2016年1月14日木曜日

160114

Ruby


√5 の近似値の連分数展開(2)

√n の近似値または√n を連分数展開してみた。
(ただし、[a0; a1, … , an] を[a0, a1, … , an] と出力)

require 'bigdecimal'

# aが分子、bが分母
def f(a, b)
  return [a / b] if a % b == 0
  [a / b] + f(b, a % b)
end

d1, d2, n = 33, 30, 101
(1..n).each{|i|
  # √i の近似値
  str = BigDecimal.new(i).sqrt(d1).to_s("F")
  ary = str.scan(/\d+/).to_a
  # 小数点第d2位まで
  ary[1] = ary[1][0..d2 - 1] if ary[1].size > d2
  m = ary[1].size
  p [i, a = ary[0].to_i * 10 ** m + ary[1].to_i, b = 10 ** m]
  p f(a, b)
}

出力結果
[1, 10, 10]
[1]
[2, 1414213562373095048801688724209, 1000000000000000000000000000000]
[1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 41, 1, 1, 1, 1, 2, 3, 2, 1, 1, 7, 2, 3, 1, 3, 1, 1, 6, 1, 7, 1, 246, 3, 1, 1, 9, 138]
[3, 1732050807568877293527446341505, 1000000000000000000000000000000]
[1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 4, 2, 1, 1, 12, 2, 29, 23, 1, 7, 4, 1, 3, 4, 88, 1, 3, 1, 12, 6, 10]
[4, 20, 10]
[2]
[5, 2236067977499789696409173668731, 1000000000000000000000000000000]
[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1, 11, 9, 1, 10, 1, 27, 1, 2, 2, 1, 3, 3, 1, 4, 21, 4, 1, 1, 3, 1, 3, 1, 16, 1, 4, 2, 1, 1, 15]
[6, 2449489742783178098197284074705, 1000000000000000000000000000000]
[2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 3, 1, 6, 1, 2, 4, 1, 7, 1, 2, 1, 1, 4, 1, 7, 44, 2, 5, 1, 1, 3, 2, 10, 1, 7, 24, 1, 41]
[7, 2645751311064590590501615753639, 1000000000000000000000000000000]
[2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 7, 3, 1, 1, 2, 3, 32, 1, 1, 2, 18, 2, 1, 81, 89, 24, 8, 77]
[8, 2828427124746190097603377448419, 1000000000000000000000000000000]
[2, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 3, 1, 1, 4, 1, 1197, 3, 1, 3, 4, 4, 19, 1, 3, 2, 10, 1, 12, 1, 2, 1, 1, 1, 1, 1, 1, 16, 8]
[9, 30, 10]
[3]
[10, 3162277660168379331998893544432, 1000000000000000000000000000000]
[3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 185, 2, 8, 1, 1, 1, 1, 24, 3, 2, 52, 1, 1, 2, 1, 1, 67, 2, 1, 1, 2, 1, 23]
[11, 3316624790355399849114932736670, 1000000000000000000000000000000]
[3, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 2, 4, 1, 85, 1, 7, 1, 2, 1, 6, 3, 1, 7, 5, 6, 1, 7, 1, 1, 1, 1, 1, 1, 1, 11, 1, 8, 13, 2]
[12, 3464101615137754587054892683011, 1000000000000000000000000000000]
[3, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 13, 18, 16, 1, 21, 1, 3, 1, 3, 1, 83, 1, 1, 3, 21, 2, 2, 5, 1, 4, 1, 9, 3, 1, 6]
[13, 3605551275463989293119221267470, 1000000000000000000000000000000]
[3, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 3, 8, 12, 2, 1, 10, 1, 34, 1, 3, 1, 12, 4, 5, 2, 1, 1, 1, 4, 2, 1, 2, 6, 8, 8, 2]
[14, 3741657386773941385583748732316, 1000000000000000000000000000000]
[3, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 1, 3, 1, 2, 1, 8, 2, 2, 1, 1, 39, 1, 2, 3, 1, 1, 12, 16, 2, 3, 3, 5, 5, 17, 18, 1, 2]
[15, 3872983346207416885179265399782, 1000000000000000000000000000000]
[3, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 5, 1, 5, 1, 3, 6, 2, 1, 1, 3, 7, 2, 5, 1, 7, 2, 2, 1, 1, 2, 1, 19, 3, 1, 2, 1, 1, 2, 2, 2, 4, 2, 1, 12, 2]
