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-928 us +- 45.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-2.51 ms +- 30.7 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+932 us +- 43.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.51 ms +- 23 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-803 us +- 24.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-1.78 ms +- 60.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+805 us +- 17.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.76 ms +- 15 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-2.39 ms +- 155 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-4.54 ms +- 161 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.35 ms +- 24.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+4.47 ms +- 17 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([0.09982097, 0.64569913, 0.10945991])\n+Out[7]: array([0.92211853, 0.31063142, 0.39304349])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.32890356, 0.16721952, 0.09815568], dtype=float32)\n+Out[8]: array([0.4325282, 0.6530782, 0.8306809], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([46, 21, 19], dtype=uint8)\n+Out[9]: array([239, 174, 112], 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([0.75102103, 0.59497974])\n+Out[12]: array([0.78030787, 0.26031849])\n \n In [13]: print(existing)\n-[0.75102103 0.59497974 0. 0. ]\n+[0.78030787 0.26031849 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([0.94551815, 0.26452129])\n+Out[4]: array([ 1.18197547, -1.21968594])\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([4.51935295, 4.25483166], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.09920367, 5.3188896 ], 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([0.26452129, 0.94551815], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([-1.21968594, 1.18197547], 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([0.94551815, 0.26452129])\n+Out[4]: array([ 1.18197547, -1.21968594])\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([4.51935295, 4.25483166], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.09920367, 5.3188896 ], 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([0.26452129, 0.94551815], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([-1.21968594, 1.18197547], 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": "@@ -32417,17 +32417,16 @@\n \"08703704\": [1113, 1543],\n \"087300000000000003\": [2346, 2392, 2441],\n \"09\": [55, 2171, 2252, 2323, 2367, 2414],\n \"090097550553843\": 2641,\n \"09417735\": [349, 2457, 2638],\n \"0943951\": 1911,\n \"09640474436813\": 675,\n- \"09815568\": 2461,\n \"09861229\": [657, 2654],\n- \"09982097\": 2461,\n+ \"09920367\": 2488,\n \"0999755859375\": 62,\n \"099975586\": 62,\n \"0a1\": 577,\n \"0a2\": 577,\n \"0b00000011\": [1519, 2235],\n \"0b1\": [34, 50, 577, 2602],\n \"0b2\": 577,\n@@ -32567,15 +32566,14 @@\n \"10862\": 2538,\n \"10868\": 2538,\n \"1088311\": 2343,\n \"10898\": 2542,\n \"109\": [136, 523, 2463],\n \"10905\": 2538,\n \"10941\": 2328,\n- \"10945991\": 2461,\n \"10946\": 28,\n \"10947\": 2538,\n \"10959\": 2538,\n \"10960\": 2538,\n \"10961\": 2538,\n \"10962\": 2538,\n \"10974\": 2538,\n@@ -32601,15 +32599,15 @@\n \"1111111111110010\": [142, 546],\n \"11170\": 2539,\n \"11174\": 2539,\n \"11181\": 2539,\n \"11194\": 2539,\n \"11198\": 2539,\n \"11199\": 2539,\n- \"112\": [333, 2158, 2463, 2665],\n+ \"112\": [333, 2158, 2461, 2463, 2665],\n \"11203\": 2539,\n \"11210\": 2542,\n \"11211\": 2539,\n \"11218\": 2542,\n \"11219\": 2539,\n \"11251\": 2539,\n \"11274\": 2540,\n@@ -33020,15 +33018,15 @@\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@@ -33081,15 +33079,15 @@\n \"16055\": 2564,\n \"16056\": 2572,\n \"16068\": 2566,\n \"16080\": 2566,\n \"16090\": 2564,\n \"16091\": 2564,\n \"160m\": 409,\n- \"161\": [2461, 2463],\n+ \"161\": 2463,\n \"16102\": 2566,\n \"16109\": 2564,\n \"16114\": 2564,\n \"16128\": 2566,\n \"16132\": 2564,\n \"16134\": 2572,\n \"16153\": 2566,\n@@ -33135,15 +33133,14 @@\n \"16693\": 2567,\n \"167\": 2463,\n \"16703\": 2567,\n \"16705\": 2567,\n \"16710\": 2572,\n \"16714\": 2567,\n \"1672\": 2612,\n- \"16721952\": 2461,\n \"16724\": 2567,\n \"16730\": 2572,\n \"1675\": 2612,\n \"16768\": 2567,\n \"16772\": 2567,\n \"16776\": 2567,\n \"16779\": 2567,\n@@ -33200,15 +33197,15 @@\n \"17284\": 2572,\n \"17296777\": 2634,\n \"17298\": 2569,\n \"173\": [669, 2636],\n \"17336\": 2569,\n \"17344\": 2572,\n \"17394\": 2572,\n- \"174\": 2463,\n+ \"174\": [2461, 2463],\n \"17446\": 2569,\n \"17450\": 2569,\n \"17456\": 2572,\n \"1747\": 2612,\n \"1749\": 2611,\n \"17492\": 2576,\n \"175\": [2463, 2658],\n@@ -33260,14 +33257,15 @@\n \"1805\": [2328, 2477],\n \"18053\": 2599,\n \"18070\": 2576,\n \"181\": 2327,\n \"18110\": 2576,\n \"18114\": 2571,\n \"18181818\": 136,\n+ \"18197547\": 2488,\n \"182\": [1526, 2463],\n \"18249173\": 1153,\n \"18306\": 2573,\n \"18310\": 2573,\n \"18322\": 2576,\n \"18326\": 2573,\n \"18327\": 2573,\n@@ -33663,15 +33661,15 @@\n \"20985\": 2585,\n \"20986\": 2585,\n \"20992\": 2585,\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, 2461, 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+ \"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 \"21029\": 2588,\n \"210306068529402873165736369884012333109\": [2275, 2280],\n \"21048\": 2586,\n \"211\": 2491,\n \"21106\": 2586,\n@@ -33744,14 +33742,15 @@\n \"21869\": 2589,\n \"21870\": 2589,\n \"219\": 2463,\n \"21925\": 2594,\n \"21949\": 2589,\n \"21951\": 2589,\n \"21952\": 2589,\n+ \"21968594\": 2488,\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, 