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.util.*;
import java.io.*;
import java.io.BufferedReader;

public class Z_C{
	public static final String TASKNAME = "";
	public static final long mod= 1000000007;

	public static void main(String[] args) throws IOException {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
//		InputReader in = new InputReader(new FileInputStream(TASKNAME+".in"));
//		PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter(TASKNAME+".out")));
		Autocompletion solver = new Autocompletion();
		solver.solve(1, in, out);
		out.close();
	}
	static class Autocompletion {

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int t=in.nextInt();
			for(int z=0;z<t;z++) {
				int n=in.nextInt()*2;
				double arr[]=new double[n];
				arr[1]=1.0;
				for(int i=2;i<=n/4;i++) {
					arr[i]=getSideB(Math.PI*(double)(n-i)/(double)n,1.0,arr[i-1]);
				}
				double ans=get(n,n/2);
				ans=get(n,n/2-1);
				if(n%8==0) {
					ans=get(n,n/2-1);
				}
				System.out.println(ans);
			}
		}
		private double get(int n,int i) {
			if(i==1) {
				return 1;
			}
			if(i%2==0) {
				return getSideB(Math.PI*(double)(n-i)/(double)n,get(n,i/2),get(n,i/2));
			}
			return getSideB(Math.PI*(double)(n-i)/(double)n,get(n,i-1),get(n,1));
		}
		public static double getSideB(double d, double e, double arr) {
		    return (double) Math.sqrt(Math.pow(e, 2) + Math.pow(arr, 2) - 2 * e * arr * Math.cos(d));
		  }
	}

	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
        	return Long.parseLong(next());
        }
        public int[] nextIntArr(int n) {
        	int arr[]=new int[n];
        	for(int i=0;i<n;i++) {
        		arr[i]=this.nextInt();
        	}
        	return arr;
        }
 
    }
}