2016年1月13日水曜日

160113

Ruby


√5 の近似値の連分数展開(1)

√5 の近似値を連分数展開してみた。
(ただし、[a0; a1, … , an] を[a0, a1, … , an] と出力)
なお、√5 の連分数展開は、
オンライン整数列大辞典の
A040002(http://oeis.org/A040002/list)
に載っています。

# 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

def g(ary)
  # √5 = 2.23…
  n, d = ary.join.to_i, 10 ** (ary.size - 1)
  [f(n, d), n]
end

# OEIS A002163のデータ
ary =
[2,2,3,6,0,6,7,9,7,7,4,9,9,7,8,9,6,9,6,4,0,9,1,7,
 3,6,6,8,7,3,1,2,7,6,2,3,5,4,4,0,6,1,8,3,5,9,6,1,1,
 5,2,5,7,2,4,2,7,0,8,9,7,2,4,5,4,1,0,5,2,0,9,2,5,6,
 3,7,8,0,4,8,9,9,4,1,4,4,1,4,4,0,8,3,7,8,7,8,2,2,7]

(0..98).each{|i| p g(ary[0..i])}

出力結果
[[2], 2]
[[2, 5], 22]
[[2, 4, 2, 1, 7], 223]
[[2, 4, 4, 4, 1, 2], 2236]
[[2, 4, 4, 4, 1, 2], 22360]
[[2, 4, 4, 4, 3, 1, 1, 6, 14], 223606]
[[2, 4, 4, 4, 4, 7, 3, 3, 8, 2, 2], 2236067]
[[2, 4, 4, 4, 4, 4, 2, 1, 1, 2, 12, 1, 12, 1, 2], 22360679]
[[2, 4, 4, 4, 4, 4, 3, 1, 960, 1, 8, 2], 223606797]
[[2, 4, 4, 4, 4, 4, 4, 4, 1, 1, 3, 1, 7, 1, 119, 1, 3], 2236067977]
[[2, 4, 4, 4, 4, 4, 4, 4, 3, 2, 1, 2, 3, 2, 2, 5, 73], 22360679774]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 7, 1, 1, 51, 1, 103, 2, 2, 2], 223606797749]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 1, 5, 1, 4, 1, 1, 1, 5, 1, 1, 2, 25, 2, 2], 2236067977499]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1, 17, 2, 3, 7, 1, 2, 2, 1, 2, 1, 3, 4, 4, 2], 22360679774997]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 13, 1, 2, 1, 1, 1, 1, 8, 1, 1, 2, 2, 20, 2, 4], 223606797749978]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1, 1, 2, 1, 5, 1, 1, 2, 10, 1, 4, 5, 1, 1, 2, 2, 5, 2, 3], 2236067977499789]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 1, 1, 1, 2, 19, 3, 1, 3, 1, 560, 1, 2], 22360679774997896]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 2, 1, 1, 6, 1, 1, 1, 1, 2, 1, 6, 5, 1, 3, 1, 2, 4, 1, 2, 1, 11, 2], 223606797749978969]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 1, 1, 1, 6, 2, 2, 2, 1, 7, 2, 5, 1, 1, 1, 2, 4], 2236067977499789696]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 1, 1, 1, 3, 5, 6, 2, 10, 2, 26, 8, 3, 4, 2], 22360679774997896964]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 1, 1, 1, 3, 5, 6, 2, 10, 2, 26, 8, 3, 4, 2], 223606797749978969640]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 5, 3, 20, 3, 1, 1, 7, 3, 7, 1, 1, 1, 1, 8, 9, 1, 1, 1, 1, 2], 2236067977499789696409]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 1, 6, 2, 1, 19, 2, 3, 3, 2, 4, 2, 2, 20, 1, 5, 1, 1, 1, 1, 2, 1, 1, 8, 2], 22360679774997896964091]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 1, 1, 1, 7, 2, 1, 2, 1, 18, 1, 5, 14, 2, 2, 7, 2, 24, 1, 6, 1, 1, 1, 2], 223606797749978969640917]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 2, 1, 2, 1, 2, 1, 12, 10, 1, 1, 2, 7, 1, 1, 1, 14, 2, 1, 1, 8, 1, 3, 1, 1, 5, 6, 1, 1, 2], 2236067977499789696409173]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1, 1, 5, 1, 1, 1, 8, 1, 73, 1, 1, 11, 8, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 34, 1, 6], 22360679774997896964091736]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 2, 8, 4, 3, 1, 3, 1, 1, 3, 1, 1, 1, 1, 4, 1, 15, 1, 1, 20, 1, 5, 1, 3, 5, 3, 2, 1, 2, 2], 223606797749978969640917366]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 1, 40, 2, 1, 42, 1, 2, 1, 3, 2, 83, 1, 4, 1, 1, 1, 1, 24, 7, 2, 2, 8], 2236067977499789696409173668]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 2, 3, 3, 1, 2, 1, 4, 1, 2, 1, 1, 5, 1, 9, 4, 1, 3, 1, 2, 107, 1, 1, 1, 2, 1, 7, 4, 1, 21], 22360679774997896964091736687]
