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.io.BufferedReader;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.util.*;

public class C {

    private void work() {
        Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = sc.nextInt();
        while (n-- > 0) {
            int d = sc.nextInt();

            if (d == 0) {
                System.out.println("Y 0 0");
                continue;
            }

            if (d == 1) {
                System.out.println("N");
                continue;
            }

            BigDecimal D = BigDecimal.valueOf(d);
            BigDecimal TWO = BigDecimal.valueOf(2);

            BigDecimal lo = BigDecimal.ZERO;
            BigDecimal hi = D.divide(TWO, 25, BigDecimal.ROUND_HALF_DOWN);

            for (int step = 0; step < 200; step++) {
                BigDecimal a = lo.add(hi).divide(BigDecimal.valueOf(2), 25, BigDecimal.ROUND_HALF_DOWN);
                BigDecimal b = D.subtract(a);
                BigDecimal m = a.multiply(b);
                if (m.compareTo(D) < 0) lo = a;
                else hi = a;
            }

            double a = lo.doubleValue();
            double b = D.subtract(lo).doubleValue();

            if (Math.abs(a * b - d) >= 1e-8) {
                System.out.println("N");
            } else {
                System.out.printf("Y %.9f %.9f\n", b, a);
            }
        }

        sc.close();
    }

    public static void main(String[] args) {
        new C().work();
    }
}