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.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Set;

import javax.lang.model.util.ElementScanner6;

import java.util.List;
/**
 * Using FastReader and Output Class
 *
 * @author Wallace
 */
 public class Main {
    static int parent[]=new int[26];
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        IAMBACK solver = new IAMBACK();
        solver.solve(1, in, out);
        out.close();
    }
    static class IAMBACK {
        static long mod=1000*1000*1000+7;
        public void solve(int testNumber, FastReader in, PrintWriter out) {
                int t=in.nextInt();
                while(t!=0){
                       int n=in.nextInt();
                       n=2*n;
                       double ans=n-2;
                       ans=(ans/n*1.0)*0.5;
                       ans=ans*Math.PI;
                       ans=Math.tan(ans);
                       out.println(String.format("%.9f", ans)); 
                    t--;
                }
         
          }
          
          public int helper1(int c,int last,int kitnasum,int l,int target,int dp[][][]){
                if(c>l || kitnasum>target)
                return 0; 
                if(c==l)
                return dp[c][kitnasum][last]=1;
                if(dp[c][kitnasum][last]>0)
                return dp[c][kitnasum][last];
                int count=0;
                for(int i=last+1;i<=52;i++){
                    count+= helper1(c+1, i, kitnasum+i, l, target,dp);
                }

                return dp[c][kitnasum][last]=count;
          }
        

       

        // public static long helper(long a, long b){
        //     long ans=1;
        //     while(b!=0)	{
        //         if(b%2==1){
        //             ans=(ans*a)%mod;
        //         }
        //         a=(a*a)%mod;
        //         b=b/2;
        //     }
        //     return ans;
        // }


    }
    // for the fastreader
    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String next() {
            return nextString();
        }

        public String nextString() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = pread();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String[] nextStringArray(int n)
        {
            String array[]=new String[n];
            for(int i=0;i<n;i++)
            {
                array[i]=nextString();
            }
            return array;
        }
        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextLong();
            }
            return array;
        }

        // pcwallace
        public double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextDouble();
            }
            return array;
        }

        public long gcd(long a, long b) {
            return b == 0 ? a : gcd(b, a % b);
        }

        public int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        public long nextLong() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            double res = 0.0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}