2513, 2517, 2519, 2534, 2588, 2634, 2636, 2640, 2656, 2665],\n \"220\": [2238, 2576],\n \"22004\": 2594,\n \"22014\": 2594,\n \"22030\": 2590,\n@@ -33894,15 +33893,15 @@\n \"22972\": 2596,\n \"22976\": 2596,\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+ \"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, 2461, 2513, 2519, 2542, 2552, 2595, 2622, 2627, 2634, 2636, 2640, 2644, 2647, 2656, 2665],\n \"230\": 409,\n \"230000071797338e\": 477,\n \"23011\": 2599,\n \"23019\": 2599,\n \"23020\": 2599,\n \"23030\": 2596,\n \"23031\": 2596,\n@@ -33979,14 +33978,15 @@\n \"23809\": 2622,\n \"23830\": 2622,\n \"23847\": 2622,\n \"2385\": 2617,\n \"23861\": 2622,\n \"23871\": 2622,\n \"23890\": 2598,\n+ \"239\": 2461,\n \"23919\": 2622,\n \"23921\": 2622,\n \"23922\": 2622,\n \"23936\": 2622,\n \"2394691\": 2312,\n \"23968\": 2600,\n \"23994\": 2598,\n@@ -34267,15 +34267,14 @@\n \"25468\": 2605,\n \"25475\": 2605,\n \"25478\": 2605,\n \"25480\": 2605,\n \"25481\": 2605,\n \"25482\": 2605,\n \"25483\": 2605,\n- \"25483166\": 2488,\n \"25485\": 2605,\n \"25486\": 2605,\n \"25489\": 2605,\n \"25490\": 2605,\n \"25491\": 2605,\n \"25495\": 2622,\n \"255\": [62, 140, 143, 144, 287, 370, 488, 570, 590, 943, 1241, 1324, 1478, 1998, 2304, 2599, 2613, 2622, 2665],\n@@ -34330,28 +34329,28 @@\n \"25954\": 2622,\n \"25d0\": 32,\n \"25j\": 2658,\n \"25t03\": 55,\n \"25x\": 138,\n \"26\": [29, 30, 40, 50, 54, 55, 58, 63, 79, 146, 944, 2204, 2208, 2310, 2333, 2377, 2424, 2513, 2519, 2534, 2536, 2537, 2577, 2599, 2601, 2622, 2625, 2629, 2640, 2656, 2657, 2665],\n \"260\": [162, 1328, 2238, 2576, 2665],\n+ \"26031849\": 2461,\n \"26064346e\": 147,\n \"26081\": 2625,\n \"26103\": 2625,\n \"26137788e\": 2104,\n \"26157\": 2625,\n \"262\": 2665,\n \"26268\": 2625,\n \"26285\": 2625,\n \"26292\": 2625,\n \"26313\": 2625,\n \"26388\": 2625,\n \"26393\": 2622,\n \"26452\": 2625,\n- \"26452129\": 2488,\n \"26501\": 2625,\n \"26579\": 2625,\n \"26580\": 2625,\n \"26590556\": 2634,\n \"26598632\": 1228,\n \"266\": 2463,\n \"26606588\": 533,\n@@ -34623,15 +34622,15 @@\n \"2nd\": [513, 641, 642, 655, 658, 669, 1526, 2335, 2378, 2425, 2636, 2640, 2665],\n \"2to3\": 2616,\n \"2x\": [1527, 1542, 2357, 2404, 2454, 2488, 2491, 2616, 2619],\n \"2x2\": 47,\n \"2x3\": [47, 72, 2664],\n \"2x3x5\": 336,\n \"3\": [1, 2, 5, 10, 11, 12, 14, 20, 24, 26, 29, 30, 31, 32, 34, 36, 37, 38, 42, 47, 50, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 66, 70, 72, 74, 76, 78, 79, 87, 89, 94, 96, 97, 98, 99, 100, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 123, 124, 127, 128, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 167, 169, 171, 176, 177, 185, 186, 194, 196, 204, 210, 213, 214, 227, 229, 234, 238, 239, 251, 260, 261, 262, 263, 264, 270, 278, 280, 284, 287, 290, 312, 316, 