160106(2)

Ruby


Number of ways to express 1 as the sum of distinct unit fractions such that the sum of the denominators is n(2)

n ≧ 2 のとき、条件を満たす分割を出力してみた。

# 和因子はmin以上max以下で互いに異なる
def partition(n, min, max)
  return [[]] if n == 0
  [max, n].min.downto(min).flat_map{|i| partition(n - i, min, i - 1).map{|rest| [i, *rest]}}
end

(2..130).each{|n|
  p [n, partition(n, 2, n).select{|ary| ary.inject(0){|s, i| s + 1 / i.to_r} == 1}]
}

出力結果
[2, []]
[3, []]
[4, []]
[5, []]
[6, []]
[7, []]
[8, []]
[9, []]
[10, []]
[11, [[6, 3, 2]]]
[12, []]
[13, []]
[14, []]
[15, []]
[16, []]
[17, []]
[18, []]
[19, []]
[20, []]
[21, []]
[22, []]
[23, []]
[24, [[12, 6, 4, 2]]]
[25, []]
[26, []]
[27, []]
[28, []]
[29, []]
[30, [[15, 10, 3, 2]]]
[31, [[20, 5, 4, 2]]]
[32, [[18, 9, 3, 2]]]
[33, []]
[34, []]
[35, []]
[36, []]
[37, [[24, 8, 3, 2]]]
[38, [[20, 6, 5, 4, 3]]]
[39, []]
[40, []]
[41, []]
[42, []]
[43, [[15, 12, 10, 4, 2]]]
[44, []]
[45, [[20, 12, 6, 5, 2], [18, 12, 9, 4, 2]]]
[46, []]
[47, []]
[48, []]
[49, []]
[50, [[24, 12, 8, 4, 2], [15, 12, 10, 6, 4, 3]]]
[51, []]
[52, [[18, 12, 9, 6, 4, 3]]]
[53, [[30, 10, 6, 5, 2]]]
[54, [[42, 7, 3, 2]]]
[55, [[28, 14, 7, 4, 2]]]
[56, []]
[57, [[24, 12, 8, 6, 4, 3], [20, 15, 10, 5, 4, 3]]]
[58, []]
[59, [[20, 18, 9, 5, 4, 3]]]
[60, [[18, 15, 10, 9, 6, 2]]]
[61, [[28, 21, 6, 4, 2]]]
[62, [[30, 20, 6, 4, 2], [28, 14, 7, 6, 4, 3]]]
[63, []]
[64, [[40, 10, 8, 4, 2], [30, 12, 10, 5, 4, 3], [24, 20, 8, 5, 4, 3], [20, 15, 12, 10, 5, 2]]]
[65, [[24, 15, 10, 8, 6, 2]]]
[66, [[36, 18, 6, 4, 2], [28, 21, 12, 3, 2], [20, 18, 12, 9, 5, 2]]]
[67, [[45, 9, 6, 5, 2], [42, 12, 7, 4, 2], [30, 20, 12, 3, 2], [24, 18, 9, 8, 6, 2]]]
[68, []]
[69, [[35, 15, 14, 3, 2], [28, 14, 12, 7, 6, 2]]]
[70, []]
[71, [[40, 10, 8, 6, 4, 3], [36, 18, 12, 3, 2], [33, 22, 11, 3, 2], [24, 20, 12, 8, 5, 2], [20, 15, 12, 10, 6, 5, 3], [18, 15, 12, 10, 9, 4, 3]]]
[72, []]
[73, [[20, 18, 12, 9, 6, 5, 3]]]
[74, [[42, 12, 7, 6, 4, 3], [30, 18, 10, 9, 5, 2]]]
[75, [[40, 15, 8, 5, 4, 3]]]
