Implementation
static const List<double> XL0 = [
10000000000,
20,
578,
920,
1100,
1124,
1136,
1148,
1217,
1226,
1229,
1229,
1229,
1229,
1937,
2363,
2618,
2633,
2660,
2666,
17534704567.0,
0.00000000000,
0.00000000000,
334165646,
4.669256804,
6283.075849991,
3489428,
4.6261024,
12566.1517000,
349706,
2.744118,
5753.384885,
341757,
2.828866,
3.523118,
313590,
3.627670,
77713.771468,
267622,
4.418084,
7860.419392,
234269,
6.135162,
3930.209696,
132429,
0.742464,
11506.769770,
127317,
2.037097,
529.690965,
119917,
1.109629,
1577.343542,
99025,
5.23268,
5884.92685,
90186,
2.04505,
26.29832,
85722,
3.50849,
398.14900,
77979,
1.17883,
5223.69392,
75314,
2.53339,
5507.55324,
50526,
4.58293,
18849.22755,
49238,
4.20507,
775.52261,
35666,
2.91954,
0.06731,
31709,
5.84902,
11790.62909,
28413,
1.89869,
796.29801,
27104,
0.31489,
10977.07880,
24281,
0.34481,
5486.77784,
20616,
4.80647,
2544.31442,
20539,
1.86948,
5573.14280,
20226,
2.45768,
6069.77675,
15552,
0.83306,
213.29910,
13221,
3.41118,
2942.46342,
12618,
1.08303,
20.77540,
11513,
0.64545,
0.98032,
10285,
0.63600,
4694.00295,
10190,
0.97569,
15720.83878,
10172,
4.26680,
7.11355,
9921,
6.2099,
2146.1654,
9761,
0.6810,
155.4204,
8580,
5.9832,
161000.6857,
8513,
1.2987,
6275.9623,
8471,
3.6708,
71430.6956,
7964,
1.8079,
17260.1547,
7876,
3.0370,
12036.4607,
7465,
1.7551,
5088.6288,
7387,
3.5032,
3154.6871,
7355,
4.6793,
801.8209,
6963,
0.8330,
9437.7629,
6245,
3.9776,
8827.3903,
6115,
1.8184,
7084.8968,
5696,
2.7843,
6286.5990,
5612,
4.3869,
14143.4952,
5558,
3.4701,
6279.5527,
5199,
0.1891,
12139.5535,
5161,
1.3328,
1748.0164,
5115,
0.2831,
5856.4777,
4900,
0.4874,
1194.4470,
4104,
5.3682,
8429.2413,
4094,
2.3985,
19651.0485,
3920,
6.1683,
10447.3878,
3677,
6.0413,
10213.2855,
3660,
2.5696,
1059.3819,
3595,
1.7088,
2352.8662,
3557,
1.7760,
6812.7668,
3329,
0.5931,
17789.8456,
3041,
0.4429,
83996.8473,
3005,
2.7398,
1349.8674,
2535,
3.1647,
4690.4798,
2474,
0.2148,
3.5904,
2366,
0.4847,
8031.0923,
2357,
2.0653,
3340.6124,
2282,
5.2220,
4705.7323,
2189,
5.5559,
553.5694,
2142,
1.4256,
16730.4637,
2109,
4.1483,
951.7184,
2030,
0.3713,
283.8593,
1992,
5.2221,
12168.0027,
1986,
5.7747,
6309.3742,
1912,
3.8222,
23581.2582,
1889,
5.3863,
149854.4001,
1790,
2.2149,
13367.9726,
1748,
4.5605,
135.0651,
1622,
5.9884,
11769.8537,
1508,
4.1957,
6256.7775,
1442,
4.1932,
242.7286,
1435,
3.7236,
38.0277,
1397,
4.4014,
6681.2249,
1362,
1.8893,
7632.9433,
1250,
1.1305,
5.5229,
1205,
2.6223,
955.5997,
1200,
1.0035,
632.7837,
1129,
0.1774,
4164.3120,
1083,
0.3273,
103.0928,
1052,
0.9387,
11926.2544,
1050,
5.3591,
1592.5960,
1033,
6.1998,
6438.4962,
1001,
6.0291,
5746.2713,
980,