[16, 40, 10]
[4]
[17, 4123105625617660549821409855974, 1000000000000000000000000000000]
[4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 5, 9, 5, 4, 1, 13, 2, 6, 1, 2, 195, 7, 12, 17, 2, 9, 1, 8, 1, 2]
[18, 4242640687119285146405066172629, 1000000000000000000000000000000]
[4, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 7, 1, 6, 2, 3, 3, 1, 1, 13, 3, 10, 3, 1, 1, 1, 1, 1, 4, 51, 1, 13, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 31]
[19, 4358898943540673552236981983859, 1000000000000000000000000000000]
[4, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 7, 9, 1, 5, 37, 2, 1, 2, 2, 2, 1, 8, 1, 1, 3, 1, 1, 7, 2, 6, 1, 6, 6, 8, 1, 4, 1, 1, 2, 1, 1, 11]
[20, 4472135954999579392818347337462, 1000000000000000000000000000000]
[4, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 7, 1, 5, 19, 1, 4, 1, 56, 2, 2, 7, 1, 1, 9, 10, 1, 1, 1, 1, 3, 1, 1, 8, 1, 7, 1, 9, 1, 3, 1, 7]
[21, 4582575694955840006588047193728, 1000000000000000000000000000000]
[4, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 5, 1, 5, 1, 1, 1, 1, 1, 2, 1, 3, 4, 1, 2, 1, 3, 1, 7, 1, 1, 4, 4, 1, 104, 1, 1, 3, 1, 1, 11]
[22, 4690415759823429554565630113544, 1000000000000000000000000000000]
[4, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 4, 1, 5, 2, 1, 25, 1, 8, 2, 71, 5, 9, 3, 1, 38, 1, 38, 1, 1, 1, 1, 3, 2, 1, 4]
[23, 4795831523312719541597438064162, 1000000000000000000000000000000]
[4, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 7, 1, 2, 6, 1, 2, 1, 2, 1, 77, 17, 1, 1, 1, 15, 2, 143, 2, 1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 2, 1, 1, 1, 1, 2]
[24, 4898979485566356196394568149411, 1000000000000000000000000000000]
[4, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 2, 1, 4, 1, 2, 1, 20, 1, 1, 1, 2, 28, 1, 2, 1, 1, 1, 1, 9, 1, 1, 1, 28, 1, 2, 3, 22, 1, 1, 1, 2, 1, 1, 1, 1, 6, 3]
[25, 50, 10]
[5]
[26, 5099019513592784830028224109022, 1000000000000000000000000000000]
[5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 3, 1, 2, 3, 1, 2, 1, 1, 2, 1, 8, 1, 7, 1, 19, 1, 1, 1, 3, 2, 2, 5, 20, 1, 30, 1, 10, 1, 3, 2, 1, 5]
[27, 5196152422706631880582339024517, 1000000000000000000000000000000]
[5, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 6, 1, 16, 3, 3, 2, 1, 5, 6, 16, 4, 1, 5, 1, 1, 1, 8, 1, 2, 11, 9, 5, 1, 1, 3, 4, 2, 1, 4, 2]
[28, 5291502622129181181003231507278, 1000000000000000000000000000000]
[5, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 1, 14, 1, 1, 3, 1, 6, 16, 3, 2, 1, 8, 1, 2, 163, 44, 1, 1, 11, 1, 1, 3, 1, 1, 38]
[29, 5385164807134504031250710491540, 1000000000000000000000000000000]
[5, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 1, 3, 4, 20, 2, 1, 2, 3, 4, 1, 3, 1, 5, 3, 2, 16, 1, 9, 6, 1, 8, 2, 1, 1, 1, 9, 5]
[30, 5477225575051661134569697828008, 1000000000000000000000000000000]
[5, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 7, 1, 9, 1, 19, 2, 4, 1, 2, 5, 4, 2, 2, 3, 1, 9, 1, 4, 7, 7, 1, 2, 3, 2, 5, 1, 7]
[31, 5567764362830021922119471298918, 1000000000000000000000000000000]
