Problem: Try guessing the statement from this picture: 

<image>

You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.

Input

The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.

Each test case contains one integer d (0 ≤ d ≤ 10^3).

Output

For each test print one line.

If there is an answer for the i-th test, print "Y", and then the numbers a and b.

If there is no answer for the i-th test, print "N".

Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.

Example

Input


7
69
0
1
4
5
999
1000


Output


Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005

Solution (in JAVA):

Solution:
// package com.company.EdCodRound54;

import java.io.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class ProbC {
    public static void main (String[] args){
        FastReader fr =  new FastReader();

        int c = fr.nextInt();
        for (int i = 0; i < c ;  i++){
            double d = (double) fr.nextInt();
            double inroot = Math.pow(d, 2.0d) - 4.0d * d;
            if (d == 0.0){
                System.out.println("Y 0.000000000 0.000000000");
                continue;
            }

            if (inroot < 0){
                System.out.println("N");
                continue;
            }

            double b1 = (- d + Math.sqrt(inroot)) / (-2);
            double b2 = (- d - Math.sqrt(inroot)) / (-2);

            if (b1 > 0 && b1 < d){
                double a = d - b1;
                System.out.println("Y " + b1 +" "+ a);
            } else if (b2 > 0 && b2 < d){
                double a = d - b2;
                System.out.println("Y " + b2 +" "+ a);
            } else {
                System.out.println("N");
            }

        }


    }


    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String path) {
            try {
                br = new BufferedReader(new FileReader(path));
            } catch (FileNotFoundException e){
                e.printStackTrace();
            }
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }



}