/* -*- coding: utf-8 -*- * * 108.cc: No.108 トリプルカードコンプ - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const int MAX_N = 100; /* typedef */ /* global variables */ int n; int n1 = 0, n2 = 0, n3 = 0; double dp[MAX_N + 1][MAX_N + 1][MAX_N + 1]; /* subroutines */ double rec(int i3, int i2, int i1) { if (dp[i3][i2][i1] >= 0.0) return dp[i3][i2][i1]; double sum = 0.0; if (i3 > 0) sum += rec(i3 - 1, i2 + 1, i1) * i3; if (i2 > 0) sum += rec(i3, i2 - 1, i1 + 1) * i2; if (i1 > 0) sum += rec(i3, i2, i1 - 1) * i1; return (dp[i3][i2][i1] = (sum + n) / (i3 + i2 + i1)); } /* main */ int main() { cin >> n; for (int i = 0; i < n; i++) { int ai; cin >> ai; switch (ai) { case 0: n3++; break; case 1: n2++; break; case 2: n1++; break; } } for (int i3 = 0; i3 <= n; i3++) for (int i2 = 0; i2 <= n; i2++) for (int i1 = 0; i1 <= n; i1++) dp[i3][i2][i1] = -1.0; dp[0][0][0] = 0.0; double ans = rec(n3, n2, n1); printf("%.10lf\n", ans); return 0; }