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:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.util.Scanner;

/**
 *
 * @author sang
 */
public class MemeProblem {
    static double d;
    static Scanner in = new Scanner(System.in);
    static void inp(){
        d = in.nextDouble();
    }
    static void solve(){
        if( d < 4 && d != 0) System.out.println("N");
        else {
            double f = d*(d-4), x = (d+Math.sqrt(f))/2;
            System.out.printf("Y %.9f %.9f\n", x,d-x);
        }
    }
    public static void main(String[] args){
        int n = in.nextInt();
        while( n-- != 0){
            inp();
            solve(); 
        }
    }
}