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.*;
public class Main {
	public static void main (String[] args){
	    Scanner sc = new Scanner(System.in);
	    int t = sc.nextInt();
	    for(int tt = 0; tt < t; ++tt){
	        double d = sc.nextDouble();
	        double b = (d + Math.sqrt((d * d) - 4 * 1 * d)) / (2 * 1);
	        double b1 = (d - Math.sqrt((d * d) - 4 * 1 * d)) / (2 * 1);
	        if(b < 0) b = b1;
	        double a = d - b;
	        if(Math.abs(a * b - d) <= Math.pow(10, -6)){
	            System.out.println("Y " + a + " " + b);
	        }
	        else{
	            System.out.println("N");
	        }
	    }
	}
}