0.999,
11371.705,
980,
5.244,
27511.468,
938,
2.624,
5760.498,
923,
0.483,
522.577,
922,
4.571,
4292.331,
905,
5.337,
6386.169,
862,
4.165,
7058.598,
841,
3.299,
7234.794,
836,
4.539,
25132.303,
813,
6.112,
4732.031,
812,
6.271,
426.598,
801,
5.821,
28.449,
787,
0.996,
5643.179,
776,
2.957,
23013.540,
769,
3.121,
7238.676,
758,
3.974,
11499.656,
735,
4.386,
316.392,
731,
0.607,
11513.883,
719,
3.998,
74.782,
706,
0.323,
263.084,
676,
5.911,
90955.552,
663,
3.665,
17298.182,
653,
5.791,
18073.705,
630,
4.717,
6836.645,
615,
1.458,
233141.314,
612,
1.075,
19804.827,
596,
3.321,
6283.009,
596,
2.876,
6283.143,
555,
2.452,
12352.853,
541,
5.392,
419.485,
531,
0.382,
31441.678,
519,
4.065,
6208.294,
513,
2.361,
10973.556,
494,
5.737,
9917.697,
450,
3.272,
11015.106,
449,
3.653,
206.186,
447,
2.064,
7079.374,
435,
4.423,
5216.580,
421,
1.906,
245.832,
413,
0.921,
3738.761,
402,
0.840,
20.355,
387,
1.826,
11856.219,
379,
2.344,
3.881,
374,
2.954,
3128.389,
370,
5.031,
536.805,
365,
1.018,
16200.773,
365,
1.083,
88860.057,
352,
5.978,
3894.182,
352,
2.056,
244287.600,
351,
3.713,
6290.189,
340,
1.106,
14712.317,
339,
0.978,
8635.942,
339,
3.202,
5120.601,
333,
0.837,
6496.375,
325,
3.479,
6133.513,
316,
5.089,
21228.392,
316,
1.328,
10873.986,
309,
3.646,
10.637,
303,
1.802,
35371.887,
296,
3.397,
9225.539,
288,
6.026,
154717.610,
281,
2.585,
14314.168,
262,
3.856,
266.607,
262,
2.579,
22483.849,
257,
1.561,
23543.231,
255,
3.949,
1990.745,
251,
3.744,
10575.407,
240,
1.161,
10984.192,
238,
0.106,
7.046,
236,
4.272,
6040.347,
234,
3.577,
10969.965,
211,
3.714,
65147.620,
210,
0.754,
13521.751,
207,
4.228,
5650.292,
202,
0.814,
170.673,
201,
4.629,
6037.244,
200,
0.381,
6172.870,
199,
3.933,
6206.810,
199,
5.197,
6262.300,
197,
1.046,
18209.330,
195,
1.070,
5230.807,
195,
4.869,
36.028,
194,
4.313,
6244.943,
192,
1.229,
709.933,
192,
5.595,
6282.096,
192,
0.602,
6284.056,
189,
3.744,
23.878,
188,
1.904,
15.252,
188,
0.867,
22003.915,
182,
3.681,
15110.466,
181,
0.491,
1.484,
179,
3.222,
39302.097,
179,
1.259,
12559.038,
62833196674749.0,
0.000000000000,
0.000000000000,
20605886,
2.67823456,
6283.07584999,
430343,
2.635127,
12566.151700,
42526,
1.59047,
3.52312,
11926,
5.79557,
26.29832,
10898,
2.96618,
1577.34354,
9348,
2.5921,
18849.2275,
7212,
1.1385,
529.6910,
6777,
1.8747,
398.1490,
6733,
4.4092,
5507.5532,
5903,
2.8880,
5223.6939,
5598,
2.1747,
155.4204,
4541,
0.3980,
796.2980,
3637,
0.4662,
775.5226,
2896,
2.6471,
7.1135,
2084,
5.3414,
0.9803,
1910,
1.8463,
5486.7778,
1851,
4.9686,
213.2991,
1729,
2.9912,
6275.9623,
1623,
0.0322,
2544.3144,
1583,
1.4305,
2146.1654,
1462,
1.2053,
10977.0788,
1246,
2.8343,