[76, [[48, 16, 6, 4, 2], [28, 20, 14, 7, 5, 2], [24, 15, 12, 10, 8, 4, 3]]]
[77, []]
[78, [[45, 12, 9, 5, 4, 3], [40, 12, 10, 8, 6, 2], [24, 20, 12, 8, 6, 5, 3], [24, 18, 12, 9, 8, 4, 3]]]
[79, [[40, 24, 10, 3, 2], [30, 24, 10, 8, 5, 2]]]
[80, [[28, 21, 15, 10, 4, 2]]]
[81, [[48, 16, 12, 3, 2], [42, 20, 7, 5, 4, 3], [30, 20, 15, 10, 4, 2], [30, 18, 10, 9, 6, 5, 3], [28, 15, 14, 10, 7, 4, 3]]]
[82, [[42, 15, 10, 7, 6, 2], [40, 15, 12, 8, 5, 2], [35, 15, 14, 12, 4, 2], [28, 21, 20, 6, 5, 2], [28, 21, 18, 9, 4, 2]]]
[83, [[30, 20, 18, 9, 4, 2], [28, 20, 14, 7, 6, 5, 3], [28, 18, 14, 9, 7, 4, 3]]]
[84, [[42, 18, 9, 7, 6, 2], [33, 22, 12, 11, 4, 2]]]
[85, [[40, 20, 10, 8, 5, 2], [36, 18, 15, 10, 4, 2], [35, 20, 14, 10, 4, 2]]]
[86, [[45, 15, 10, 9, 5, 2], [30, 24, 10, 8, 6, 5, 3], [24, 18, 15, 10, 9, 8, 2]]]
[87, [[60, 15, 6, 4, 2], [36, 20, 18, 6, 5, 2], [28, 24, 21, 8, 4, 2], [28, 21, 15, 10, 6, 4, 3], [20, 18, 15, 10, 9, 6, 5, 4]]]
[88, [[42, 20, 12, 7, 5, 2], [30, 24, 20, 8, 4, 2], [30, 20, 15, 10, 6, 4, 3], [28, 24, 14, 8, 7, 4, 3], [28, 15, 14, 12, 10, 7, 2]]]
[89, [[45, 30, 9, 3, 2], [42, 24, 8, 7, 6, 2], [40, 15, 12, 8, 6, 5, 3], [35, 15, 14, 12, 6, 4, 3], [28, 21, 18, 9, 6, 4, 3]]]
[90, [[30, 20, 18, 9, 6, 4, 3], [28, 18, 14, 12, 9, 7, 2]]]
[91, [[33, 22, 12, 11, 6, 4, 3]]]
[92, [[60, 15, 12, 3, 2], [45, 36, 5, 4, 2], [40, 24, 15, 6, 5, 2], [40, 24, 12, 10, 4, 2], [40, 20, 10, 8, 6, 5, 3], [40, 18, 10, 9, 8, 4, 3], [36, 24, 18, 8, 4, 2], [36, 18, 15, 10, 6, 4, 3], [35, 30, 14, 6, 5, 2], [35, 20, 14, 10, 6, 4, 3], [24, 20, 15, 10, 8, 6, 5, 4], [20, 18, 15, 12, 10, 9, 5, 3]]]
[93, [[45, 24, 9, 8, 5, 2], [45, 15, 10, 9, 6, 5, 3], [42, 15, 12, 10, 7, 4, 3], [28, 21, 20, 12, 5, 4, 3], [24, 18, 15, 10, 9, 8, 6, 3]]]
[94, [[30, 18, 12, 10, 9, 6, 5, 4], [28, 24, 21, 8, 6, 4, 3], [28, 21, 15, 12, 10, 6, 2], [24, 20, 18, 9, 8, 6, 5, 4]]]
[95, [[72, 9, 8, 4, 2], [60, 20, 10, 3, 2], [54, 27, 9, 3, 2], [48, 16, 15, 10, 4, 2], [45, 20, 15, 9, 4, 2], [42, 20, 12, 7, 6, 5, 3], [42, 18, 12, 9, 7, 4, 3], [30, 24, 20, 8, 6, 4, 3], [30, 20, 15, 12, 10, 6, 2], [28, 24, 14, 12, 8, 7, 2], [28, 15, 14, 12, 10, 7, 6, 3]]]
