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.util.*;
import java.io.*;
import java.math.*;
public class loser
{
    static class InputReader {
        public BufferedReader br;
        public StringTokenizer token;
        public InputReader(InputStream stream)
        {
            br=new BufferedReader(new InputStreamReader(stream),32768);
            token=null;
        }

        public String next()
        {
            while(token==null || !token.hasMoreTokens())
            {
                try
                {
                    token=new StringTokenizer(br.readLine());
                }
                catch(IOException e)
                {
                    throw new RuntimeException(e);
                }
            }
            return token.nextToken();
        }

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

        public long nextLong()
        {
            return Long.parseLong(next());
        }
    }
    static class card{
        String s;
        int l;
        public card(String s,int i)
        {
            this.s=s;
            this.l=i;
        }
    }
    static class sort implements Comparator<card>
    {
        public int compare(card o1,card o2)
        {
            if(o1.l!=o2.l)
                return (o1.l-o2.l);
            else
                return o1.s.compareTo(o2.s);
        }
    }
    static void shuffle(int a[])
    {
        List<Integer> l=new ArrayList<>();
        for(int i=0;i<a.length;i++)
            l.add(a[i]);
        Collections.shuffle(l);
        for(int i=0;i<a.length;i++)
            a[i]=l.get(i);
    }

    /*static long gcd(long a,long b)
    {
    if(b==0)
    return a;
    else
    return gcd(b,a%b);
    }
    static boolean valid(int i,int j,int r,int c)
    {
    if(i<r && i>=0 && j<c && j>=0)
    return true;
    else
    return false;
    }*/
    static class Pair
    {
        int a;int b;
        public Pair(int a,int b)
        {
            this.a =a;
            this.b =b;
        }
    }
    public  static void main(String[] args) 
    {
        InputReader sc=new InputReader(System.in);
        int t=sc.nextInt();
        while(t>0)
        {
            int d=sc.nextInt();
            if(d==1 || d==2 || d==3)
            {
                System.out.println("N");
            }
            else if(d==0)
            System.out.println("Y"+" "+"0.00000000"+" "+"0.00000000");
            else
            {
                double b=(d+Math.sqrt((d*d)-(4*d)))/2d;
                double a=d/b;
                System.out.println("Y"+" "+b+" "+a);
            }
            t--;
        }
    }
}