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.math.BigInteger;
 public class Solution
{
     static class Pair<A,B>
     {
        A parent;
        B rank;
        Pair(A parent,B rank)
        {
            this.rank=rank;
            this.parent=parent;
        }
    }
     static class Node{
         int left;
         int right;
         Node(int l,int r)
         {
             left=l;
             right=r;
         }
     }
     static int m=1000000007;
    public static void main (String[] args) throws IOException
    {
        StringBuilder sb = new StringBuilder();
        FastReader s1 = new FastReader();
        int t=s1.I();
        while(t--!=0)
        {
            int n=4*s1.I();
            double ansgle=Math.toRadians(((double)360)/n);
            double ans=Math.tan(ansgle);
            ans=(1/ans);
            sb.append(ans+"\n");
        }
        System.out.println(sb);
    }
       static long computeXOR(long n) 
    {
        if (n % 4 == 0) 
            return n;
        if (n % 4 == 1) 
            return 1; 
        if (n % 4 == 2) 
            return n + 1;
        return 0; 
    }
    static ArrayList<Integer> primeFactor(int n)
    {
        ArrayList<Integer> ans = new ArrayList<>();
        if(n%2==0)
            ans.add(2);
        while (n%2==0)
        {   
            n /= 2;
        }
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            if(n%i==0)
                ans.add(i);
            while (n%i == 0)
            {
                n /= i;
            }
        }
        if (n > 2)
            ans.add(n);
        return ans;
    }
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader()
        {
            br = new BufferedReader(new
                             InputStreamReader(System.in));
        }
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int I()
        {
            return Integer.parseInt(next());
        }
        
        long L()
        {
            return Long.parseLong(next());
        }
        
        double D()
        {
            return Double.parseDouble(next());
        }
        
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    static long gcd(long a,long b)
    {
        if(a%b==0)
            return b;
        return gcd(b,a%b);
    }
    static float power(float x, int y)
    {
        float temp;
        if( y == 0)
            return 1;
        temp = power(x, y/2);
        
        if (y%2 == 0)
            return temp*temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    }
    static long pow(long x, long y)
    {
        int p =  1000000007;
        long res = 1;
        x = x % p;
        if(x<0)
            x+=p;
        while (y > 0)
        {
            if((y & 1)==1){
                res = (res * x) % p;
                if(res<0)
                    res+=p;
            }
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }
    static void sieveOfEratosthenes(int n)
    {
        ArrayList<Integer> prime=new ArrayList<Integer>();
        boolean Prime[] = new boolean[n+1];
        for(int i=2;i<n;i++)
            Prime[i] = true;
        
        for(int p = 2; p*p <=n; p++)
        {
            if(Prime[p] == true)
            {
                prime.add(p);
                for(int i = p*p; i <= n; i += p)
                    Prime[i] = false;
            }
        }
    }
}