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.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;

public class Main{
    public static void main(String[] args)throws IOException{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	PrintWriter out = new PrintWriter(System.out);
	int c = Integer.parseInt(br.readLine());
	while(c-->0){
	    double a = Double.parseDouble(br.readLine());
	    double t = (a-Math.sqrt(a*a-4*a))/2.0;
	    double y = (a+Math.sqrt(a*a-4*a))/2.0;
	    if(t>=0 && y>=0){
		out.println("Y "+t+" "+y);
	    }else{
		out.println("N");
	    }
	}
	out.close();
    }
}