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.util.*;
import java.math.*;
import java.io.*;
public class Solution{
   
   
    
   
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int z=0;z<t;z++){
            double d = sc.nextDouble();
            double b1 = -1,b2 = -1;
            if(d==0){
                System.out.println("Y 0 0");
                continue;
            }
            double delta = d*d - 4*d;
            if(delta>0){
                b1 = (-d + Math.sqrt(delta))/(-2.0);
                b2 = (-d - Math.sqrt(delta))/(-2.0);
            }else if(delta==0){
                b1 = (-d)/(-2.0);
            }
            double a1=-1,a2=-1;
            if(b1>=0) a1 = d - b1;
            if(b2>=0) a2 = d - b2;
            if(a1>=0 && b1>=0) System.out.println("Y "+a1+" "+b1);
            else if(a2>=0 && b2>=0) System.out.println("Y "+a2+" "+b2);
            else{
                System.out.println("N");
            } 
        }
    }
    
}