[5, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 2, 2, 1, 2, 44, 1, 12, 1, 7, 2, 1, 4, 1, 3, 1, 6, 1, 36, 1, 4, 4, 2, 2, 1, 2, 1, 2, 1, 1, 10, 1, 6]
[32, 5656854249492380195206754896838, 1000000000000000000000000000000]
[5, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 8, 10, 1, 598, 7, 1, 1, 8, 2, 39, 1, 1, 4, 5, 2, 6, 2, 1, 3, 4, 33, 4]
[33, 5744562646538028659850611468218, 1000000000000000000000000000000]
[5, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 91, 7, 3, 4, 167, 1, 1, 9, 1, 4, 1, 1, 29, 1, 5, 2, 2, 1, 1, 3, 5, 2, 2, 7]
[34, 5830951894845300470874152877545, 1000000000000000000000000000000]
[5, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 1, 1, 3, 1, 1, 1, 8, 1, 15, 1, 1, 2, 1, 1, 11, 1, 1, 1, 1, 5, 2, 1, 1, 1, 6, 1, 3, 2, 375, 1, 64]
[35, 5916079783099616042567328291561, 1000000000000000000000000000000]
[5, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 7, 2, 1, 1, 1, 2, 1, 1, 2, 11, 3, 7, 1, 5, 11, 4, 2, 10, 2, 2, 1, 3, 38, 2, 1, 32, 1, 4]
[36, 60, 10]
[6]
[37, 6082762530298219688999684245202, 1000000000000000000000000000000]
[6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 1, 19, 11, 1, 1, 1, 1, 1, 1, 3, 5, 2, 2, 1, 4, 3, 2, 2, 19, 2, 1, 1, 34, 3, 1, 3, 1, 10, 2, 6]
[38, 6164414002968976450250192381454, 1000000000000000000000000000000]
[6, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 11, 1, 33, 30, 2, 2, 1, 1, 3, 8, 1, 1, 5, 1, 1, 1, 1, 5, 1, 5, 1, 1, 1, 35, 2, 1, 1, 11, 2, 1, 13, 2]
[39, 6244997998398398205846893120939, 1000000000000000000000000000000]
[6, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 9, 1, 4, 1, 1, 3, 2, 4, 7, 1, 4, 1, 1, 9, 1, 1, 1, 108, 1, 1, 1, 1, 1, 33, 1, 1, 10, 4, 19, 12]
[40, 6324555320336758663997787088865, 1000000000000000000000000000000]
[6, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 5, 13, 1, 1, 2, 1, 15, 1, 3, 2, 1, 2, 3, 2, 1, 4, 1, 8, 1, 1, 8, 3, 2, 1, 75, 2, 1, 7, 1, 1, 3]
[41, 6403124237432848686488217674621, 1000000000000000000000000000000]
[6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 1, 19, 1, 3, 1, 5, 1, 38, 1, 5, 3, 2, 38, 1, 1355, 1, 1, 1, 1, 1, 4, 3, 2, 7, 1, 7]
[42, 6480740698407860230965967436087, 1000000000000000000000000000000]
[6, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 5, 1, 116, 1, 1, 2, 6, 1, 2, 1, 2, 3, 6, 3, 1, 1, 5, 3, 1, 3, 1, 1, 2, 2, 5, 1, 10, 4, 6, 5, 1, 5]
[43, 6557438524302000652344109997636, 1000000000000000000000000000000]
[6, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 4, 1, 1, 1, 19, 3, 3, 4, 1, 1, 7, 5, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1036, 1, 6, 8, 2]
[44, 6633249580710799698229865473341, 1000000000000000000000000000000]
[6, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 4, 2, 5, 2, 5, 1, 23, 3, 1, 1, 1, 1, 1, 1, 1, 7, 2, 3, 1, 1, 8, 1, 6, 1, 3, 5, 1, 2, 18, 1, 9]
[45, 6708203932499369089227521006193, 1000000000000000000000000000000]
[6, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 12, 1, 2, 2, 2, 1, 11, 1, 3, 29, 1, 2, 1, 85, 9, 3, 2, 1, 1, 1, 63, 1, 1, 1, 12, 2, 1, 1, 5, 3, 1, 2, 6, 1, 4, 3]
[46, 6782329983125268139064556326625, 1000000000000000000000000000000]
