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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
public class cdfer87c
{
	static void merge(int arr[], int l, int m, int r) 
    { 
        int n1 = m - l + 1; 
        int n2 = r - m; 
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
        int i = 0, j = 0; 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
    static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            int m = (l+r)/2; 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
            merge(arr, l, m, r); 
        } 
    } 
    public static int lowerBound(int[] array, int length, int value) 
	{
        int low = 0;
        int high = length;
        while (low < high) 
        {
            final int mid = (low + high) / 2;
            //checks if the value is less than middle element of the array
            if (value <= array[mid]) 
            {
                high = mid;
            } 
            else 
            {
                low = mid + 1;
            }
        }
        return low;
    }
	public static int upperBound(int[] array, int length, int value) 
	{
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value >= array[mid]) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }
    static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 
    static long power(long n,long m)
    {
    	if(m==0)
    		return 1;
    	long ans=1;
    	while(m>0)
    	{
    		ans=ans*n;
    		m--;
    	}
    	return ans;
    }
    static int BinarySearch(int arr[], int x) 
    { 
        int l = 0, r = arr.length - 1; 
        while (l <= r) { 
            int m = l + (r - l) / 2; 
            if (arr[m] == x) 
                return m; 
            if (arr[m] < x) 
                l = m + 1; 
            else
                r = m - 1; 
        } 
        return -1; 
    } 
	public static void main(String args[])throws Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		//System.out.println(Math.asin(radians));
	    for(int i=1;i<=t;i++)
	    {
	        double n=Integer.parseInt(br.readLine());
	        double radians =Math.toRadians(180/(4*n)); 
	        double rad=1/(2*Math.sin(radians));
//	        //System.out.println(rad);
//	        n*=2;
//	        radians =Math.toRadians(((n-2)/n)*90);
//	        double ans=rad*Math.sin(radians);
//	        //System.out.println(ans);
	       // rad*=2;
	        System.out.println(rad);
	    }
	}
}