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.util.*;
import java.lang.*;
import java.io.*;

public class Main
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuffer sb = new StringBuffer();
		double a[] = new double[101];
		a[0] = 0;
		for(int i = 1; i <= 100; i++){
		    double angle = 90.0 / (i + 1);
		    double val = 0.0;
		    for(int j = 1; j <= i; j++){
		        val += Math.cos(Math.toRadians(angle * j));
		    }
		    a[i] = val;
		}
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0){
		    int n = Integer.parseInt(br.readLine());
		    n /= 2; n--;
		    double ans = 1.0 + (2.0 * a[n]);
		    sb.append(ans+"\n");
		}
		System.out.println(sb);
	}	
}