A - Arcade Game Gym - 100814A

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 4e5 + 10;
double dp[maxn];
int main()
{
    ios::sync_with_stdio(0);
    int t;
//    s.resize(20);
//    scanf("%d", &t);
    cin >> t;
    while(t--)
    {
        string s;
        cin >> s;
        memset(dp,0,sizeof(dp));        
//        scanf("%s",&s[0]);
        int len = s.length();
        int n = 1;
        for(int i = 1; i <= len; i ++)n *= i;
        int pos = 0;
        while(next_permutation(s.begin(),s.end())) pos++;
        double o = 1;
        dp[0] = 1;
        for(int i = 1; i <= pos; i ++)
        {
            dp[i] = 1.0 /n*o;
            o += dp[i];
        }
        dp[0] = 0;
        printf("%.9lf\n",dp[pos]);
    }
    return 0;
}