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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class GFG {

  static StringBuffer str = new StringBuffer("");
  static long n;

  // Refer whatsapp chat with Harsha
  static void solve() {
    n = 2 * n;
    str.append(String.format("%.9f", ((float) 1 / Math.sin((float) Math.PI / (2.0 * n))) / 2.0) + "\n");
  }

  public static void main(String[] args) throws Exception {

    BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    int t = Integer.parseInt(bf.readLine());
    while (t-- > 0) {
      n = Long.parseLong(bf.readLine());
      solve();
    }
    System.out.println(str);
  }
}