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 long long oo = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
const double pi = 2 * acos(0);
double solve(long long n) {
  if (n % 2 == 0) {
    return 1 / tan(pi / 2 / n);
  }
  double beta = (n / 2) * pi / n;
  double x = (1 - sin(beta)) / cos(beta);
  double alpha = atan(x);
  return cos(alpha) / sin(pi / 2 / n);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long tc;
  cin >> tc;
  while (tc--) {
    long long n;
    cin >> n;
    cout << fixed << setprecision(20) << solve(n) << endl;
  }
}