1748.0164,
1188,
3.2580,
5088.6288,
1181,
5.2738,
1194.4470,
1151,
2.0750,
4694.0030,
1064,
0.7661,
553.5694,
997,
1.303,
6286.599,
972,
4.239,
1349.867,
945,
2.700,
242.729,
858,
5.645,
951.718,
758,
5.301,
2352.866,
639,
2.650,
9437.763,
610,
4.666,
4690.480,
583,
1.766,
1059.382,
531,
0.909,
3154.687,
522,
5.661,
71430.696,
520,
1.854,
801.821,
504,
1.425,
6438.496,
433,
0.241,
6812.767,
426,
0.774,
10447.388,
413,
5.240,
7084.897,
374,
2.001,
8031.092,
356,
2.429,
14143.495,
350,
4.800,
6279.553,
337,
0.888,
12036.461,
337,
3.862,
1592.596,
325,
3.400,
7632.943,
322,
0.616,
8429.241,
318,
3.188,
4705.732,
297,
6.070,
4292.331,
295,
1.431,
5746.271,
290,
2.325,
20.355,
275,
0.935,
5760.498,
270,
4.804,
7234.794,
253,
6.223,
6836.645,
228,
5.003,
17789.846,
225,
5.672,
11499.656,
215,
5.202,
11513.883,
208,
3.955,
10213.286,
208,
2.268,
522.577,
206,
2.224,
5856.478,
206,
2.550,
25132.303,
203,
0.910,
6256.778,
189,
0.532,
3340.612,
188,
4.735,
83996.847,
179,
1.474,
4164.312,
178,
3.025,
5.523,
177,
3.026,
5753.385,
159,
4.637,
3.286,
157,
6.124,
5216.580,
155,
3.077,
6681.225,
154,
4.200,
13367.973,
143,
1.191,
3894.182,
138,
3.093,
135.065,
136,
4.245,
426.598,
134,
5.765,
6040.347,
128,
3.085,
5643.179,
127,
2.092,
6290.189,
125,
3.077,
11926.254,
125,
3.445,
536.805,
114,
3.244,
12168.003,
112,
2.318,
16730.464,
111,
3.901,
11506.770,
111,
5.320,
23.878,
105,
3.750,
7860.419,
103,
2.447,
1990.745,
96,
0.82,
3.88,
96,
4.08,
6127.66,
91,
5.42,
206.19,
91,
0.42,
7079.37,
88,
5.17,
11790.63,
81,
0.34,
9917.70,
80,
3.89,
10973.56,
78,
2.40,
1589.07,
78,
2.58,
11371.70,
77,
3.98,
955.60,
77,
3.36,
36.03,
76,
1.30,
103.09,
75,
5.18,
10969.97,
75,
4.96,
6496.37,
73,
5.21,
38.03,
72,
2.65,
6309.37,
70,
5.61,
3738.76,
69,
2.60,
3496.03,
69,
0.39,
15.25,
69,
2.78,
20.78,
65,
1.13,
7058.60,
64,
4.28,
28.45,
61,
5.63,
10984.19,
60,
0.73,
419.48,
60,
5.28,
10575.41,
58,
5.55,
17298.18,
58,
3.19,
4732.03,
5291887,
0.0000000,
0.0000000,
871984,
1.072097,
6283.075850,
30913,
0.86729,
12566.15170,
2734,
0.0530,
3.5231,
1633,
5.1883,
26.2983,
1575,
3.6846,
155.4204,
954,
0.757,
18849.228,
894,
2.057,
77713.771,
695,
0.827,
775.523,
506,
4.663,
1577.344,
406,
1.031,
7.114,
381,
3.441,
5573.143,
346,
5.141,
796.298,
317,
6.053,
5507.553,
302,
1.192,
242.729,
289,
6.117,
529.691,
271,
0.306,
398.149,
254,
2.280,
553.569,
237,
4.381,
5223.694,
208,
3.754,
0.980,
168,
0.902,
951.718,
153,
5.759,
1349.867,
145,
4.364,
1748.016,
134,
3.721,
1194.447,
125,
2.948,
6438.496,
122,
2.973,
2146.165,
110,
1.271,
161000.686,
104,
0.604,
3154.687,
100,
5.986,
6286.599,
92,
4.80,
5088.63,
89,
5.23,
7084.90,
83,
3.31,
213.30,
76,
