#include<bits/stdc++.h>
#define AC return 0;
#define int long long 
#define pii pair<int,int>
#define all(tar) tar.begin(),tar.end()
const int N = 3e5 + 10;
const int mod=998244353; 
using namespace std;

int pre[N];
double val[N];

void Init()
{
    for (int i = 2; i < N; i++)
        pre[i] = pre[i - 1] + i;
    for (int i = 2; i < N; i++)
        val[i] = val[i - 1] + log(i);
}

void Solve()
{
    int n;
    cin >> n;
    int l, r;
    l = 1, r = n;
    int tot = -1;
    while (l <= r)
    {
        int mid = (l + r) >> 1;
        if (pre[mid] <= n)
        {
            tot = mid;
            l = mid + 1;
        }
        else 
            r = mid - 1;
    }
    int rm = n - pre[tot];
    double res = val[tot - rm] + val[tot + 1] - val[tot - rm + 1];
    cout << setprecision(10) << res << "\n";
    return ; 
}

signed main(){
   ios::sync_with_stdio(false);
   cin.tie(0);
   cout.tie(0);cout.setf(ios::fixed);
   int T;cin>>T;
   Init();
   while(T--){
        Solve();
   }
   AC
}