318, 322, 323, 333, 335, 336, 337, 338, 340, 341, 342, 345, 346, 347, 348, 349, 350, 351, 353, 354, 355, 356, 357, 358, 359, 362, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 396, 398, 401, 404, 408, 409, 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2667],\n- \"30\": [28, 41, 42, 54, 55, 57, 58, 63, 263, 336, 355, 360, 363, 409, 454, 484, 533, 864, 875, 977, 1049, 1064, 1113, 1117, 1118, 1225, 1308, 1462, 1543, 1638, 1906, 1911, 1982, 2089, 2103, 2115, 2165, 2204, 2216, 2224, 2241, 2316, 2319, 2322, 2323, 2325, 2326, 2329, 2339, 2340, 2344, 2371, 2373, 2382, 2383, 2386, 2394, 2418, 2420, 2429, 2430, 2433, 2444, 2461, 2463, 2513, 2531, 2587, 2608, 2636, 2640, 2644, 2656, 2665],\n+ \"30\": [28, 41, 42, 54, 55, 57, 58, 63, 263, 336, 355, 360, 363, 409, 454, 484, 533, 864, 875, 977, 1049, 1064, 1113, 1117, 1118, 1225, 1308, 1462, 1543, 1638, 1906, 1911, 1982, 2089, 2103, 2115, 2165, 2204, 2216, 2224, 2241, 2316, 2319, 2322, 2323, 2325, 2326, 2329, 2339, 2340, 2344, 2371, 2373, 2382, 2383, 2386, 2394, 2418, 2420, 2429, 2430, 2433, 2444, 2463, 2513, 2531, 2587, 2608, 2636, 2640, 2644, 2656, 2665],\n \"300\": [66, 363, 2238, 2576, 2644],\n \"3000\": 2594,\n \"30000\": 533,\n \"3000488281\": 476,\n \"3003003\": 1999,\n \"3006\": 2614,\n \"3007\": 2614,\n@@ -34649,14 +34648,15 @@\n \"3083169284\": [850, 1030],\n \"308j\": 1335,\n \"309\": [420, 421, 947, 948, 1149, 2460],\n \"30z\": 360,\n \"31\": [54, 55, 146, 336, 514, 669, 1088, 1094, 1638, 1711, 1867, 1913, 2204, 2236, 2327, 2331, 2375, 2422, 2513, 2520, 2636, 2640, 2656, 2665],\n \"31018314\": 2458,\n \"3105\": 2614,\n+ \"31063142\": 2461,\n \"3108\": 2614,\n \"3117\": 2614,\n \"3118\": [57, 2547],\n \"31183145\": 2665,\n \"312088\": 1867,\n \"3124\": 2614,\n \"3125\": 2081,\n@@ -34674,25 +34674,25 @@\n \"3160\": 2615,\n \"3168\": 2615,\n \"3173\": 2617,\n \"3175\": 2617,\n \"317811\": 28,\n \"317j\": [411, 617],\n \"318\": 1526,\n+ \"3188896\": 2488,\n \"3192\": 2615,\n \"31962608\": [196, 836, 1008, 1179, 1266, 1421, 1940],\n \"32\": [1, 13, 21, 50, 54, 55, 56, 59, 61, 62, 63, 65, 69, 74, 137, 144, 215, 270, 336, 390, 434, 514, 584, 661, 880, 893, 1027, 1069, 1083, 1143, 1198, 1229, 1249, 1281, 1312, 1345, 1348, 1435, 1466, 1519, 1884, 1886, 1902, 1955, 1986, 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1922, 1999, 2173, 2175, 2176, 2208, 2303, 2513, 2621, 2636, 2640, 2656, 2665],\n \"330\": 363,\n \"3301\": 2615,\n@@ -34731,15 +34731,15 @@\n \"34784527\": 2634,\n \"3480\": 2615,\n \"3484692283495345\": [648, 653],\n \"34889999999999999\": [2325, 2369, 2416],\n \"34890909\": 523,\n \"34960421\": 680,\n \"3497\": 2615,\n- \"35\": [409, 489, 669, 870, 1056, 2204, 2325, 2369, 2416, 2572, 2634, 2640, 2656, 2665],\n+ \"35\": [409, 489, 669, 870, 1056, 2204, 2325, 2369, 2416, 2461, 2572, 2634, 