import math def preprocess(): Bingos = [0] * 26 Counts = [0] * 26 masks12 = get_masks() for pat in range(2**25): bits_on = bin(pat).count('1') Bingos[bits_on] += 12 - len([1 for mask in masks12 if ~pat & mask]) Counts[bits_on] += 1 return [bingo/count for bingo, count in zip(Bingos, Counts)] def get_masks(): bingo_patterns = [[0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19], [20, 21, 22, 23, 24], [0, 5, 10, 15, 20], [1, 6, 11, 16, 21], [2, 7, 12, 17, 22], [3, 8, 13, 18, 23], [4, 9, 14, 19, 24], [0, 6, 12, 18, 24], [4, 8, 12, 16, 20]] return [sum(1 << i for i in pat) for pat in bingo_patterns] # E = preprocess() # 2秒では計算が終わらなかったので、オフラインで事前に計算しました。。。 E = [0.0, 0.0, 0.0, 0.0, 0.0, 0.00022586109542631282, 0.0013551665725578769, 0.0047430830039525695, 0.012648221343873518, 0.028458498023715414, 0.05691699604743083, 0.10434782608695652, 0.17888198757763976, 0.2906832298136646, 0.45217391304347826, 0.6782608695652174, 0.9865612648221344, 1.3976284584980236, 1.9351778656126482, 2.6263128176171655, 3.501750423489554, 4.59604743083004, 5.947826086956522, 7.6, 9.6, 12.0] def prob(N): '''1-99 までの N 個を選んだときに、1-25までの数字が n 個含まれる確率 prob[n] のリストを返す。 1-25から n 個とり、26-99から N-n 個とればよい。 ''' probs = [0] * 26 base = math.factorial(99) // math.factorial(N) // math.factorial(99 - N) fac25 = math.factorial(25) fac74 = math.factorial(74) for n in range(max(0, N - 74), min(25, N) + 1): pats1_25 = fac25 // math.factorial(n) // math.factorial(25 - n) pats26_99 = fac74 // math.factorial(N - n) // math.factorial(74 - N + n) probs[n] = pats1_25 * pats26_99 / base return probs N = int(input()) probs = prob(N) Expected = sum(e * p for e, p in zip(E, probs)) print(Expected)