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:
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.TreeSet;

public class Main{
	
	static PrintWriter pr;
	
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		pr = new PrintWriter(System.out);
		
		double eps = 1e-6;
		double eps2 = 1e-9;
		int n = sc.nextInt();
		while(n-->0){
			double d = sc.nextDouble();
			double zero = 0;
			if(d==0){
				pr.println("Y "+zero+" "+zero);
				continue;
			}
			double lo = 0.0;
			double hi = d*1.0;
			double ans = -1;
			while(Math.abs(hi-lo)>eps2){
				double mid = (hi+lo)/2;
				double second = d-mid;
				if(Math.abs(mid*second-d)<=eps){
					ans = mid;
					break;
				}else if(mid*second+eps>d){
					lo = mid;
				}else{
					hi = mid;
				}
			}
			
			if(ans==-1){
				pr.println("N");
			}else
				pr.println("Y "+ ans+" "+(d-ans));
		}
		pr.close();
	}
	
	
}