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.io.*;
import java.lang.*;

public class Main {

    static int[] primes;

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

        int t = sc.nextInt();
        for (int a = 1; a <= t; a++) {
            int d = sc.nextInt();
            if (d < 4 && d > 0) {System.out.println("N"); continue;}
            double x1 = Math.sqrt(d * d - 4 * d);
            double sol1 = (x1 + d) / 2;
            double sol2 = ((x1 - d) / 2) * (-1);
            System.out.println(String.format("Y %.9f %.9f", sol1, sol2));
        }
    }
}