[6, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 1, 1, 2, 6, 2, 1, 1, 3, 1, 12, 1, 3, 2, 1, 24, 1, 19, 2, 8, 9, 2, 7, 1, 1, 6, 5, 1, 5, 1, 1, 3, 1, 1, 1, 303]
[47, 6855654600401044124935871449084, 1000000000000000000000000000000]
[6, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 12, 1, 5, 1, 2, 2, 1, 1, 9, 1, 2, 12, 3, 2, 2, 3, 5, 85, 1, 6, 1, 10, 1, 1, 3, 2, 3, 1, 3, 2, 9, 1, 4]
[48, 6928203230275509174109785366023, 1000000000000000000000000000000]
[6, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 1, 1, 35, 2, 1, 2, 2, 2, 1, 2, 3, 4, 1, 404, 1, 5, 1, 2, 4, 1, 21, 4, 1, 1, 2, 11, 1, 6, 2]
[49, 70, 10]
[7]
[50, 7071067811865475244008443621048, 1000000000000000000000000000000]
[7, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 2, 3, 4, 1, 13, 1, 1, 36, 6932, 1, 2, 4, 1, 2, 1, 6, 1, 1, 8, 2, 1, 1, 13]
[51, 7141428428542849997999399811367, 1000000000000000000000000000000]
[7, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 4, 1, 6, 3, 1, 2, 3, 3, 3, 2, 1, 2, 5, 10, 1, 5, 2, 4, 1, 3, 1, 11, 2, 2, 3, 19, 1, 1, 2, 1, 1, 1, 1, 1, 2]
[52, 7211102550927978586238442534940, 1000000000000000000000000000000]
[7, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 7, 4, 24, 1, 2, 5, 2, 17, 2, 1, 1, 25, 2, 10, 1, 3, 9, 1, 2, 1, 12, 4, 17]
[53, 7280109889280518271097302491527, 1000000000000000000000000000000]
[7, 3, 1, 1, 3, 14, 3, 1, 1, 3, 14, 3, 1, 1, 3, 14, 3, 1, 1, 3, 14, 3, 1, 1, 3, 14, 3, 1, 1, 3, 14, 9, 1, 1, 5, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 6, 2, 3, 1, 1, 1, 4, 4, 1, 5, 2, 1, 2, 1, 1, 1, 3, 7, 3, 2, 10, 1, 2, 2]
[54, 7348469228349534294591852224117, 1000000000000000000000000000000]
[7, 2, 1, 6, 1, 2, 14, 2, 1, 6, 1, 2, 14, 2, 1, 6, 1, 2, 14, 2, 1, 6, 1, 2, 14, 2, 1, 6, 1, 2, 13, 1, 6, 1, 1, 4, 3, 2, 2, 2, 2, 4, 9, 1, 1, 64, 2, 1, 6, 6, 1, 2, 2, 4, 1, 3, 2, 2, 1, 1, 4, 1, 1, 2, 4]
[55, 7416198487095662948711397440800, 1000000000000000000000000000000]
[7, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 5, 2, 2, 1, 2, 1, 2, 1, 3, 4, 1, 7, 1, 1, 3, 1, 6, 1, 6, 11, 6, 22, 3, 1, 2, 4]
[56, 7483314773547882771167497464633, 1000000000000000000000000000000]
[7, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 4, 2, 10, 4, 4, 1, 1, 69, 2, 12, 1, 3, 4, 27, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 5, 2, 4, 1, 2]
[57, 7549834435270749697236684806946, 1000000000000000000000000000000]
[7, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 2, 14, 108, 3, 1, 1, 1, 1, 1, 12, 1, 7, 1, 131, 1, 1, 9, 1, 1, 1, 67, 4, 1, 1, 5, 2]
[58, 7615773105863908285661411027158, 1000000000000000000000000000000]
[7, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 2, 7, 6, 3, 17, 1, 1, 3, 4, 1, 4, 3, 45, 3, 1, 1, 2, 1, 5, 1, 2, 1, 15, 1, 4, 2, 11, 7]
[59, 7681145747868608175769687021731, 1000000000000000000000000000000]
[7, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 23, 1, 7, 1, 2, 2, 10, 1, 3, 1, 1, 14, 1, 3, 1, 1, 2, 7, 1, 1, 1, 1, 5, 2, 2, 1, 16, 2, 6, 1, 1, 18]
[60, 7745966692414833770358530799564, 1000000000000000000000000000000]