3.42,
5486.78,
71,
6.19,
4690.48,
68,
3.43,
4694.00,
65,
1.60,
2544.31,
64,
1.98,
801.82,
61,
2.48,
10977.08,
50,
1.44,
6836.65,
49,
2.34,
1592.60,
46,
1.31,
4292.33,
46,
3.81,
149854.40,
43,
0.04,
7234.79,
40,
4.94,
7632.94,
39,
1.57,
71430.70,
38,
3.17,
6309.37,
35,
0.99,
6040.35,
35,
0.67,
1059.38,
31,
3.18,
2352.87,
31,
3.55,
8031.09,
30,
1.92,
10447.39,
30,
2.52,
6127.66,
28,
4.42,
9437.76,
28,
2.71,
3894.18,
27,
0.67,
25132.30,
26,
5.27,
6812.77,
25,
0.55,
6279.55,
23,
1.38,
4705.73,
22,
0.64,
6256.78,
20,
6.07,
640.88,
28923,
5.84384,
6283.07585,
3496,
0.0000,
0.0000,
1682,
5.4877,
12566.1517,
296,
5.196,
155.420,
129,
4.722,
3.523,
71,
5.30,
18849.23,
64,
5.97,
242.73,
40,
3.79,
553.57,
11408,
3.14159,
0.00000,
772,
4.134,
6283.076,
77,
3.84,
12566.15,
42,
0.42,
155.42,
88,
3.14,
0.00,
17,
2.77,
6283.08,
5,
2.01,
155.42,
3,
2.21,
12566.15,
27962,
3.19870,
84334.66158,
10164,
5.42249,
5507.55324,
8045,
3.8801,
5223.6939,
4381,
3.7044,
2352.8662,
3193,
4.0003,
1577.3435,
2272,
3.9847,
1047.7473,
1814,
4.9837,
6283.0758,
1639,
3.5646,
5856.4777,
1444,
3.7028,
9437.7629,
1430,
3.4112,
10213.2855,
1125,
4.8282,
14143.4952,
1090,
2.0857,
6812.7668,
1037,
4.0566,
71092.8814,
971,
3.473,
4694.003,
915,
1.142,
6620.890,
878,
4.440,
5753.385,
837,
4.993,
7084.897,
770,
5.554,
167621.576,
719,
3.602,
529.691,
692,
4.326,
6275.962,
558,
4.410,
7860.419,
529,
2.484,
4705.732,
521,
6.250,
18073.705,
903,
3.897,
5507.553,
618,
1.730,
5223.694,
380,
5.244,
2352.866,
166,
1.627,
84334.662,
10001398880.0,
0.00000000000,
0.00000000000,
167069963,
3.098463508,
6283.075849991,
1395602,
3.0552461,
12566.1517000,
308372,
5.198467,
77713.771468,
162846,
1.173877,
5753.384885,
157557,
2.846852,
7860.419392,
92480,
5.45292,
11506.76977,
54244,
4.56409,
3930.20970,
47211,
3.66100,
5884.92685,
34598,
0.96369,
5507.55324,
32878,
5.89984,
5223.69392,
30678,
0.29867,
5573.14280,
24319,
4.27350,
11790.62909,
21183,
5.84715,
1577.34354,
18575,
5.02194,
10977.07880,
17484,
3.01194,
18849.22755,
10984,
5.05511,
5486.77784,
9832,
0.8868,
6069.7768,
8650,
5.6896,
15720.8388,
8583,
1.2708,
161000.6857,
6490,
0.2725,
17260.1547,
6292,
0.9218,
529.6910,
5706,
2.0137,
83996.8473,
5574,
5.2416,
71430.6956,
4938,
3.2450,
2544.3144,
4696,
2.5781,
775.5226,
4466,
5.5372,
9437.7629,
4252,
6.0111,
6275.9623,
3897,
5.3607,
4694.0030,
3825,
2.3926,
8827.3903,
3749,
0.8295,
19651.0485,
3696,
4.9011,
12139.5535,
3566,
1.6747,
12036.4607,
3454,
1.8427,
2942.4634,
3319,
0.2437,
7084.8968,
3192,
0.1837,
5088.6288,
3185,
1.7778,
398.1490,
2846,
1.2134,
6286.5990,
2779,
1.8993,
6279.5527,
2628,
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