886, 1887, 1888, 1889, 1890, 1893, 1896, 1897, 1899, 1900, 1902, 1904, 1905, 1908, 1909, 1911, 1912, 1913, 1914, 1915, 1916, 1919, 1922, 1923, 1924, 1932, 1939, 1953, 1954, 1955, 1960, 1965, 1968, 1981, 1983, 1986, 1993, 1996, 1998, 2071, 2072, 2074, 2075, 2079, 2080, 2081, 2082, 2083, 2084, 2085, 2087, 2088, 2089, 2090, 2091, 2093, 2095, 2096, 2097, 2098, 2101, 2104, 2106, 2107, 2110, 2111, 2114, 2115, 2116, 2119, 2123, 2124, 2126, 2127, 2131, 2134, 2139, 2145, 2161, 2163, 2164, 2168, 2175, 2176, 2178, 2184, 2195, 2199, 2201, 2202, 2204, 2205, 2206, 2208, 2209, 2210, 2211, 2217, 2223, 2224, 2225, 2229, 2230, 2236, 2237, 2238, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2248, 2250, 2251, 2256, 2257, 2290, 2303, 2304, 2308, 2312, 2316, 2319, 2320, 2322, 2324, 2327, 2328, 2329, 2332, 2333, 2334, 2339, 2340, 2341, 2342, 2343, 2347, 2352, 2356, 2359, 2361, 2363, 2364, 2366, 2368, 2373, 2376, 2377, 2382, 2383, 2384, 2388, 2389, 2390, 2395, 2399, 2403, 2406, 2408, 2410, 2411, 2413, 2415, 2420, 2423, 2424, 2429, 2430, 2431, 2435, 2436, 2438, 2445, 2449, 2453, 2456, 2457, 2460, 2461, 2462, 2463, 2470, 2488, 2489, 2490, 2491, 2510, 2513, 2519, 2529, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2540, 2541, 2542, 2543, 2544, 2545, 2547, 2548, 2549, 2550, 2552, 2559, 2566, 2572, 2579, 2581, 2588, 2591, 2593, 2599, 2602, 2607, 2609, 2610, 2613, 2614, 2615, 2616, 2617, 2619, 2620, 2622, 2624, 2625, 2628, 2634, 2636, 2637, 2639, 2640, 2641, 2643, 2644, 2645, 2646, 2648, 2649, 2651, 2652, 2654, 2656, 2657, 2658, 2664, 2665],\n \"40\": [32, 99, 143, 270, 409, 444, 446, 454, 568, 569, 570, 880, 906, 1069, 1117, 1229, 1312, 1466, 1906, 1986, 2089, 2165, 2204, 2208, 2323, 2367, 2414, 2634, 2638, 2640, 2656, 2665],\n \"400\": [55, 444],\n \"4000000000000p\": 669,\n \"4001\": [99, 906],\n+ \"40015244\": 2461,\n \"40067661\": 2634,\n \"4007\": 2620,\n \"40077\": [1644, 1656],\n \"400e\": 2657,\n \"4018\": [2615, 2617],\n \"4024\": 2617,\n \"4027\": 2617,\n@@ -34857,15 +34855,15 @@\n \"4167\": 1643,\n \"4170\": 2617,\n \"4176\": 2617,\n \"4181\": [28, 2621],\n \"4187\": 2617,\n \"4191\": 2617,\n \"4197\": 2617,\n- \"42\": [31, 58, 63, 147, 349, 669, 896, 897, 974, 1029, 2090, 2208, 2256, 2332, 2376, 2423, 2457, 2566, 2605, 2622, 2634, 2638, 2656, 2663, 2664, 2665],\n+ \"42\": [31, 58, 63, 147, 349, 669, 896, 897, 974, 1029, 2090, 2208, 2256, 2332, 2376, 2423, 2457, 2461, 2566, 2605, 2622, 2634, 2638, 2656, 2663, 2664, 2665],\n \"420\": [2238, 2576],\n \"42016704\": 2665,\n \"4206\": 2617,\n \"4220\": 2617,\n \"4223\": 2617,\n \"4225\": 2617,\n \"423\": 55,\n@@ -34881,15 +34879,15 @@\n \"42667924\": 1154,\n \"4267\": 2617,\n \"4270\": 2617,\n \"4276\": 2617,\n \"429\": 136,\n \"4294967293\": 2638,\n \"4294967296\": [196, 836, 1008, 1179, 1266, 1421, 1940],\n- \"43\": [2208, 2583, 2634, 2640, 2656, 2665],\n+ \"43\": [2208, 2461, 2583, 2634, 2640, 2656, 2665],\n \"430148\": 2634,\n \"43014843\": 2634,\n \"43181166\": 2458,\n \"4354\": 2617,\n \"4359\": 2617,\n \"4368\": [287, 1241, 1324, 1478, 1998],\n \"4375\": 2491,\n@@ -34930,21 +34928,20 @@\n \"4532\": [409, 661, 2168],\n \"4545724517479104\": 2460,\n \"45560727e\": 54,\n \"456\": 1921,\n \"4567\": 2643,\n \"45674898e\": 566,\n \"45a3d84\": 2521,\n- \"46\": [409, 523, 905, 1707, 2204, 2208, 2640, 2656],\n+ \"46\": [409, 523, 905, 1707, 2204, 2208, 2461, 2640, 2656],\n \"460\": [2238, 2576],\n \"46009194e\": 566,\n \"4602\": 2618,\n \"4610935\": 457,\n \"4613\": 2618,\n- \"46245968\": 2461,\n \"4628\": 2618,\n \"46351241j\": 2081,\n \"46368\": 28,\n \"464\": 680,\n \"4642\": 2618,\n \"465\": [58, 1157],\n \"4656\": 2618,\n@@ -35065,15 +35062,15 @@\n \"52359878\": 1911,\n \"52380952e\": 1816,\n \"5240\": 2620,\n \"5251\": 2620,\n \"526\": 2463,\n \"5260\": [2353, 2400, 2450],\n \"5271\": 42,\n- \"53\": [162, 457, 1638, 2208, 2461, 2551, 2554, 2656, 2665],\n+ \"53\": [162, 457, 1638, 2208, 2551, 2554, 2656, 2665],\n \"5306\": [409, 661, 2168],\n \"5313\": 2621,\n \"5316\": 2621,\n \"5324j\": [416, 417, 622, 623],\n \"5354\": 2621,\n \"5359\": 2621,\n \"5363922081269535\": 2458,\n@@ -35081,15 +35078,15 @@\n \"536870910\": 1902,\n \"5374\": 2621,\n \"53814331\": 2665,\n \"5388\": 2621,\n \"5390\": 2621,\n \"5393\": 2621,\n \"5396\": [287, 1241, 1324, 1478, 1998],\n- \"54\": [38, 59, 523, 1638, 1711, 1764, 2208, 2641, 2656],\n+ \"54\": [38, 59, 523, 1638, 1711, 1764, 2208, 2461, 2641, 2656],\n \"540\": [2238, 2576],\n \"54030231\": 2665,\n \"54030231j\": 2665,\n \"541\": 2463,\n \"54117\": 1644,\n \"5424\": 2621,\n \"54323428\": [2345, 2391, 2439],\n@@ -35124,15 +35121,15 @@\n \"5620499351813308\": 86,\n \"5625\": 2491,\n \"56294995342131\": 2083,\n \"5640\": [2353, 2400, 2450],\n \"567\": 2643,\n \"56826729e\": 2104,\n \"56917101\": 2634,\n- \"57\": [58, 669, 2204, 2322, 2366, 2413, 2461, 2463, 2491, 2636, 2656],\n+ \"57\": [58, 669, 2204, 2322, 2366, 2413, 2463, 2491, 2636, 2656],\n \"5707963267948966\": [102, 125],\n \"57079633\": [94, 105, 130, 1911, 2238, 2665],\n \"5708\": [412, 618],\n \"57115742\": 524,\n \"57136612e\": 2173,\n \"57510612\": 660,\n \"576\": 2615,\n@@ -35275,15 +35272,15 @@\n \"6586976\": 1149,\n \"6590\": 2522,\n \"6596\": 2522,\n \"6596288841243357\": 2458,\n \"659885634118668e\": 645,\n \"65_535\": 62,\n \"65x\": 2594,\n- \"66\": [13, 