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.io.*;
import java.util.*;

public class Main {
    public void solve()
    {
        int t = nextInt();
        double a, b, D;
        int d;
        for (int i = 0; i < t; i++)
        {
            d = nextInt();
            D = d*d - 4*d;
            if (D < 0)
            {
                System.out.println("N");
                continue;
            } else {
                D = Math.sqrt(D);
                if (d*(-1) + D / (-2) > 0)
                {
                    b = (d*(-1) + D) / (-2);
                } else {
                    b = (d*(-1) - D) / (-2);
                }
                System.out.print("Y ");
                System.out.print(d - b);
                System.out.print(" ");
                System.out.println (b);
            }
        }
    }
    public static void main (String[]args){
        new Main().run();
    }

    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

    private void run () {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            //br = new BufferedReader(new FileReader("birthday.in"));
            //out = new PrintWriter(new FileWriter("birthday.out"));
            solve();
            br.close();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    private int nextInt () {
        return Integer.parseInt(next());
    }

    private String next () {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
                return "END_OF_FILE";
            }
        }
        return st.nextToken();
    }
}