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:
// package CF1076;

import java.util.Scanner;

public class CF1076C {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);

        int t = s.nextInt();
        StringBuilder ans = new StringBuilder();
        while(t-- > 0){
            int d = s.nextInt();
            double ans1 = func(d);
            if(ans1 == Double.MAX_VALUE ){
                ans.append("N\n");
            }else{
                double ans2 = d - ans1;
                ans.append("Y" + " " +ans1 + " " + ans2 + "\n");
            }

        }
        System.out.println(ans);
    }

    public static double func(double b) {

        b *= -1;
        double a = 1.0, c = -1*b;
        double root1, root2;

        double determinant = b * b - 4 * a * c;

        // condition for real and different roots
        if(determinant > 0) {
            root1 = (-b + Math.sqrt(determinant)) / (2 * a);
            root2 = (-b - Math.sqrt(determinant)) / (2 * a);

//            System.out.format("root1 = %.2f and root2 = %.2f", root1 , root2);
            return root1;
        }
        // Condition for real and equal roots
        else if(determinant == 0) {
            root1 = -b / (2 * a);

            return root1;
        }
        // If roots are not real
        else {
            return Double.MAX_VALUE;
        }
    }


}