[96, [[42, 30, 10, 7, 5, 2], [35, 20, 15, 14, 5, 4, 3], [28, 21, 18, 12, 9, 6, 2], [28, 20, 14, 12, 7, 6, 5, 4]]]
[97, [[48, 20, 16, 6, 5, 2], [48, 18, 16, 9, 4, 2], [30, 20, 18, 12, 9, 6, 2], [28, 18, 14, 12, 9, 7, 6, 3], [24, 20, 15, 12, 10, 8, 5, 3]]]
[98, [[36, 20, 18, 12, 5, 4, 3], [33, 22, 20, 11, 5, 4, 3]]]
[99, [[45, 36, 6, 5, 4, 3], [40, 30, 15, 8, 4, 2], [40, 24, 12, 10, 6, 4, 3], [40, 18, 12, 10, 9, 8, 2], [36, 24, 18, 8, 6, 4, 3], [36, 18, 15, 12, 10, 6, 2], [35, 20, 14, 12, 10, 6, 2], [35, 18, 15, 14, 9, 6, 2], [33, 22, 15, 11, 10, 6, 2], [30, 24, 12, 10, 8, 6, 5, 4], [24, 20, 18, 12, 9, 8, 5, 3]]]
[100, [[56, 21, 8, 7, 6, 2], [45, 24, 9, 8, 6, 5, 3], [42, 24, 12, 8, 7, 4, 3]]]
[101, [[60, 30, 5, 4, 2], [33, 22, 18, 11, 9, 6, 2], [30, 28, 21, 10, 5, 4, 3], [28, 24, 21, 12, 8, 6, 2], [28, 21, 20, 15, 10, 5, 2]]]
[102, [[72, 9, 8, 6, 4, 3], [48, 24, 16, 8, 4, 2], [48, 16, 15, 10, 6, 4, 3], [45, 30, 12, 9, 4, 2], [45, 20, 15, 9, 6, 4, 3], [30, 24, 20, 12, 8, 6, 2], [28, 24, 14, 12, 8, 7, 6, 3], [28, 20, 15, 14, 10, 7, 5, 3]]]
[103, [[42, 30, 10, 7, 6, 5, 3], [42, 18, 15, 10, 9, 7, 2], [40, 35, 14, 8, 4, 2], [40, 24, 15, 12, 5, 4, 3], [35, 30, 14, 12, 5, 4, 3], [35, 20, 15, 14, 12, 5, 2], [28, 21, 20, 18, 9, 5, 2]]]
[104, [[48, 18, 16, 9, 6, 4, 3], [42, 28, 21, 7, 4, 2], [35, 24, 15, 14, 8, 6, 2], [30, 28, 21, 20, 3, 2], [30, 28, 14, 10, 7, 6, 5, 4], [28, 20, 18, 14, 9, 7, 5, 3]]]
[105, [[42, 30, 20, 7, 4, 2], [40, 20, 12, 10, 8, 6, 5, 4], [40, 18, 15, 9, 8, 6, 5, 4], [33, 22, 20, 12, 11, 5, 2]]]
[106, [[45, 36, 12, 6, 5, 2], [45, 15, 12, 10, 9, 6, 5, 4], [40, 30, 15, 8, 6, 4, 3], [40, 24, 20, 10, 5, 4, 3], [40, 18, 12, 10, 9, 8, 6, 3], [36, 30, 18, 10, 5, 4, 3], [36, 24, 18, 12, 8, 6, 2], [36, 20, 18, 15, 10, 5, 2], [33, 24, 22, 11, 8, 6, 2], [24, 18, 15, 12, 10, 9, 8, 6, 4]]]
[107, [[30, 28, 20, 14, 7, 6, 2], [30, 24, 18, 10, 9, 8, 5, 3]]]
