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.*;
import java.util.Arrays;
import java.util.Locale;
import java.util.StringTokenizer;

public class SolutionD {
    static BufferedReader input;
    static StringTokenizer _stk;

    static String readln() throws IOException {
        String l = input.readLine();
        if (l != null)
            _stk = new StringTokenizer(l, " ");
        return l;
    }

    static String next() {
        return _stk.nextToken();
    }

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

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


    static void dbg(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }

    static PrintWriter output = new PrintWriter(new BufferedWriter(
            new OutputStreamWriter(System.out)));

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        input = new BufferedReader(new InputStreamReader(System.in));
        readln();
        int t = nextInt();
        for (int testI = 0; testI < t; testI++) {
            readln();
            int n = nextInt() * 2;
            double angle = 360. / (2 * n);
            double r = 1. / (2 * Math.sin(Math.toRadians(angle)));

            double angle2 = (360. / n) * ((n / 2.) - 1);
            double angle3 = 90 - angle2 / 2;

            double ang4 = angle3 / 2;
            double ans = 2 * r * Math.cos(Math.toRadians(ang4));


            output.println(ans);
        }
        output.close();
    }
}