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 Main
{

    public static void process()throws IOException
    {
        int d=ni();
        double a=-1,b=-1;
        double x1,x2;

        double D=d*d-4.0d*d;
        D=Math.sqrt(D);

        x1=d+D;
        x1/=2.0d;

        x2=d-D;
        x2/=2.0d;

        if(x1>=0){
        	double a_=d-x1,b_=x1;

        	if(Math.abs(a_*b_ - d)<=Math.pow(10, -6) && a_>=0){
        		pn("Y "+a_+" "+b_);
        		return;
        	}
        }

        if(x2>=0){
        	double a_=d-x2,b_=x2;
        	if(Math.abs(a_*b_ - d)<=Math.pow(10, -6) && a_>=0){
        		pn("Y "+a_+" "+b_);
        		return;
        	}
        }

        pn("N");
    }


    static FastReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new FastReader();

        long s = System.currentTimeMillis();
        int t=1;
        t=ni();
        while(t-->0)
            process();

        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }
    
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return Integer.parseInt(sc.next());}
    static long nl()throws IOException{return Long.parseLong(sc.next());}
    static double nd()throws IOException{return Double.parseDouble(sc.next());}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;
    static long mod=(long)1e9+7l;

    static<T> void r_sort(T arr[],int n){
        Random r = new Random(); 
        for (int i = n-1; i > 0; i--){ 
            int j = r.nextInt(i+1); 
                  
            T temp = arr[i]; 
            arr[i] = arr[j]; 
            arr[j] = temp; 
        } 
        Arrays.sort(arr); 
    }
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static 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(); 
        } 
  
        String nextLine() { 
            String str = ""; 
            try{ 
                str = br.readLine(); 
            } 
            catch (IOException e) { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}