[108, [[60, 30, 6, 5, 4, 3], [60, 20, 15, 6, 5, 2], [60, 20, 12, 10, 4, 2], [60, 18, 15, 9, 4, 2], [54, 27, 12, 9, 4, 2], [48, 20, 16, 12, 5, 4, 3], [42, 24, 15, 10, 8, 7, 2], [36, 28, 21, 18, 3, 2], [30, 28, 21, 12, 10, 5, 2], [28, 24, 21, 20, 8, 5, 2], [28, 21, 20, 15, 10, 6, 5, 3], [28, 21, 18, 15, 10, 9, 4, 3]]]
[109, [[72, 12, 9, 8, 6, 2], [70, 28, 5, 4, 2], [48, 24, 16, 8, 6, 4, 3], [48, 16, 15, 12, 10, 6, 2], [45, 30, 12, 9, 6, 4, 3], [45, 20, 15, 12, 9, 6, 2], [42, 36, 18, 7, 4, 2], [42, 20, 15, 10, 7, 6, 5, 4], [40, 28, 14, 10, 8, 7, 2], [40, 24, 18, 10, 9, 6, 2], [36, 30, 20, 18, 3, 2], [30, 28, 14, 12, 10, 7, 5, 3], [30, 20, 18, 15, 10, 9, 4, 3], [28, 24, 20, 14, 8, 7, 5, 3]]]
[110, [[84, 14, 6, 4, 2], [72, 24, 9, 3, 2], [45, 42, 9, 7, 5, 2], [42, 24, 18, 9, 8, 7, 2], [42, 18, 15, 10, 9, 7, 6, 3], [40, 35, 14, 8, 6, 4, 3], [40, 18, 15, 12, 9, 8, 5, 3], [35, 20, 15, 14, 12, 6, 5, 3], [35, 18, 15, 14, 12, 9, 4, 3], [33, 22, 15, 12, 11, 10, 4, 3], [28, 21, 20, 18, 9, 6, 5, 3]]]
[111, [[56, 42, 8, 3, 2], [56, 21, 12, 8, 7, 4, 3], [48, 18, 16, 12, 9, 6, 2], [42, 28, 21, 7, 6, 4, 3], [42, 20, 18, 9, 7, 6, 5, 4], [36, 28, 18, 14, 7, 6, 2], [35, 30, 15, 14, 10, 5, 2], [28, 18, 15, 14, 10, 9, 7, 6, 4]]]
[112, [[56, 28, 14, 8, 4, 2], [42, 30, 20, 7, 6, 4, 3], [33, 22, 20, 12, 11, 6, 5, 3], [33, 22, 18, 12, 11, 9, 4, 3]]]
[113, [[60, 40, 8, 3, 2], [60, 24, 15, 8, 4, 2], [45, 24, 12, 9, 8, 6, 5, 4], [40, 30, 15, 12, 8, 6, 2], [40, 24, 20, 12, 10, 5, 2], [40, 24, 18, 15, 9, 5, 2], [40, 20, 18, 10, 9, 8, 5, 3], [36, 30, 18, 12, 10, 5, 2], [36, 24, 20, 18, 8, 5, 2], [36, 20, 18, 15, 10, 6, 5, 3], [35, 30, 18, 14, 9, 5, 2], [35, 20, 18, 14, 10, 9, 4, 3], [33, 30, 22, 11, 10, 5, 2], [28, 24, 21, 15, 10, 8, 4, 3], [24, 20, 18, 15, 10, 9, 8, 5, 4]]]
[114, [[56, 24, 21, 7, 4, 2], [42, 40, 10, 8, 7, 4, 3], [42, 20, 15, 12, 10, 7, 5, 3], [40, 30, 24, 15, 3, 2], [30, 24, 20, 15, 10, 8, 4, 3]]]
