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.io.BufferedOutputStream;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.OutputStream;
import java.util.ArrayList;

public class Main {
	
	private static FastReader fr;
    private static OutputStream out;
    
	private static class FastReader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public FastReader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public FastReader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[1024];
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
        
        public int[] nextIntArray(int n) throws IOException {
        	int arr[] = new int[n];
        	for(int i=0;i<n;i++){
        		arr[i] = nextInt();
        	}
        	return arr;
        }
    } 
 
	private static void print(Object str) {
        try {
            out.write(str.toString().getBytes());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
	
	private static void println(Object str) {
        try {
            out.write((str.toString() + "\n").getBytes());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
	
	private static void printArray(int arr[]){
		for(int val: arr){
			print(val + " ");
		}
	}
	
	public static void main(String args[]) throws IOException{
		run();
	}
	
	private static void run() throws IOException{
		fr = new FastReader();
		out = new BufferedOutputStream(System.out);
		solve();
		out.flush();
		out.close();
	}
	
	private static void solve() throws IOException{
		int t = fr.nextInt();
		while(t-- > 0){
			double d = fr.nextDouble();
			double x =0,y = 0;
			boolean b = true;
			double temp = (Math.pow(d, 2) - 4 * d);
			if(temp < 0){
				b = false;
			}
			if(b){
				temp = Math.sqrt(temp);
				x = (d + temp)/2;
				y = d - x;
				if(x < 0 || y < 0){
					x = (d - temp)/2;
					y = d - x;
				}
			}
			if(b){
				println("Y " + x + " " + y);
			}else{
				println("N");
			}
		}
	}
	
	private static int factorial(long n){
		int fac = 1;
		for(int i=2;i<=n;i++){
			fac *= i;
		}
		
		return fac;
	}
	
	private static boolean isPrime(long n){
		if(n == 0 || n == 1){
			return false;
		}else if(n == 2){
			return true;	
		}else if(n%2 == 0){
			return false;
		}else{
			int x = (int)(Math.sqrt(n)) + 1;
			for(int i=3;i<=x;i+=2){
				if(n % i == 0){
					return false;
				}
			}
			return true;
		}
	}
	
	private long pow(int base,int exp){
		if(exp == 0){
			return 1;
		}else if(exp == 1){
			return base;
		}else{
			long a = pow(base,exp/2);
			if(exp%2 == 0){
				return a * a;
			}else{
				return a * a * base;
			}
		}
		
	}

	private static int gcd(int a,int b){
		if(a == 0){
			return b;
		}
		
		return gcd(b%a,a);
	}
	
	private static int lcm(int a,int b){
		return (a * b)/gcd(a,b);
	}
	
	private static ArrayList<Integer> SieveOfEratosthenes(long n){
		boolean b[];
		if(n > 999999999){
			n = 999999998;
		}
		b = new boolean[(int)(n+1)];
		b[0] = true;
		b[1] = true;
		for(int i=2;i<=n;i++){
			int j = 2;
			while(i * j <= n && !b[i]){
				b[i * j] = true;
				j++;
			}
		}
		
		ArrayList<Integer> arr = new ArrayList<>();
		for(int i=2;i<n;i++){
			if(!b[i]){
				arr.add(i);
			}
		}
		
		return arr;
	}

}