[7, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 2, 2, 1, 7, 3, 5, 7, 3, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 9, 1, 1, 1, 2, 1, 3, 2, 2, 2, 1, 1, 1, 2, 26]
[61, 7810249675906654394129722735759, 1000000000000000000000000000000]
[7, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 2, 1, 1, 14, 6, 5, 5, 3, 1, 3, 39, 1, 2, 1, 4, 1, 1, 45, 2, 1, 2, 1, 7, 1, 1, 1, 109, 2]
[62, 7874007874011811019685034448812, 1000000000000000000000000000000]
[7, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 4, 2, 1, 5, 5, 4, 3, 1, 1, 1, 227, 2, 1, 5, 3, 1, 1, 1, 18, 2, 1, 1, 5, 1, 1, 1, 1, 6, 3]
[63, 7937253933193771771504847260917, 1000000000000000000000000000000]
[7, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 14, 1, 7, 2, 2, 2, 1, 7, 1, 97, 1, 3, 1, 5, 2, 4, 27, 267, 8, 24, 25, 1, 2]
[64, 80, 10]
[8]
[65, 8062257748298549652366613230303, 1000000000000000000000000000000]
[8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 15, 1, 219, 1, 5, 1, 1, 4, 4, 2, 4, 7, 1, 5, 4, 65, 1, 4, 3, 18, 7, 1, 2, 1, 1, 1, 18]
[66, 8124038404635960360459883568266, 1000000000000000000000000000000]
[8, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 9, 4, 9, 1, 6, 1, 3, 13, 1, 1, 2, 14, 7, 2, 23, 1, 2, 9, 8, 1, 2, 1, 11, 1, 14]
[67, 8185352771872449969953703724733, 1000000000000000000000000000000]
[8, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 5, 15, 2, 2, 2, 7, 3, 1, 2, 6, 35, 1, 2, 370, 1, 2, 4, 2, 312, 1, 20, 1, 6, 3]
[68, 8246211251235321099642819711948, 1000000000000000000000000000000]
[8, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 2, 2, 1, 1, 4, 10, 2, 2, 6, 1, 2, 1, 2, 1, 5, 97, 1, 1, 3, 24, 8, 1, 2, 1, 4, 2, 4, 3]
[69, 8306623862918074852584262744907, 1000000000000000000000000000000]
[8, 3, 3, 1, 4, 1, 3, 3, 16, 3, 3, 1, 4, 1, 3, 3, 16, 3, 3, 1, 4, 1, 3, 3, 16, 3, 3, 1, 4, 1, 2, 1, 2, 1, 15, 8, 1, 21, 3, 1, 13, 1, 3, 1, 1, 49, 4, 4, 18, 11, 9, 5, 1, 15]
[70, 8366600265340755479781720257851, 1000000000000000000000000000000]
[8, 2, 1, 2, 1, 2, 16, 2, 1, 2, 1, 2, 16, 2, 1, 2, 1, 2, 16, 2, 1, 2, 1, 2, 16, 2, 1, 2, 1, 2, 16, 2, 1, 2, 1, 3, 3, 1, 9, 1, 2, 5, 47, 4, 4, 1, 6, 3, 4, 6, 59, 1, 2, 6, 30, 4, 6, 2]
[71, 8426149773176358630634139906202, 1000000000000000000000000000000]
[8, 2, 2, 1, 7, 1, 2, 2, 16, 2, 2, 1, 7, 1, 2, 2, 16, 2, 2, 1, 7, 1, 2, 2, 16, 2, 2, 1, 7, 1, 2, 2, 13, 6, 3, 2, 3, 1, 1, 8, 1, 13, 2, 23, 1, 3, 1, 1, 1, 24, 4, 11, 1, 3, 1, 3, 4, 9, 9]
[72, 8485281374238570292810132345258, 1000000000000000000000000000000]
[8, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 15, 1, 2, 1, 2, 1, 1, 7, 27, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 1, 25, 2, 6, 1, 4, 3, 1, 2, 1, 2, 1, 1, 2, 1, 15]
[73, 8544003745317531167871648326239, 1000000000000000000000000000000]
[8, 1, 1, 5, 5, 1, 1, 16, 1, 1, 5, 5, 1, 1, 16, 1, 1, 5, 5, 1, 1, 16, 1, 1, 5, 5, 1, 1, 16, 1, 1, 5, 4, 1, 1, 10, 1, 3, 1, 1, 4, 2, 1, 20, 1, 1, 1, 3, 1, 4, 1, 1, 7, 1, 3, 1, 3, 15, 143, 4, 71]
[74, 8602325267042626771729473535049, 1000000000000000000000000000000]
