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;
void solv() {
  long long n;
  cin >> n;
  long long k = n / 2 + (n & 1);
  long double y = 1 / sqrt(2 * (1 - cos(3.14159265359 / n)));
  long double h = sqrt((1 - cos((k - 1) * 3.14159265359 / n)) * 2) * y;
  long double d = cos(3.14159265359 / 4) * h / sqrt(2) +
                  cos((k - 1) * 3.14159265359 / (n * 2)) * y;
  long double ans = d * sqrt(2);
  cout << fixed << setprecision(15) << ans << '\n';
}
signed main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(false);
  long long t;
  cin >> t;
  while (t--) solv();
}