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;
bool isprime(long long x) {
  if (x == 2) return true;
  if (x == 3) return true;
  for (long long i = 2; i * i <= x; i++) {
    if (x % i == 0) return false;
  }
  return true;
}
bool issort(long long a[], long long n) {
  for (long long i = 1; i < n; i++) {
    if (a[i - 1] >= a[i]) {
      return false;
    }
  }
  return true;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
void solve() {
  long double n, pi;
  cin >> n;
  n *= 2;
  pi = 2 * acos(0.0);
  cout.precision(10);
  cout << 1 / (long double)(tan((long double)pi / (long double)n)) << "\n";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long t;
  t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}