[8, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 11, 1, 14, 1, 1, 1, 1, 3, 5, 2, 5, 2, 2, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 31, 2, 1, 17, 2, 1, 5, 1, 8, 1, 3, 5]
[75, 8660254037844386467637231707529, 1000000000000000000000000000000]
[8, 1, 1, 1, 16, 1, 1, 1, 16, 1, 1, 1, 16, 1, 1, 1, 16, 1, 1, 1, 16, 1, 1, 1, 16, 1, 1, 1, 16, 1, 1, 1, 16, 1, 1, 1, 14, 3, 1, 3, 24, 3, 1, 1, 33, 12, 1, 1, 1, 1, 7, 3, 1, 3, 1, 4, 2, 1, 38, 2, 6, 1, 5, 2, 4]
[76, 8717797887081347104473963967719, 1000000000000000000000000000000]
[8, 1, 2, 1, 1, 5, 4, 5, 1, 1, 2, 1, 16, 1, 2, 1, 1, 5, 4, 5, 1, 1, 2, 1, 16, 1, 2, 1, 1, 5, 4, 5, 1, 1, 2, 1, 16, 5, 2, 8, 4, 2, 1, 1, 3, 1, 4, 5, 11, 5, 3, 1, 11, 1, 6, 1, 4, 1, 1, 1, 2, 49, 1, 9, 2, 2]
[77, 8774964387392122060406388307416, 1000000000000000000000000000000]
[8, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 3, 1, 1, 1, 30, 1, 19, 1, 13, 1, 7, 1, 13, 1, 1, 38, 17, 3, 43, 1, 8, 1, 6]
[78, 8831760866327846854764042726959, 1000000000000000000000000000000]
[8, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 16, 1, 4, 1, 2, 1, 31, 3, 8, 4, 1, 1, 3, 1, 6, 1, 16, 9, 1, 19, 4, 4, 2, 3, 1, 50, 1, 5, 6]
[79, 8888194417315588850091441675408, 1000000000000000000000000000000]
[8, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 16, 1, 7, 1, 12, 1, 5, 3, 1, 7, 2, 8, 3, 1, 4, 1, 1, 5, 1, 7, 1, 2, 2, 1, 5, 2, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 5]
[80, 8944271909999158785636694674925, 1000000000000000000000000000000]
[8, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 16, 1, 4, 2, 2, 41, 9, 3, 1, 1, 2, 4, 1, 1, 5, 4, 2, 1, 2, 2, 2, 1, 14, 2, 4, 88]
[81, 90, 10]
[9]
[82, 9055385138137416626573808166984, 1000000000000000000000000000000]
[9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 17, 1, 24, 7, 1, 1, 1, 1, 3, 1, 4, 1, 1, 1, 11, 1, 45, 1, 1, 2, 2, 79, 2, 3, 33, 3, 1, 2]
[83, 9110433579144298881945626104688, 1000000000000000000000000000000]
[9, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 13, 6, 1, 1, 9, 1, 3, 7, 2, 11, 6, 1, 1, 1, 1, 1, 10, 1, 4, 1, 2, 4, 1, 3, 2, 2, 1, 2, 12, 5]
[84, 9165151389911680013176094387456, 1000000000000000000000000000000]
[9, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 12, 1, 2, 3, 4, 2, 7, 2, 2, 1, 2, 1, 1, 16, 9, 2, 2, 52, 3, 1, 1, 3, 1, 5]
[85, 9219544457292887310002274281762, 1000000000000000000000000000000]
[9, 4, 1, 1, 4, 18, 4, 1, 1, 4, 18, 4, 1, 1, 4, 18, 4, 1, 1, 4, 18, 4, 1, 1, 4, 18, 3, 1, 2, 1, 2, 2, 74, 2, 1, 1, 1, 1, 8, 1, 1, 1, 44, 2, 2, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 1, 3, 5, 7, 3, 1, 3, 2]
[86, 9273618495495703752516416073990, 1000000000000000000000000000000]
[9, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 1, 1, 3, 18, 3, 1, 1, 1, 8, 1, 3, 1, 2, 4, 1, 1, 12, 1, 1, 2, 1, 8, 2, 1, 1, 1, 2, 9, 1, 1, 21, 1, 17, 1, 1, 1, 6, 5, 17, 3]
[87, 9327379053088815045554475542320, 1000000000000000000000000000000]
[9, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 9, 1, 1, 1, 4, 4, 1, 2, 5, 5, 1, 1, 1, 3, 6, 41, 2, 4, 78, 111, 1, 2]
[88, 9380831519646859109131260227088, 1000000000000000000000000000000]