2640, 2656, 2665],\n \"350\": [544, 635],\n \"3504\": 2617,\n \"3534857623790153\": 666,\n \"35355339\": 1636,\n \"3541\": 2615,\n \"35489284e\": 2104,\n \"36\": [58, 137, 355, 1752, 1761, 2204, 2225, 2323, 2367, 2414, 2463, 2491, 2536, 2648, 2656, 2658, 2665],\n@@ -34782,20 +34782,21 @@\n \"3871\": 2615,\n \"38777878e\": [147, 1651],\n \"38791518e\": [421, 948],\n \"38885\": [2361, 2408],\n \"389056\": 2641,\n \"3890561\": [38, 2665],\n \"3891\": 2641,\n- \"39\": [30, 58, 2208, 2461, 2463, 2640, 2656],\n+ \"39\": [30, 58, 2208, 2463, 2640, 2656],\n \"390\": [2270, 2300],\n \"3900\": 2615,\n \"3900x\": 2463,\n \"39015\": 2316,\n \"39211752\": 1153,\n+ \"39304349\": 2461,\n \"39337286e\": 1149,\n \"3971\": 2615,\n \"39804426\": 1153,\n \"3992\": 2615,\n \"39924804\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"3_000\": 669,\n \"3abcd\": 513,\n@@ -34877,18 +34878,19 @@\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+ \"4325282\": 2461,\n \"4354\": 2617,\n \"4359\": 2617,\n \"4368\": [287, 1241, 1324, 1478, 1998],\n \"4375\": 2491,\n \"43857224\": 1153,\n \"43887844\": [349, 2457, 2638],\n \"43999999999998\": 1114,\n@@ -34912,29 +34914,29 @@\n \"4476\": 2621,\n \"4483\": 2617,\n \"4485\": 2617,\n \"4486\": 2617,\n \"449294e\": 2170,\n \"44948974\": 2658,\n \"44999999925494177\": 2115,\n- \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2461, 2636, 2643, 2656, 2665],\n+ \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2636, 2643, 2656, 2665],\n \"450\": 55,\n \"45000005\": 2115,\n \"45038594\": [349, 2638],\n \"45053314\": 2634,\n \"4511316\": 2665,\n \"4520525295346629\": 1228,\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, 2461, 2640, 2656],\n+ \"46\": [409, 523, 905, 1707, 2204, 2208, 2640, 2656],\n \"460\": [2238, 2576],\n \"46009194e\": 566,\n \"4602\": 2618,\n \"4610935\": 457,\n \"4613\": 2618,\n \"4628\": 2618,\n \"46351241j\": 2081,\n@@ -34947,15 +34949,15 @@\n \"46666491\": 349,\n \"46716228e\": 1586,\n \"46755891e\": 54,\n \"468\": [136, 147],\n \"4685006\": [2352, 2399, 2449],\n \"4686\": 12,\n \"46957616e\": [470, 1899, 1900],\n- \"47\": [52, 2208, 2323, 2367, 2414, 2656, 2665],\n+ \"47\": [52, 2208, 2323, 2367, 2414, 2461, 2656, 2665],\n \"4702687338396767\": 2348,\n \"471\": [136, 147, 2463],\n \"47108547995356098\": [2345, 2391, 2439],\n \"47140452j\": 2491,\n \"472\": 55,\n \"4722\": 2618,\n \"4723\": 2621,\n@@ -35046,15 +35048,14 @@\n \"5163\": 2620,\n \"51640373\": 2458,\n \"51658839e\": 1586,\n \"517\": 10,\n \"5170\": 2620,\n \"5184\": 2620,\n \"51851852\": 1809,\n- \"51935295\": 2488,\n \"519928\": 2634,\n \"51992837\": 2634,\n \"52\": [10, 50, 62, 457, 1638, 1647, 1650, 2204, 2208, 2554, 2634, 2640, 2647, 2656, 2658, 2659, 2665],\n \"5203\": 2620,\n \"5225\": 2620,\n \"5231\": 2620,\n \"52338984\": [2345, 2391, 