#include using namespace std; #define int long long int N; double memo[110][110][110]; double rec(int i, int j, int k) { if (memo[i][j][k] >= 0) return memo[i][j][k]; double res = 0; if (i > 0) res += i*rec(i-1, j+1, k); if (j > 0) res += j*rec(i, j-1, k+1); if (k > 0) res += k*rec(i, j, k-1); res += N; res /= i+j+k; return memo[i][j][k] = res; } signed main() { cin >> N; int zero=0, one=0, two=0; for (int i=0; i> ai; if (ai == 0) zero++; else if (ai == 1) one++; else if (ai == 2) two++; } memset(memo, -1, sizeof(memo)); memo[0][0][0] = 0; cout << setprecision(10) << rec(zero, one, two) << endl; }