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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.lang.Math;

public class Solution{

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

		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		
		double pi = (double)180;
		pi = Math.toRadians(pi);
		

		int t = fs.nextInt();
		
		while(t-->0) {
			int n = fs.nextInt();
			out.println(String.format("%.9f",Math.cos(pi/(4*n))/Math.sin(pi/(2*n))));
		}
		
		
		out.close();
		
	
		
		
	
	}

	
	

	
	static class FastScanner{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		public String next(){
			while(!st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				} catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		public int nextInt(){
			return Integer.parseInt(next());
		}

		public int[] readArray(int n){
			int[] a = new int[n];
			for(int i=0;i<n;i++)
				a[i] = nextInt();
			return a;
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	
	static int lowerBound(int[] arr, int l, int r, int k) {
		while(r>l) {
			int mid = (l+r)/2;
			if(arr[mid]>=k) {
				r = mid;
			}
			else {
				l = mid+1;
			}
		}
		if(arr[l]<k)
			return -1;
		return l;
	}
	
	
	
	static int upperBound(int[] arr, int l, int r, int k) {
		while(r>l) {
			int mid = (l+r)/2;
			if(arr[mid]>k) {
				r = mid;
			}
			else {
				l = mid+1;
			}
		}
		if(arr[l]<=k)
			return -1;
		return l;
	}

}