2439],\n@@ -35077,15 +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, 2461, 2641, 2656],\n+ \"54\": [38, 59, 523, 1638, 1711, 1764, 2208, 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@@ -35143,15 +35144,14 @@\n \"58289208\": 2634,\n \"584388\": 55,\n \"585\": [378, 1358, 1514, 2583],\n \"58578644\": 1756,\n \"58826587\": 349,\n \"59\": [55, 2208, 2602, 2656],\n \"5910\": [287, 1241, 1324, 1478, 1998],\n- \"59497974\": 2461,\n \"595726\": 2634,\n \"59572603\": 2634,\n \"5969\": [99, 906],\n \"598150\": 2641,\n \"59815003\": 38,\n \"5982\": 2641,\n \"59903635e\": 147,\n@@ -35160,15 +35160,15 @@\n \"5e16\": 55,\n \"5f\": 2086,\n \"5j\": [350, 541, 544, 1326, 1515, 2108, 2658],\n \"5th\": [513, 669, 2640],\n \"5x\": 1542,\n \"5x50\": 652,\n \"6\": [0, 2, 10, 22, 32, 36, 38, 47, 55, 56, 57, 58, 59, 60, 61, 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363, 409, 444, 446, 568, 661, 977, 1808, 1906, 2103, 2165, 2168, 2238, 2248, 2319, 2518, 2576, 2585, 2634, 2644, 2656],\n \"600\": 567,\n \"600e\": 410,\n \"6019\": 2522,\n \"60393245\": 660,\n \"60546483\": 523,\n \"60663578\": 2634,\n \"607\": [2339, 2382, 2429],\n@@ -35209,15 +35209,14 @@\n \"6390\": [2353, 2400, 2450],\n \"64\": [1, 5, 13, 21, 30, 50, 55, 56, 59, 61, 62, 63, 65, 66, 69, 74, 79, 315, 339, 409, 457, 470, 514, 584, 660, 669, 944, 1345, 1348, 1519, 1899, 1900, 2076, 2083, 2143, 2261, 2262, 2264, 2268, 2269, 2273, 2274, 2278, 2279, 2283, 2284, 2287, 2288, 2299, 2300, 2303, 2304, 2314, 2328, 2458, 2462, 2464, 2513, 2520, 2542, 2547, 2578, 2579, 2580, 2583, 2599, 2602, 2603, 2610, 2615, 2616, 2634, 2638, 2647, 2648, 2656, 2658, 2664, 2665],\n \"64023025\": 2098,\n \"6416010000000001\": 1114,\n \"64386512\": 349,\n \"64402274e\": 660,\n \"6446\": [2550, 2554],\n- \"64569913\": 2461,\n \"646\": [2517, 2576],\n \"6460\": 2522,\n \"6462\": 2522,\n \"6467\": 2522,\n \"6468\": 2522,\n \"6470\": 2522,\n \"6472\": 2522,\n@@ -35240,14 +35239,15 @@\n \"65028784\": 2665,\n \"65143654\": 1154,\n \"6515\": [2353, 2400, 2450],\n \"65200189e\": 566,\n \"6526\": 2522,\n \"6527\": 2522,\n \"6530\": 2522,\n+ \"6530782\": 2461,\n \"6532\": 2522,\n \"6536\": 2522,\n \"6537\": 2522,\n \"6538\": 2522,\n \"6546\": 2522,\n \"65465\": [2335, 2378, 2425],\n \"6551\": 2525,\n@@ -35417,15 +35417,14 @@\n \"7500\": 652,\n \"75000\": 652,\n \"75008178\": 349,\n \"75025\": 28,\n \"7506\": 2526,\n \"75078643\": 349,\n \"75098725\": 2665,\n- \"75102103\": 2461,\n \"75137473\": 349,\n \"7515\": [2353, 2400, 2450],\n \"75224494\": [2345, 2391, 2439],\n \"7530\": 2526,\n \"7535\": 2526,\n \"75351311\": 2665,\n \"754\": [62, 65, 69, 76, 457, 552, 555, 556, 558, 559, 1335, 1340, 1343, 2083, 2094, 2610, 2654],\n@@ -35435,15 +35434,15 @@\n \"7568025\": 2665,\n \"75682846\": 2658,\n \"7578\": 2526,\n \"7590\": 2526,\n \"75958653\": 1911,\n \"7597\": 2526,\n \"75j\": 2658,\n- \"76\": [541, 1897, 2463, 2656, 2658],\n+ \"76\": [541, 1897, 2461, 2463, 2656, 2658],\n \"7608\": 2526,\n \"7611397\": [349, 2457, 2638],\n \"76190476e\": 1816,\n \"76322758\": 1154,\n \"7638\": 2526,\n \"76425276e\": 1149,\n \"76492172\": 349,\n@@ -35473,15 +35472,16 @@\n \"77555756e\": 1877,\n \"77598074\": 349,\n \"77714685\": 349,\n \"7774613834041182\": 2315,\n \"7776\": [99, 906],\n \"7778\": 2527,\n \"7793\": 2527,\n- \"78\": [2091, 2461, 2643, 2656],\n+ \"78\": [2091, 2643, 2656],\n+ \"78030787\": 2461,\n \"78096262\": [2352, 2399, 2449],\n \"7816\": 2527,\n \"7821\": 2527,\n \"7824\": 2527,\n \"7835\": 2527,\n \"784\": 2463,\n \"7847\": 2527,\n@@ -35525,18 +35525,18 @@\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- \"803\": 2461,\n \"8031\": 2527,\n \"804\": 2508,\n \"8044\": 2527,\n+ \"805\": 2461,\n \"8058837395885292\": 666,\n \"80b3a34\": 2614,\n \"81\": [1650, 1884, 2634, 2640, 2644, 2656, 2665],\n \"81299683\": 2634,\n \"812997\": 2634,\n \"813\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"81327024\": 2634,\n@@ -35553,14 +35553,15 @@\n \"826716f\": 2521,\n \"82743037\": 524,\n \"82770259\": 2665,\n \"8277025938204418\": 2665,\n \"827941\": [514, 680, 2658],\n \"82842712\": [642, 644],\n \"83\": [2105, 2167, 2353, 2400, 2450, 2554, 2656],\n+ \"8306809\": 2461,\n \"83314899\": 1154,\n \"83333333\": 1702,\n \"833333333333333\": [893, 1083, 1143, 2240],\n \"8341\": 2528,\n \"8346\": 2528,\n \"83571711\": 349,\n \"83697020e\": [470, 1899, 1900],\n@@ -35640,14 +35641,15 @@\n \"909297\": 2641,\n \"90929743\": 2665,\n \"91\": 2656,\n \"91275558\": 2634,\n \"916666666666666\": 1240,\n \"92\": [98, 2656, 2658],\n \"921fb54442d18p\": 2520,\n+ \"92211853\": 2461,\n \"9223372036854775807\": 2647,\n \"9223372036854775808\": 2647,\n \"92346708\": 349,\n \"92362781e\": 2104,\n \"92387953\": 642,\n \"92387953j\": 642,\n \"9240\": 2532,\n@@ -35655,21 +35657,21 @@\n \"9261\": 2532,\n \"9262\": 2532,\n \"9263\": 2532,\n \"9267\": 2532,\n \"92676499\": [349, 2638],\n \"927\": [539, 554],\n \"92771843\": 1154,\n- \"928\": 2461,\n \"9299\": 2532,\n \"93\": 2656,\n \"9304e\": 2091,\n \"931\": 2587,\n \"9317\": 2532,\n \"9319\": 2532,\n+ \"932\": 2461,\n \"9339\": 2532,\n \"9340\": 2532,\n \"934284\": 349,\n \"93657855\": 349,\n \"9371\": 2532,\n \"9372\": 2532,\n \"9373\": 2532,\n@@ -35680,15 +35682,14 @@\n \"9378\": 2532,\n \"9379\": 2532,\n \"9390\": [2533, 2534],\n \"94\": [409, 669, 2634, 2656],\n \"940\": 2587,\n \"941257\": 2634,\n \"94125714\": 2634,\n- \"94551815\": 2488,\n \"94708397920832\": 2641,\n \"9475673279178444\": 2348,\n \"94864945\": 2665,\n \"94909878\": [2387, 2434],\n \"95\": [37, 39, 646, 2353, 2400, 2450, 2634, 2653, 2656],\n \"9504637\": 2665,\n \"950684\": 2634,\n"}]}]}]}]}]}