[[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, 15, 4, 40, 2, 2, 5, 1, 2, 18, 1, 1, 73, 3, 2, 18, 2, 65, 1, 10], 223606797749978969640917366873]
[[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], 2236067977499789696409173668731]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 1, 42, 1, 1, 1, 168, 4, 1, 6, 1, 3, 8, 1, 22, 1, 14, 1, 7, 2, 1, 6, 1, 1, 19], 22360679774997896964091736687312]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 1, 1, 2, 1, 4, 1, 3, 1, 1, 2, 1, 9, 2, 1, 2, 1, 2, 2, 4, 1, 1, 1, 1, 1, 11, 2, 1, 5, 1, 1, 1, 2, 1, 1, 2, 2, 5, 2, 4, 49, 2], 223606797749978969640917366873127]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 1, 20, 11, 1, 1, 11, 2, 2, 1, 5, 12, 1, 2, 1, 4, 2, 10, 2, 1, 1, 1, 62, 19, 2, 1, 5, 8], 2236067977499789696409173668731276]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 42, 1, 1, 2, 31, 3, 1, 4, 1, 1, 1, 1, 32, 15, 13, 3, 1, 3, 1, 5, 1, 8, 5, 1, 3, 6, 6, 1, 4], 22360679774997896964091736687312762]
[[2, 4, 4, 4, 4, 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, 1, 1, 2, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 5, 2, 11, 6, 2, 141, 8, 2, 4, 3, 1, 94, 1, 23, 1, 6, 1, 5, 2, 4], 223606797749978969640917366873127623]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 1, 1, 4, 14, 1, 6, 1, 1, 1, 18, 1, 7, 39, 2, 2, 24, 1, 2, 1, 4, 2, 4, 39, 18, 1, 3, 3, 1, 1, 4, 2], 2236067977499789696409173668731276235]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 80, 1, 1, 1, 1, 2, 2, 1, 3, 1, 52, 1, 1, 1, 2, 22, 1, 1, 1, 3, 2, 3, 5, 13, 4, 2, 1, 3, 3, 1, 1, 1, 2, 1, 1, 13, 22], 22360679774997896964091736687312762354]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 2, 1, 65, 11, 1, 3, 9, 1, 1, 21, 3, 2, 1, 3, 1, 27, 4, 3, 1, 1, 42, 47, 6, 2, 1, 12, 4], 223606797749978969640917366873127623544]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 2, 1, 65, 11, 1, 3, 9, 1, 1, 21, 3, 2, 1, 3, 1, 27, 4, 3, 1, 1, 42, 47, 6, 2, 1, 12, 4], 2236067977499789696409173668731276235440]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 275, 1, 1, 1, 1, 4, 1, 7, 1, 3, 1, 1, 3, 2, 1, 2, 13, 2, 1, 1, 2, 14, 2, 1, 1, 1, 1, 1, 2, 1, 27, 4, 8, 3, 2, 3, 1, 2, 11, 1, 11], 22360679774997896964091736687312762354406]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 1, 6, 2, 1, 1, 12, 4, 5, 9, 3, 6, 1, 1, 1, 4, 6, 1, 1, 2, 9, 4, 1, 1, 8, 1, 2076, 2, 2, 7, 1, 1, 10, 1, 1, 2, 1, 1, 6], 223606797749978969640917366873127623544061]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 11, 2, 30, 6, 1, 3, 3, 1, 1, 5, 1, 1, 2, 2, 9, 1, 1, 5, 11, 7, 304, 1, 661, 2, 1, 2, 2, 16, 1, 1, 1, 5, 3], 2236067977499789696409173668731276235440618]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 155, 1, 20, 9, 2, 1, 1, 2, 12, 84, 2, 52, 3, 1, 1, 3, 1, 6, 1, 1, 1, 23, 1, 1, 1, 125, 1, 5, 1, 1, 1, 1, 2, 3, 1, 8, 2, 2], 22360679774997896964091736687312762354406183]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 1, 97, 1, 3, 3, 1, 1, 1, 2, 6, 2, 4, 1, 4, 2, 11, 4, 1, 2, 1, 4, 1, 4, 2, 2, 3, 7, 1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 22, 1, 6, 1, 10, 2, 1, 1, 4], 223606797749978969640917366873127623544061835]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 1, 9, 1, 6, 7, 1, 4, 1, 1, 2, 2, 2, 8, 1, 2, 1, 1, 1, 1, 1, 1, 2, 96, 11, 3, 4, 5, 21, 1, 51, 26, 2, 2, 6, 12, 3, 1, 1, 2, 9], 2236067977499789696409173668731276235440618359]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 5, 2, 4, 2, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 3, 1, 16, 1, 1, 1, 4, 3, 1, 1, 15, 2, 1, 2, 1, 21, 1, 31, 3, 1, 2, 1, 3, 19, 1, 9, 2, 8, 1, 1, 19, 1, 2], 