Problem: Try guessing the statement from this picture: 

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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 ClassProjects;

import java.util.Scanner;
//import java.math.BigInteger;

public class Sample1 {
    
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		for(int i = 0 ; i < t ; i++){
		    int n = sc.nextInt();
		    double s = n * n - 4 * n;
		    if(s < 0){
		        System.out.println("N");
		        continue;
		    }
		    double ss = Math.sqrt(s);
		    double a = (ss + n) / 2;
		    double b = n - a;
		    System.out.print("Y ");
		    System.out.print(a);
		    System.out.print(" ");
		    System.out.print(b);
		    System.out.println();
		}
	}

	public static int abs(int x){
	    if(x < 0)
	        x = x * -1;
	    return x;
	}
	
	public static int min(int x , int y){
	    if(x < y)
	        return x;
	    return y;
	}
	
	public static int max(int x , int y){
	    if(x > y)
	       return x;
	    return y;
	}
}