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;
struct node {
  vector<int> v;
  int s = 0;
  int e = 0;
};
int gcd(int a, int b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}
bool cmp(pair<int, int> p1, pair<int, int> p2) { return p1.second > p2.second; }
struct mycmp {
  constexpr bool operator()(pair<int, int> const& p1,
                            pair<int, int> const& p2) const noexcept {
    return p1.second < p2.second;
  }
};
bool isprime(int n) {
  for (int i = 3; i * i <= n; i += 2) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
void solve() {
  int n;
  cin >> n;
  double ans = 1.0 / tan(acos(-1) / n / 2);
  cout << setprecision(10) << ans << '\n';
}
int main() {
  int t;
  cin >> t;
  while (t > 0) {
    solve();
    t--;
  }
  return 0;
}