[115, [[84, 14, 12, 3, 2], [60, 30, 12, 6, 5, 2], [60, 20, 12, 10, 6, 4, 3], [60, 18, 15, 9, 6, 4, 3], [54, 27, 12, 9, 6, 4, 3], [45, 28, 21, 9, 5, 4, 3], [42, 24, 15, 10, 8, 7, 6, 3], [40, 28, 21, 10, 8, 6, 2], [35, 24, 15, 14, 12, 8, 4, 3], [30, 28, 21, 12, 10, 6, 5, 3], [28, 24, 21, 20, 8, 6, 5, 3], [28, 24, 21, 18, 9, 8, 4, 3], [28, 21, 18, 15, 12, 10, 9, 2], [28, 20, 15, 14, 12, 10, 7, 5, 4]]]
[116, [[72, 20, 9, 8, 5, 2], [70, 28, 6, 5, 4, 3], [48, 30, 16, 10, 5, 4, 3], [48, 24, 16, 12, 8, 6, 2], [48, 20, 16, 15, 10, 5, 2], [45, 30, 20, 9, 5, 4, 3], [42, 36, 18, 7, 6, 4, 3], [42, 30, 12, 10, 7, 6, 5, 4], [42, 24, 20, 8, 7, 6, 5, 4], [42, 20, 18, 12, 9, 7, 5, 3], [40, 30, 20, 10, 8, 6, 2], [40, 28, 14, 10, 8, 7, 6, 3], [30, 24, 20, 18, 9, 8, 4, 3], [30, 20, 18, 15, 12, 10, 9, 2], [28, 24, 15, 14, 10, 8, 7, 6, 4], [28, 18, 15, 14, 12, 10, 9, 7, 3]]]
[117, [[45, 42, 9, 7, 6, 5, 3], [45, 30, 15, 10, 9, 6, 2], [42, 24, 18, 9, 8, 7, 6, 3], [40, 35, 14, 12, 8, 6, 2], [33, 24, 22, 12, 11, 8, 4, 3], [30, 28, 21, 20, 12, 4, 2], [28, 20, 18, 14, 12, 9, 7, 5, 4]]]
[118, [[70, 21, 14, 6, 5, 2], [48, 28, 21, 16, 3, 2], [48, 20, 18, 16, 9, 5, 2], [45, 36, 15, 10, 5, 4, 3], [45, 28, 14, 9, 7, 6, 5, 4], [42, 35, 21, 15, 3, 2], [42, 28, 21, 12, 7, 6, 2], [40, 35, 24, 14, 3, 2], [36, 24, 18, 15, 10, 8, 4, 3], [35, 30, 24, 14, 8, 5, 2], [35, 30, 15, 14, 10, 6, 5, 3], [35, 24, 20, 14, 10, 8, 4, 3], [30, 28, 20, 14, 12, 7, 4, 3], [28, 24, 18, 14, 9, 8, 7, 6, 4]]]
[119, [[60, 20, 15, 12, 5, 4, 3], [56, 28, 14, 8, 6, 4, 3], [56, 21, 15, 10, 8, 7, 2], [48, 42, 16, 7, 4, 2], [48, 30, 20, 16, 3, 2], [45, 24, 15, 10, 9, 8, 5, 3], [42, 30, 20, 12, 7, 6, 2], [40, 28, 21, 15, 8, 5, 2], [35, 28, 21, 15, 14, 4, 2]]]
[120, [[60, 24, 15, 8, 6, 4, 3], [45, 36, 18, 9, 5, 4, 3], [40, 36, 18, 10, 8, 6, 2], [40, 30, 20, 15, 8, 5, 2], [40, 28, 15, 14, 8, 7, 5, 3], [40, 24, 20, 12, 10, 6, 5, 3], [40, 24, 18, 15, 9, 6, 5, 3], [40, 24, 18, 12, 10, 9, 4, 3], [36, 30, 18, 12, 10, 6, 5, 3], [36, 24, 20, 18, 8, 6, 5, 3], [35, 30, 20, 15, 14, 4, 2], [35, 30, 18, 14, 9, 6, 5, 3], [35, 20, 18, 14, 12, 10, 9, 2], [33, 30, 22, 11, 10, 6, 5, 3], [33, 22, 18, 15, 11, 10, 9, 2], [30, 24, 18, 12, 10, 9, 8, 5, 4], [28, 24, 21, 15, 12, 10, 8, 2]]]
