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.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.Stack;

public class CF {
	
	private static Scanner sc = new Scanner(System.in);
	
	public static void main(String[] args){
		int t = sc.nextInt();
		StringBuilder ret = new StringBuilder();
		while(t-- > 0) {
			double d = sc.nextDouble();
			if(d*d - 4*d >= 0) {
				double temp = (double)Math.sqrt(d*d - 4*d);
				double a = (d + temp)/2;
				double b = (temp - d)/2;
				ret.append("Y " + a + " " + Math.abs(b) + "\n");
			} else ret.append("N\n");
		}
		System.out.println(ret);
	}
	
	private static int[] input(int n) {
		sc.nextLine();
		String in = sc.nextLine();
		String[] temp = in.trim().split(" ");
		int[] a = new int[n];
		for(int i = 0; i < n; i++) a[i] = Integer.valueOf(temp[i]);
		return a;
	}
	
	private static long sum(int[] a) {
		long sum = 0;
		for(int aa:a) sum += aa;
		return sum;
	}

}