[9, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 18, 2, 1, 1, 1, 2, 10, 1, 2, 5, 1, 12, 2, 4, 4, 35, 1, 1, 2, 18, 1, 1, 78, 1, 18, 1, 4, 7, 1, 2, 2]
[89, 9433981132056603811320660377622, 1000000000000000000000000000000]
[9, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 19, 10, 3, 1, 1, 38, 12, 1, 7, 2, 2, 265, 3, 20, 1, 2, 3, 6, 3, 9, 3, 3]
[90, 9486832980505137995996680633298, 1000000000000000000000000000000]
[9, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 13, 1, 9, 34, 1, 16, 1, 3, 1, 2, 1, 3, 1, 8, 2, 36, 2, 1, 2, 1, 1, 18, 3, 2, 1, 1, 1, 1, 3, 1, 3]
[91, 9539392014169456491526215860232, 1000000000000000000000000000000]
[9, 1, 1, 5, 1, 5, 1, 1, 18, 1, 1, 5, 1, 5, 1, 1, 18, 1, 1, 5, 1, 5, 1, 1, 18, 1, 1, 5, 1, 5, 1, 1, 18, 1, 1, 6, 3, 2, 11, 2, 1, 9, 3, 1, 405, 1, 3, 2, 1, 1, 60, 1, 70, 2, 4, 1, 3, 1, 1, 2]
[92, 9591663046625439083194876128325, 1000000000000000000000000000000]
[9, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 4, 2, 1, 1, 1, 1, 4, 13, 1, 5, 1, 3, 3, 8, 1, 4, 2, 6, 16, 1, 8, 3, 3, 2, 3, 23]
[93, 9643650760992954995760031047432, 1000000000000000000000000000000]
[9, 1, 1, 1, 4, 6, 4, 1, 1, 1, 18, 1, 1, 1, 4, 6, 4, 1, 1, 1, 18, 1, 1, 1, 4, 6, 4, 1, 1, 1, 18, 1, 1, 1, 4, 7, 1, 1, 4, 2, 1, 2, 126, 2, 2, 3, 5, 5, 1, 1, 20, 1, 5, 3, 2, 4, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3]
[94, 9695359714832658028148881150845, 1000000000000000000000000000000]
[9, 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1, 18, 1, 2, 3, 1, 1, 5, 1, 8, 1, 5, 1, 1, 3, 2, 1, 18, 1, 2, 3, 1, 1, 4, 5, 1, 1, 12, 1, 2, 3, 1, 2, 1, 7, 2, 1, 4, 9, 7, 1, 8, 1, 1, 4, 10, 6, 2, 1, 1, 9, 6]
[95, 9746794344808963906838413199899, 1000000000000000000000000000000]
[9, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 17, 1, 2, 6, 36, 14, 2, 3, 1, 1, 1, 25, 4, 2, 1, 2, 1, 47, 1, 1, 1, 8, 3, 17, 1, 16, 2]
[96, 9797958971132712392789136298823, 1000000000000000000000000000000]
[9, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 5, 1, 1, 4, 4, 1, 1, 2, 1, 1, 28, 1, 3, 2, 2, 2, 3, 3, 2, 1, 3, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 3, 14, 1, 1, 3, 3, 1, 1, 2]
[97, 9848857801796104721746211414917, 1000000000000000000000000000000]
[9, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 2, 1, 3, 4, 8, 3, 4, 1, 1, 1, 16, 1, 1, 2, 1, 1, 2, 2, 3, 4, 1, 9, 3, 1, 26, 1, 12, 25]
[98, 9899494936611665341611821069467, 1000000000000000000000000000000]
[9, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 1, 1, 3, 1, 2, 6, 282, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 2, 2, 3, 5, 1, 8, 3, 1, 1, 2, 1, 8, 3]
[99, 9949874371066199547344798210012, 1000000000000000000000000000000]
[9, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 22, 1, 1, 21, 1, 3, 8, 4, 6, 1, 3, 1, 1, 5, 2, 2, 2, 5, 1, 2, 4, 1, 1, 1, 4, 2, 2, 15]
[100, 100, 10]
[10]
[101, 10049875621120890270219264912759, 1000000000000000000000000000000]
[10, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 13, 3, 1, 9, 3, 3, 4, 2, 5, 4, 33, 6, 2, 3, 1, 66, 2, 16, 1, 1, 4, 1, 4, 1, 2, 1, 3]

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