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.lang.reflect.Array;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Solution {
    
    private static final Scanner sc = new Scanner(System.in);

    public static void main(String[] args) throws IOException {
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        //StringTokenizer st = new StringTokenizer(br.readLine());
        int t = sc.nextInt();
        for (int tt= 0; tt<t; ++tt){
            int d = sc.nextInt();
            if (d*d < 4*d){
                System.out.println("N");
                continue;
            }
            System.out.print("Y ");
            double a = (d + Math.sqrt(d*d-4*d))/2;
            double b = (d - Math.sqrt(d*d-4*d))/2;
            System.out.println(a+" "+b);
        }
        sc.close();
        br.close();
        bw.close();
    }
    
}