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;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long dot(complex<long long> c1, complex<long long> c2) {
  return imag(c1 * conj(c2));
}
double dot(complex<double> c1, complex<double> c2) {
  return imag(c1 * conj(c2));
}
long long point(complex<long long> c1, complex<long long> c2) {
  return real(c1 * conj(c2));
}
double point(complex<double> c1, complex<double> c2) {
  return real(c1 * conj(c2));
}
void solve() {
  long double n, pi2, alpha, res;
  pi2 = acos(0.0);
  cin >> n;
  alpha = pi2 * (n - 1.0) / n;
  res = tan(alpha);
  cout << res << endl;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int t, cases;
  cin >> cases;
  cout << fixed << setprecision(10);
  for (t = 0; t < cases; t++) {
    solve();
  }
}