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.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Meme_Problem {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {

                    e.printStackTrace();
                }

            }
            return st.nextToken();
        }

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return str;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
    public static void main(String[] args) {
       FastReader in = new FastReader();
       int t = in.nextInt();
       while(t-- > 0){
           int d = in.nextInt();

           if(d == 0){
               System.out.println("Y"+" "+d+" "+d);
           }else if(d < 4){
               System.out.println("N");
           }else{
               double D = Math.sqrt(d*(d - 4));
               double a = (d + D)/2.0d;
               double b = (d - D)/2.0d;
               System.out.println("Y"+" "+a+" "+b);
           }
       }
    }
}