22360679774997896964091736687312762354406183596]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 6, 1, 1, 1, 37, 20, 1, 4, 5, 26, 4, 1, 2, 61, 2, 1, 3, 1, 1, 1, 23, 1, 6, 5, 1, 1, 1, 2, 1, 4, 1, 2, 1, 14, 6], 223606797749978969640917366873127623544061835961]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 74, 1, 9, 2, 3, 7, 2, 1, 3, 5, 5, 2, 1, 7, 48, 1, 1, 3, 18, 4, 9, 1, 1, 1, 9, 2, 1, 1, 1, 15, 1, 8, 160, 1, 12, 11, 1, 2, 1, 5], 2236067977499789696409173668731276235440618359611]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 1, 2, 5, 3, 1, 6, 23, 3, 1, 1, 1, 2, 3, 1, 1, 4, 3, 1, 1, 1, 2, 2, 11, 2, 3, 1, 1, 1, 4, 1, 20, 24, 1, 1, 39, 52, 58, 2, 4, 8, 1, 1, 2], 22360679774997896964091736687312762354406183596115]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 1, 5, 2, 8, 1, 2, 2, 2, 1, 9, 6, 3, 14, 2, 6, 4, 1, 1, 1, 3, 1, 4, 1, 5, 2, 1, 3, 1, 1, 1, 1, 39, 1, 3, 1, 1, 1, 2, 4, 4, 1, 1, 3, 1, 94, 3, 5, 1, 1, 1, 3], 223606797749978969640917366873127623544061835961152]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 2, 3, 2, 219, 1, 9, 6, 3, 1, 1, 7, 1, 11, 1, 2, 3, 1, 92, 1, 2, 2, 5, 11, 2, 2, 2, 1, 5, 1, 1, 1, 1, 1, 1, 5, 4, 1, 3, 9, 78, 4, 11], 2236067977499789696409173668731276235440618359611525]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 1, 18, 2, 7, 3, 3, 1, 2, 2, 3, 1, 4, 6, 4, 1, 1, 16, 4, 4, 2, 4, 4, 21, 30, 1, 20, 6, 1, 4, 1, 2, 4, 4, 1, 2, 20, 1, 12, 25, 1, 69], 22360679774997896964091736687312762354406183596115257]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 21, 3, 1, 1, 4, 2, 1, 1, 1, 5, 3, 2, 1, 2, 1, 2, 7, 10, 1, 3, 2, 14, 3, 2, 2, 1, 2, 1, 25, 1, 18, 1, 10, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 4, 17, 2, 1, 2, 1, 1, 3, 3, 1, 61, 1, 1, 5], 223606797749978969640917366873127623544061835961152572]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 8, 1, 1, 1, 4, 2, 4, 10, 3, 3, 4, 2, 10, 1, 1, 1, 373, 1, 4, 2, 1, 1, 2, 7, 1, 6, 8, 22, 1, 10, 9, 2, 3, 3, 1, 8, 1, 2, 5, 1, 5, 1, 4, 3, 1, 1, 2, 2, 2, 1, 3], 2236067977499789696409173668731276235440618359611525724]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 1, 1, 1, 1, 1, 1, 8, 1, 5, 140, 25, 1, 26, 1, 23, 1, 2, 32, 1, 1, 1, 44, 1, 2, 2, 5, 1, 17, 1, 2, 3, 4, 2, 16, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 20, 1, 1, 1, 87, 11], 22360679774997896964091736687312762354406183596115257242]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 22, 1, 4, 1, 29, 3, 7, 4, 6, 39, 1, 1, 3, 1, 3, 6, 1, 1, 4, 1, 2, 5, 1, 2, 1, 3, 1, 4, 1, 1081, 1, 6, 2, 11, 2, 1, 2, 2, 5, 1, 1, 1, 2, 4, 2, 1, 1, 64, 1, 1, 11], 223606797749978969640917366873127623544061835961152572427]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 22, 1, 4, 1, 29, 3, 7, 4, 6, 39, 1, 1, 3, 1, 3, 6, 1, 1, 4, 1, 2, 5, 1, 2, 1, 3, 1, 4, 1, 1081, 1, 6, 2, 11, 2, 1, 2, 2, 5, 1, 1, 1, 2, 4, 2, 1, 1, 64, 1, 1, 11], 2236067977499789696409173668731276235440618359611525724270]
[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 4, 2, 1, 1, 1, 19, 1, 3, 1, 1, 7, 10, 1, 2, 8, 1, 132, 3, 1, 1, 1, 2, 1, 4, 1, 6, 14, 4, 3, 22, 1, 1, 1, 1, 5, 15, 2, 1, 1, 1, 1, 2, 7, 10, 1, 25, 1, 3, 4, 1, 2, 24, 1, 50], 22360679774997896964091736687312762354406183596115257242708]
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[[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 7, 1, 5, 3, 86, 1, 1, 5, 4, 1, 11, 6, 6, 4, 3, 6, 4, 3, 1, 3, 1, 2, 21, 1, 2, 1, 1, 1, 92, 1, 4, 6, 2, 2, 1, 17, 1, 2, 1, 1, 8, 1, 14, 1, 1, 1, 7, 1, 16, 2, 1, 5, 4, 1, 29], 2236067977499789696409173668731276235440618359611525724270897]
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