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:
//Code by Sounak, IIEST
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.Arrays;
 
public class Test2{
    public static void main(String args[])throws IOException{
        FastReader sc = new FastReader();
        int test=sc.nextInt();
        while(--test>=0)
        {
            double d=sc.nextDouble();
            double a=0,b=0;
            if(d>0 && d<4)
            System.out.println("N");
            else
            {
                double dis=Math.sqrt(d*d-4*d);
                a=(d+dis)/2.0;
                b=(d-dis)/2.0;
                System.out.println("Y "+a+" "+b);
            }
            //System.out.println(count);
        }
    }
    public static long gcd(long a, long b) 
    { 
        if (a == 0) 
            return b; 
          
        return gcd(b%a, a); 
    }
}

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 (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    int nextInt() { return Integer.parseInt(next()); }
    long nextLong() { return Long.parseLong(next()); }
    double nextDouble() { return Double.parseDouble(next()); }
    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}