#pragma GCC optimize("Ofast") #include using namespace std; #define rep(i, n) for(int i = 0; i < (n); ++i) #define all(x) (x).begin(),(x).end() #define ln '\n' constexpr long long MOD = 1000000007LL; //constexpr long long MOD = 998244353LL; typedef long long ll; typedef unsigned long long ull; typedef pair pii; typedef pair pll; template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true;} return false; } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true;} return false; } /////////////////////////////////////////////////////////////////////////////////////////////////// #define EPS (1e-10) int N; double dp[300][300][300]; double func(int a, int b, int c) { if (a+b+c==0) return 0; if (dp[a][b][c] > EPS) return dp[a][b][c]; dp[a][b][c] = N; if (a) dp[a][b][c] += func(a-1,b+1,c)*a; if (b) dp[a][b][c] += func(a,b-1,c+1)*b; if (c) dp[a][b][c] += func(a,b,c-1)*c; dp[a][b][c] /= (a+b+c); return dp[a][b][c]; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cin >> N; int a = 0, b = 0, c = 0; rep(i,N) { int A; cin >> A; if (A==0) a++; if (A==1) b++; if (A==2) c++; } cout << fixed << setprecision(10) << func(a,b,c) << ln; }