[121, [[80, 16, 10, 8, 5, 2], [72, 36, 8, 3, 2], [72, 15, 10, 9, 8, 4, 3], [56, 24, 21, 7, 6, 4, 3], [56, 21, 18, 9, 8, 7, 2], [48, 28, 16, 14, 7, 6, 2], [45, 36, 20, 15, 3, 2], [45, 35, 14, 10, 9, 6, 2], [42, 40, 12, 10, 8, 7, 2], [42, 35, 15, 14, 7, 6, 2], [42, 24, 20, 12, 8, 7, 5, 3], [36, 28, 21, 18, 12, 4, 2], [33, 28, 22, 21, 11, 4, 2], [30, 24, 20, 15, 12, 10, 8, 2], [28, 24, 15, 14, 12, 10, 8, 7, 3], [28, 21, 20, 15, 12, 10, 6, 5, 4]]]
[122, [[63, 28, 18, 7, 4, 2], [60, 18, 15, 12, 9, 6, 2], [54, 27, 20, 9, 5, 4, 3], [45, 28, 21, 12, 9, 5, 2], [36, 30, 20, 18, 12, 4, 2], [36, 28, 18, 14, 12, 7, 4, 3], [33, 30, 22, 20, 11, 4, 2], [33, 28, 22, 14, 11, 7, 4, 3], [28, 24, 21, 18, 12, 9, 8, 2], [28, 24, 20, 14, 12, 8, 7, 5, 4], [28, 21, 18, 15, 12, 10, 9, 6, 3]]]
[123, [[90, 18, 10, 3, 2], [72, 24, 12, 9, 4, 2], [72, 20, 9, 8, 6, 5, 3], [70, 28, 12, 6, 5, 2], [54, 27, 15, 10, 9, 6, 2], [48, 36, 18, 16, 3, 2], [48, 30, 16, 12, 10, 5, 2], [48, 24, 20, 16, 8, 5, 2], [48, 20, 16, 15, 10, 6, 5, 3], [48, 18, 16, 15, 10, 9, 4, 3], [45, 36, 30, 6, 4, 2], [45, 30, 20, 12, 9, 5, 2], [45, 28, 14, 12, 9, 7, 5, 3], [42, 36, 18, 12, 7, 6, 2], [42, 33, 22, 11, 7, 6, 2], [42, 18, 15, 12, 10, 9, 7, 6, 4], [30, 24, 20, 18, 12, 9, 8, 2], [30, 20, 18, 15, 12, 10, 9, 6, 3], [28, 24, 18, 14, 12, 9, 8, 7, 3], [28, 21, 20, 18, 12, 9, 6, 5, 4]]]
[124, [[56, 42, 12, 8, 4, 2], [45, 30, 24, 9, 8, 6, 2], [42, 30, 18, 10, 9, 7, 5, 3], [40, 36, 18, 15, 8, 5, 2], [40, 35, 20, 14, 8, 5, 2], [36, 35, 18, 15, 14, 4, 2], [30, 28, 21, 20, 12, 6, 4, 3]]]
[125, [[60, 20, 18, 10, 9, 6, 2], [48, 20, 18, 16, 9, 6, 5, 3], [45, 36, 24, 8, 5, 4, 3], [45, 36, 15, 12, 10, 5, 2], [45, 35, 15, 14, 9, 5, 2], [42, 28, 21, 20, 7, 5, 2], [36, 24, 18, 15, 12, 10, 8, 2], [35, 30, 24, 14, 8, 6, 5, 3], [35, 24, 20, 14, 12, 10, 8, 2], [35, 24, 18, 15, 14, 9, 8, 2], [33, 24, 22, 15, 11, 10, 8, 2], [30, 28, 18, 14, 10, 9, 7, 5, 4]]]
