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

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	PrintWriter out = new PrintWriter(System.out);
	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tok = new StringTokenizer("");
    String next() throws IOException {
        if (!tok.hasMoreTokens()) { tok = new StringTokenizer(in.readLine()); }
        return tok.nextToken();
    }
    int ni() throws IOException { return Integer.parseInt(next()); }
    long nl() throws IOException { return Long.parseLong(next()); }
    
    void solve() throws IOException {
        int T=ni();
        for (int t=0;t<T;t++) {
            int a=ni();
            if (a==0) {System.out.println("Y 0.0 0.0"); continue; }
            if (a<4) {System.out.println("N"); continue; }
            if (a==4) {System.out.println("Y 2.0 2.0"); continue; }
            
            double b=a;
            double l=1.0;
            double r=1.4;
            double av=0.0;
            while (true) {
                av=(l+r)/2;
                if (Math.abs(b-(b-av)*av)>0.0000001) {
                    if ((b-av)*av>b) r=av;
                    else l=av;
                }
                else break;
            }
            System.out.println("Y "+(b-av)+" "+av);
        }
    }
    
    public static void main(String[] args) throws IOException {
        new Main().solve();
    }
}