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:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */


import java.util.Scanner;

/**
 *
 * @author Vessi
 */
public class ACM_TEST {

    final int N = 1 << 15;
    int[][] f = new int[N + 1][5];

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        new ACM_TEST().run();
    }

   

    void run() {

        
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        
        for(int i = 0; i < t; i++){
            double d = in.nextDouble();
            double delta = d * d - 4 * d;
            if (delta < 0){
                System.out.println("N");
            }else{
                double x1, x2;
                x1 = d + Math.sqrt(delta);
                x2 = d - Math.sqrt(delta);
                x1/=2; x2/=2;
                System.out.println("Y " + x1 + " " + x2);
            }
        }
       
    }
}