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.math.*;
import java.util.*;

public class practice {

    // Faster Input...
    static class Reader{
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[100000]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

    public static void debug(int[] ...var) {
        for(int[] row : var) {
            debug(row);
        }
    }

    public static void debug(long[] ...var) {
        for(long[] row : var) {
            debug(row);
        }
    }

    public static void debug(String[] ...var) {
        for(String[] row : var) {
            debug(row);
        }
    }

    public static void debug(double[] ...var) {
        for(double[] row : var) {
            debug(row);
        }
    }

    public static void debug(int ...var) {
        for(int i:var)  System.err.print(i+" ");
        System.err.println();
    }
    public static void debug(String ...var) {
        for(String i:var)  System.err.print(i+" ");
        System.err.println();
    }
    public static void debug(double ...var) {
        for(double i:var)  System.err.print(i+" ");
        System.err.println();
    }
    
    public static void debug(long ...var) {
        for(long i:var)  System.err.print(i+" ");
        System.err.println();
    }

    /*
    public static <T> void debug(T ...varargs) {
        // Warning
        // Heap Pollution might occur
        // this overrides even 1d and 2d array methods as it is an object... 
        // + i am not using object based array like Integer[]
        // I am using int[] so that is a problem as i need Wrapper class as an argument
        for(T val:varargs)  System.err.printf("%s ",val);
        System.err.println();
    }
    */


    private static Reader scan = new Reader();
    
    public static void main(String args[]) throws Exception{
        //Faster Output...
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        //StringBuilder sb = new StringBuilder();

        //be careful of readLine() -- length of string;

        //Scanner scan = new Scanner(System.in);
        //scan.useDelimiter("");  // for reading character by character

        // 1 4 3 2 3 1 2
        // 1 2 3 2 1
        // 3 4 1 2 1 2 
        // 3 2 1 4 1
        // 1 2 3 4

        int t = scan.nextInt();
        while(t-->0) {
            int n = scan.nextInt();
            double tan = Math.tan(Math.PI/(n+n));
            double cot = 1/tan;
            out.println(cot);
        }

        scan.close();
        out.close();
    }
}