[126, [[60, 40, 12, 8, 4, 2], [56, 28, 14, 12, 8, 6, 2], [56, 21, 15, 10, 8, 7, 6, 3], [48, 42, 16, 7, 6, 4, 3], [40, 28, 21, 15, 8, 6, 5, 3], [40, 28, 21, 12, 10, 8, 4, 3], [40, 20, 18, 12, 10, 9, 8, 5, 4], [36, 33, 22, 18, 11, 4, 2], [36, 20, 18, 15, 12, 10, 6, 5, 4], [35, 28, 21, 15, 14, 6, 4, 3], [35, 20, 18, 15, 14, 9, 6, 5, 4], [33, 22, 20, 15, 11, 10, 6, 5, 4], [30, 28, 20, 15, 14, 10, 7, 2]]]
[127, [[60, 30, 15, 10, 5, 4, 3], [60, 24, 15, 12, 8, 6, 2], [56, 28, 24, 14, 3, 2], [56, 21, 20, 8, 7, 6, 5, 4], [45, 40, 10, 9, 8, 6, 5, 4], [45, 36, 18, 12, 9, 5, 2], [45, 33, 22, 11, 9, 5, 2], [42, 40, 15, 8, 7, 6, 5, 4], [40, 30, 24, 15, 12, 4, 2], [40, 30, 20, 15, 8, 6, 5, 3], [40, 30, 20, 12, 10, 8, 4, 3], [40, 30, 18, 15, 9, 8, 4, 3], [35, 30, 20, 15, 14, 6, 4, 3], [35, 20, 18, 14, 12, 10, 9, 6, 3], [33, 24, 22, 18, 11, 9, 8, 2], [33, 22, 18, 15, 11, 10, 9, 6, 3], [28, 24, 21, 15, 12, 10, 8, 6, 3], [24, 20, 18, 15, 12, 10, 9, 8, 6, 5]]]
[128, [[80, 16, 10, 8, 6, 5, 3], [72, 15, 12, 10, 9, 8, 2], [56, 24, 21, 12, 7, 6, 2], [56, 21, 18, 9, 8, 7, 6, 3], [48, 24, 16, 15, 10, 8, 4, 3], [45, 36, 30, 12, 3, 2], [45, 30, 15, 12, 10, 9, 4, 3], [45, 24, 20, 15, 9, 8, 4, 3], [42, 40, 12, 10, 8, 7, 6, 3], [42, 24, 15, 12, 10, 8, 7, 6, 4], [36, 28, 21, 18, 12, 6, 4, 3], [33, 28, 22, 21, 11, 6, 4, 3], [33, 22, 20, 18, 11, 9, 6, 5, 4], [30, 28, 20, 18, 14, 9, 7, 2], [30, 24, 20, 15, 12, 10, 8, 6, 3], [28, 24, 21, 20, 12, 8, 6, 5, 4]]]
[129, [[84, 15, 14, 10, 4, 2], [70, 21, 14, 12, 5, 4, 3], [63, 28, 18, 7, 6, 4, 3], [60, 30, 18, 9, 5, 4, 3], [60, 28, 21, 15, 3, 2], [60, 20, 18, 15, 9, 5, 2], [54, 36, 27, 6, 4, 2], [54, 27, 20, 12, 9, 5, 2], [52, 39, 26, 6, 4, 2], [45, 28, 21, 12, 9, 6, 5, 3], [42, 30, 24, 10, 8, 7, 5, 3], [40, 35, 15, 14, 10, 8, 4, 3], [40, 28, 24, 21, 10, 4, 2], [40, 28, 14, 12, 10, 8, 7, 6, 4], [36, 30, 20, 18, 12, 6, 4, 3], [33, 30, 22, 20, 11, 6, 4, 3], [33, 28, 22, 14, 12, 11, 7, 2], [28, 24, 21, 18, 12, 9, 8, 6, 3], [28, 21, 20, 18, 15, 10, 9, 5, 3]]]
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