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J.cpp
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J.cpp
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> Pii;
typedef pair<int, ll> Pil;
typedef pair<ll, ll> Pll;
typedef pair<ll, int> Pli;
typedef vector<vector<ll>> Mat;
#define fi first
#define se second
const ll MOD = 1e9 + 7;
const ll MOD2 = 998244353;
const ll MOD3 = 1812447359;
const ll INF = 1ll << 62;
const double PI = 2 * asin(1);
void yes() { printf("yes\n"); }
void no() { printf("no\n"); }
void Yes() { printf("Yes\n"); }
void No() { printf("No\n"); }
void YES() { printf("YES\n"); }
void NO() { printf("NO\n"); }
int n, a[305], cnt[4];
double dp[305][305][305];
bool visited[305][305][305];
double solve(int i, int j, int k) {
if (i < 0 || j < 0 || k < 0) {
return 0;
}
if (i == 0 && j == 0 && k == 0) {
return 0;
}
if (visited[i][j][k]) {
return dp[i][j][k];
}
visited[i][j][k] = true;
double ans = (double)(n) / (double)(i + j + k);
ans += (double)(i) / (double)(i + j + k) * solve(i - 1, j, k);
ans += (double)(j) / (double)(i + j + k) * solve(i + 1, j - 1, k);
ans += (double)(k) / (double)(i + j + k) * solve(i, j + 1, k - 1);
return dp[i][j][k] = ans;
}
int main() {
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> a[i];
cnt[a[i]]++;
}
cout << fixed << setprecision(32) << solve(cnt[1], cnt[2], cnt[3]) << endl;
return 0;
}