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:
//package CodeForces.C;

import java.util.Scanner;

public class Task1076C {
    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        int t = scn.nextInt();
        for(int i = 0; i<t; i++){
            int x = scn.nextInt();
            if(x>0 && x<4){
                System.out.println("N");
                continue;
            }
            double l = 0;
            double r = x;
            while (Math.abs(l*(x-l)-x)>0.0000001){
                double m = (r+l)/2;
                double b = x-m;
                if(m*b>=x){
                    l=m;
                }
                else{
                    r=m;
                }
            }
            System.out.println("Y "+l+" "+(x-l));
        }
    }
}