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:

import java.util.Scanner;

public class Main {

	
	public static void main(String [] args) {
		int t=0;
		Scanner sc=new Scanner(System.in);
		t=sc.nextInt();
		for(int i=0;i<t;i++) {
			double d=(double)sc.nextInt();
			if(d==1) {System.out.println("N");continue;}
			double a=0,b=0;
			int ff=1;
			double r=d,l=0,m=0;
			while(Math.abs(a*b-d)>Math.pow(10,-6)) {
				if(Math.abs(m-(r+l)/2)<Math.pow(10, -12)) {ff=0;System.out.println("N");break;}
				m=(r+l)/2;
				a=(d+m)/2;
				b=(d-m)/2;
				if(a*b>d) {
					l=m;
				}else {
					r=m;
				}
			}
			if(ff==1)
			System.out.println("Y "+a+" "+b);
		}
	}
	
}