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.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;


public class CodeForce {

static boolean flag=false;
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuilder sb = new StringBuilder();
		int t=Integer.parseInt(br.readLine());
		while(t-->0)
		{
		String[] sr=br.readLine().split(" ");
		
	double n=Double.parseDouble(sr[0]);
	

			
		if((Math.pow(n, 2)-4*n)<0)	
			{System.out.println("N");continue;}
	double a=n+Math.sqrt(Math.pow(n, 2)-4*n);
	a=a/2;
	System.out.println("Y "+a+" " +(n-a));
			
	}}
			
			
	
}