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.IOException;
import java.util.ArrayList;
import java.util.Scanner;

public class C {

	public static class pair implements Comparable<pair> {
		int id;
		int ans;

		pair(int x, int y) {

			id = x;
			ans = y;

		}

		public pair() {

		}

		public int compareTo(pair o) {
			// TODO Auto-generated method stub

			return this.ans - o.ans;
		}
	}

//	static int mod = (int) 998244353.;
	static int mod=(int)1e9+7;
	static ArrayList<Integer> gr[];
	static int  ar[];
	static Scanner sc = new Scanner(System.in);
	static int pri[] = new int[(int) 1e6 + 5];
	static StringBuilder out = new StringBuilder();

	static int[] dp;

	public static void main(String[] args) throws IOException {
		int t = sc.nextInt();
		
		while (t-- > 0) {
			int n = sc.nextInt();
			double x = Math.PI / (2 * n);
			double ans = Math.sin(x);
			ans = 1 / ans;
			double s = (Math.sqrt(ans * ans - 1.0));
			out.append(s+"\n");
		}
		System.out.println(out);
	}
	
	

}