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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int T = sc.nextInt();
		for(int t = 0; t<T; t++){
		    int n = sc.nextInt();
		    double x_1 =-1, x_2 = -1;
		    if(n*n - 4 * n < 0)out.println("N");
		    else{
		        x_1 = (n + Math.sqrt(n*n - 4*n)) / 2;
		        x_2 = (n - Math.sqrt(n*n - 4*n)) / 2;
		        double y_1 = n - x_1;
		        double y_2 = n - x_2;
		        if(x_1 >= 0 && y_1 >= 0)out.println("Y " + x_1 + " " + y_1);
		        else if(x_2 >= 0 && y_2 >= 0)out.println("Y " + x_2 + " " + y_2);
		    }
		    out.flush();
		}
	}
}