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:
//package ;
import java.io.*;
import java.util.*;

public class C
{
	public static void main(String[] args) throws IOException 
	{
		Scanner sc = new Scanner();
		PrintWriter pw = new PrintWriter(System.out);
		int t=sc.nextInt();
		big:while(t-->0)
		{
			int d=sc.nextInt();
			if(d==1)
			{	
				pw.println("N");
				continue;
			}
			if(d==0)
			{
				pw.println("Y 0 0");
				continue;
			}
			if(d==4)
			{
				pw.println("Y 2 2");
				continue;
			}
//			if(d==2)
//			{
//				pw.println("Y 1 1");
//				continue;
//			}
			double low=1,hi=d;
			for(int i=0;i<100;i++)
			{
				double mid=(low+hi)/2.0;
				double a=d/mid;
				if((a+mid) -(a*mid)<= 1e-6 && (a+mid) -d <=1e-6 && (a+mid) -d>0 )
				{
					pw.println("Y "+a+" "+mid);
					continue big;
				}
				else
				{
					if(mid+a < d)
						hi=mid;
					else
						low=mid;
				}
			}
			pw.println("N");
		}
		pw.close();    
	}
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;
		
		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		String next() throws IOException {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return st.nextToken();
		}
		
		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		
		long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		
		double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		String nextLine() throws IOException {
			return br.readLine();
		}
		boolean hasnext() throws IOException{
			return br.ready();
		}
		
	}
}