#include <bits/stdc++.h>

#define show(x) cerr << #x << " = " << x << endl

using namespace std;
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v)
{
    os << "sz=" << v.size() << "\n[";
    for (const auto& p : v) {
        os << p << ",";
    }
    os << "]\n";
    return os;
}

template <typename S, typename T>
ostream& operator<<(ostream& os, const pair<S, T>& p)
{
    os << "(" << p.first << "," << p.second
       << ")";
    return os;
}


constexpr ll MOD = 1e9 + 7;

template <typename T>
constexpr T INF = numeric_limits<T>::max() / 100;

// dp[0]=0;
// dp[i] = p0*dp[i-1]+p1*dp[i-2]+p2*dp[i-3]+p3*dp[i-4]+p4*dp[i-4]+p5*dp[i-6]+1
constexpr int MAX = 1e6;
long double dp[MAX + 1];
long double p[6];
int main()
{
    dp[0] = 0.0000000000000000;
    dp[1] = 1.0000000000000000;
    dp[2] = 1.0833333333333333;
    dp[3] = 1.2569444444444444;
    dp[4] = 1.5353009259259260;
    dp[5] = 1.6915991512345676;
    dp[6] = 2.0513639724794235;


    for (int i = 2; i <= 6; i++) {
        long double sum = dp[i] - 1;
        for (int j = 0; j < i - 2; j++) {
            sum -= p[j] * dp[i - j - 1];
        }
        p[i - 2] = sum / dp[1];
    }
    p[5] = 1.0;
    for (int i = 0; i < 5; i++) {
        p[5] -= p[i];
    }

    for (int i = 7; i <= MAX; i++) {
        long double sum = 1.0;
        for (int j = 0; j < 6; j++) {
            sum += dp[i - j - 1] * p[j];
        }
        dp[i] = sum;
    }

    int T;
    cin >> T;
    for (int i = 0; i < T; i++) {
        int N;
        cin >> N;
        cout << fixed << setprecision(10) << dp[N] << endl;
    }

    return 0;
}