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.*;

public class Solution {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for (int i = 0; i < n; i++) {

            int d = sc.nextInt();
            if(d==0.0d) {
                System.out.println("Y 0.0 0.0");
                continue;
            }
            double[] ret = solve(d);
            if(ret==null)
                System.out.println("N");
            else
                System.out.println("Y "+ret[0]+" "+ret[1]);
        }
    }

    static double[] solve(int d) {
        if(d<4) return null;
        double b = (d+Math.sqrt(d*d-4*d))/2.0d;
        double a = d/b;
        if(a<b) {
            double tmp = a;
            a = b;
            b =tmp;
        }
        return new double[]{a, b};
    }
}