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:
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	DecimalFormat df = new DecimalFormat("0.000000000");
	int t=Integer.parseInt(bf.readLine());
	while(t-->0)
	{
	    int n=Integer.parseInt(bf.readLine());
	   // double area=0.0
	    double a=2.0*(1/(2.0 * Math.tan(3.141592653589793238/(2.00*n))));
	   // double z=Math.tan(3.14/4.0);
	  //  double p=2.0*n;
	  //  double area=(a*p)/2.0;
	    System.out.println(df.format(a));
	}
	
	}
}