Problem: The statement of this problem is the same as the statement of problem C2. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.

You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.

Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.

You can rotate 2n-gon and/or the square.

Input

The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.

Next T lines contain descriptions of test cases — one per line. Each line contains single even integer n (2 ≤ n ≤ 200). Don't forget you need to embed 2n-gon, not an n-gon.

Output

Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.

Example

Input


3
2
4
200


Output


1.000000000
2.414213562
127.321336469

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 144, M = 144, mod = 1e9 + 7, inf = 2e9, LOG = 20;
const long long INF = 1e18;
const double pi = acos(-1), eps = 1e-9;
long long bp(long long x, long long y) {
  if (y == 0) return 1;
  if (y & 1) return (x * bp(x, y - 1)) % mod;
  long long z = bp(x, y / 2);
  return (z * z) % mod;
}
void file() {
  freopen("mines.in", "r", stdin);
  freopen("mines.out", "w", stdout);
}
void solve() {
  double n;
  cin >> n;
  n *= 2;
  double R = (double)1 / sin(pi / n) / 2;
  cout << fixed << setprecision(9) << sqrt(R * R - (double)1 / 4) * 2;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int q = 1;
  cin >> q;
  while (q--) {
    solve();
    cout << "\n";
  }
  return 0;
}