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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;



public class TaskC {
	public static void main(String[] arg) {
		final FastScanner in = new FastScanner(System.in);
		final PrintWriter out = new PrintWriter(System.out);
		StringBuilder result = new StringBuilder();
		final int T = in.nextInt();
		for(int t=0;t<T;t++) {
			final int n = in.nextInt();
			final double N=2*n;
			final double c = 180.0-90.0-360.0/(2*N);
			final double resp =Math.tan(Math.toRadians(c));
			result.append(resp).append("\n");
		}
		out.println(result);
		out.close();
		in.close();
	}
	
	private static class Solution {
		
	}
	
	
	
	private static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(InputStream stream) {
			try {
				br = new BufferedReader(new InputStreamReader(stream));
			} catch (Exception e) {
				e.printStackTrace();
			}
		}

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

		int nextInt() {
			return Integer.parseInt(next());
		}
		
		int [] readIntArr(int n){
			int [] result = new int[n];
			for(int i=0;i<n;i++){
				result[i]=Integer.parseInt(next());
			}
			return result;
		}
		
		void close(){
			try {
				br.close();
			} catch (IOException e) {
				e.printStackTrace();
			}
		}

		long nextLong() {
			return Long.parseLong(next());
		}

	}
	
}