58, 1922, 2547, 2656, 2665],\n+ \"66\": [13, 58, 1922, 2461, 2547, 2656, 2665],\n \"6600475\": 1149,\n \"6602\": 2522,\n \"6606\": 2522,\n \"6611\": 2522,\n \"6614\": 2522,\n \"6618\": 2522,\n \"6621\": 2522,\n@@ -35324,15 +35321,15 @@\n \"6765\": 28,\n \"6771\": 2522,\n \"6775\": 2522,\n \"6780\": 2522,\n \"6781\": 2522,\n \"6783\": 2522,\n \"6785\": 2522,\n- \"68\": [2461, 2656, 2658, 2665],\n+ \"68\": [2656, 2658, 2665],\n \"6805\": [2353, 2400, 2450],\n \"6807\": 2522,\n \"68080986\": 349,\n \"6813\": 2522,\n \"6817\": 2522,\n \"6819\": 2522,\n \"68206631e\": 2104,\n@@ -35378,15 +35375,17 @@\n \"70710678\": [216, 247, 641, 1199, 1216, 1282, 1299, 1436, 1453, 1636, 1642, 1956, 1973, 2103],\n \"70710678118654746\": 637,\n \"70710678j\": 641,\n \"7083\": 2529,\n \"71\": [354, 650, 2460, 2656],\n \"71080601\": 2658,\n \"71238898\": 1911,\n+ \"71288877\": 2488,\n \"71387850e\": 1586,\n+ \"71719118\": 2461,\n \"718281\": 431,\n \"71828182845904523536028747135266249775724709369995\": 76,\n \"71828183\": [38, 2665],\n \"718282\": 2641,\n \"7183\": 2641,\n \"7185\": [99, 906],\n \"71946897\": 1153,\n@@ -35511,14 +35510,15 @@\n \"7954\": 2527,\n \"7955\": 2527,\n \"79579319e\": 1867,\n \"79694221e\": 1586,\n \"7972\": 2527,\n \"7976931348623157e\": 1335,\n \"79769313e\": 1335,\n+ \"799\": 2461,\n \"79ff\": [102, 125],\n \"7e\": 669,\n \"7e13\": 55,\n \"7e17\": 55,\n \"7x\": [2566, 2599],\n \"8\": [9, 11, 13, 17, 18, 24, 26, 28, 30, 31, 32, 34, 36, 38, 39, 43, 47, 50, 56, 57, 58, 59, 60, 61, 62, 69, 72, 73, 74, 76, 89, 91, 96, 97, 98, 99, 114, 117, 118, 119, 132, 135, 141, 142, 149, 150, 169, 171, 172, 173, 209, 215, 229, 234, 261, 262, 270, 295, 313, 315, 320, 331, 332, 334, 337, 348, 355, 364, 365, 366, 367, 369, 370, 375, 385, 387, 391, 396, 399, 401, 406, 409, 410, 416, 417, 432, 435, 438, 440, 454, 455, 467, 470, 478, 486, 514, 520, 529, 530, 533, 538, 541, 543, 544, 546, 548, 554, 565, 566, 577, 608, 622, 623, 639, 640, 645, 651, 653, 656, 657, 659, 660, 661, 662, 664, 665, 666, 667, 680, 830, 854, 860, 863, 864, 865, 873, 880, 881, 883, 886, 887, 888, 893, 896, 903, 904, 905, 906, 912, 913, 914, 917, 919, 920, 921, 924, 926, 927, 936, 943, 950, 952, 953, 957, 963, 1002, 1027, 1029, 1035, 1044, 1048, 1049, 1050, 1060, 1061, 1069, 1070, 1072, 1076, 1077, 1078, 1083, 1100, 1104, 1106, 1107, 1111, 1112, 1113, 1116, 1119, 1122, 1123, 1124, 1135, 1142, 1143, 1145, 1148, 1159, 1160, 1161, 1164, 1166, 1167, 1193, 1194, 1195, 1198, 1202, 1203, 1204, 1205, 1206, 1212, 1213, 1223, 1224, 1228, 1229, 1236, 1240, 1242, 1243, 1246, 1249, 1281, 1285, 1286, 1306, 1307, 1312, 1334, 1435, 1439, 1440, 1460, 