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:
import java.util.*;
public class MemeProblem {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int T = scanner.nextInt();
        final double EPS = 1e-7;
        StringBuilder stringBuilder = new StringBuilder();
        while(T-->0) {
            double D = scanner.nextInt();
            if (D == 0) {
                stringBuilder.append("Y ").append(0).append(" ").append(0).append("\n");
                continue;
            }
            if (D < 4) {
                stringBuilder.append("N\n");
                continue;
            }
            double lo = 0;
            double hi = D;
            int c = 0;
            while(lo < hi && c < 60) {
                double mid = (lo+hi)/2;
                if (Math.abs(mid + (D/mid) - D) < EPS) {
                    hi = mid;
                    break;
                }
                if (mid + (D/mid) < D) lo = mid;
                else hi = mid;
                c++;
            }
            stringBuilder.append("Y ").append(D/hi).append(" ").append(hi).append("\n");
        }
        System.out.println(stringBuilder.toString());
    }
}