1461, 1466, 1482, 1510, 1512, 1518, 1520, 1521, 1543, 1574, 1578, 1579, 1585, 1586, 1590, 1591, 1604, 1605, 1637, 1639, 1644, 1649, 1656, 1661, 1662, 1696, 1706, 1718, 1719, 1752, 1753, 1758, 1761, 1763, 1765, 1770, 1775, 1776, 1809, 1810, 1816, 1819, 1820, 1832, 1833, 1865, 1866, 1867, 1870, 1873, 1875, 1882, 1884, 1886, 1887, 1888, 1899, 1900, 1902, 1904, 1908, 1912, 1913, 1914, 1916, 1955, 1959, 1960, 1980, 1981, 1986, 2076, 2079, 2082, 2085, 2087, 2091, 2095, 2104, 2107, 2110, 2115, 2116, 2124, 2141, 2143, 2148, 2156, 2157, 2159, 2164, 2168, 2172, 2200, 2202, 2204, 2205, 2206, 2208, 2209, 2210, 2223, 2224, 2225, 2236, 2237, 2238, 2239, 2240, 2242, 2246, 2248, 2256, 2257, 2290, 2308, 2312, 2313, 2320, 2328, 2329, 2334, 2335, 2341, 2342, 2347, 2354, 2373, 2378, 2384, 2388, 2390, 2394, 2395, 2401, 2420, 2425, 2431, 2435, 2438, 2444, 2445, 2451, 2457, 2458, 2460, 2461, 2463, 2470, 2508, 2513, 2519, 2525, 2535, 2538, 2542, 2544, 2545, 2547, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 2571, 2572, 2573, 2576, 2579, 2580, 2583, 2584, 2585, 2586, 2587, 2589, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 2613, 2615, 2619, 2622, 2623, 2631, 2634, 2636, 2637, 2638, 2640, 2641, 2643, 2644, 2645, 2647, 2648, 2652, 2654, 2656, 2657, 2658, 2659, 2664, 2665],\n \"80\": [69, 396, 409, 446, 977, 2248, 2346, 2357, 2383, 2392, 2404, 2430, 2441, 2454, 2588, 2622, 2647, 2648, 2656],\n@@ -35526,14 +35526,15 @@\n \"8000\": [2350, 2352, 2397, 2399, 2447, 2449],\n \"80000000000000204\": [1113, 1543],\n \"8005\": 2527,\n \"801\": [941, 1114, 1123, 1124, 1131],\n \"8010\": 2527,\n \"8020\": 2527,\n \"8024\": 2527,\n+ \"80287287\": 2488,\n \"8031\": 2527,\n \"804\": 2508,\n \"8044\": 2527,\n \"8058837395885292\": 666,\n \"80b3a34\": 2614,\n \"81\": [1650, 1884, 2634, 2640, 2644, 2656, 2665],\n \"81299683\": 2634,\n@@ -35664,14 +35665,15 @@\n \"9304e\": 2091,\n \"931\": 2587,\n \"9317\": 2532,\n \"9319\": 2532,\n \"9339\": 2532,\n \"9340\": 2532,\n \"934284\": 349,\n+ \"935\": 2461,\n \"93657855\": 349,\n \"9371\": 2532,\n \"9372\": 2532,\n \"9373\": 2532,\n \"9374\": 2532,\n \"9376\": 2532,\n \"9377\": 2532,\n@@ -35683,15 +35685,15 @@\n \"940\": 2587,\n \"941257\": 2634,\n \"94125714\": 2634,\n \"94708397920832\": 2641,\n \"9475673279178444\": 2348,\n \"94864945\": 2665,\n \"94909878\": [2387, 2434],\n- \"95\": [37, 39, 646, 2353, 2400, 2450, 2461, 2634, 2653, 2656],\n+ \"95\": [37, 39, 646, 2353, 2400, 2450, 2634, 2653, 2656],\n \"9504637\": 2665,\n \"950684\": 2634,\n \"95068423\": 2634,\n \"9555\": [2533, 2534],\n \"9556\": [2533, 2534],\n \"9557\": [2533, 2534],\n \"9558\": [2533, 2534],\n"}]}]}]}]}]}