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.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;
 
public class B {
	static DecimalFormat df = new DecimalFormat("0.000000000"); 
	public static void main(String[] args) throws IOException {
		try {
		BufferInput in = new BufferInput();
		int t = in.nextInt();
		StringBuilder sb = new StringBuilder();
		while(t-->0) {
			double d = in.nextDouble();
			if(d==1||d==2||d==3) {
				sb.append("N").append("\n");
				continue;
			}
			double a = (d+ Math.sqrt(d*d-4*d))/2;
			double b = (d- Math.sqrt(d*d-4*d))/2;
			sb.append("Y ").append(df.format(a)).append(" ").append(df.format(b)).append("\n");
		}
		System.out.print(sb);
		}catch(Exception e) {}
	}
	static void revOrder(int[] arr) {
		for(int i=0;i<arr.length;i++) {
			int t = arr[0];
			arr[0] = arr[arr.length-i-1];
			arr[arr.length-i-1] = t;
		}
	}
static class BufferInput {
		final private int BUFFER_SIZE = 1 << 16;
		
		private DataInputStream din;
		
		private byte[] buffer;
		
		private int bufferPointer, bytesRead;
		
		public BufferInput() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
 
		public BufferInput(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}
 
		/**
		 * Reads the input bytes until it encounters a new line char.
		 * @return
		 * @throws IOException
		 */
		public String readLine() throws IOException {
			byte[] buf = new byte[64];
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}
		
		/**
		 * 
		 * @return
		 * @throws IOException
		 */
		public String nextString() throws IOException{
			
			// Skip all whitespace characters from the stream
			byte c = read();
			while(Character.isWhitespace(c)){
				c = read();
			}
			
			StringBuilder builder = new StringBuilder();
			builder.append((char)c);
			c = read();
			while(!Character.isWhitespace(c)){
				builder.append((char)c);
				c = read();
			}
			
			return builder.toString();
		}
			
		/**
		 * Reads an integer value.
		 * @return
		 * @throws IOException
		 */
		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;
		}
		
 
		/**
		 * Reads an array of integers.
		 * @return
		 * @throws IOException
		 */
		public int[] nextIntArray(int n) throws IOException {
			int arr[] = new int[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextInt();
			}
			return arr;
		}
 
 
		/**
		 * Reads a long value.
		 * @return
		 * @throws IOException
		 */
		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;
		}
		
		
		/**
		 * Reads an array of long integers.
		 * @return
		 * @throws IOException
		 */
		public long[] nextLongArray(int n) throws IOException {
			long arr[] = new long[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextLong();
			}
			return arr;
		}
		
		/**
		 * 
		 * @return
		 * @throws IOException
		 */
		public char nextChar() throws IOException{
			byte c = read();
			while(Character.isWhitespace(c)){
				c = read();
			}
			return (char) c;	
		}
		
 
		/**
		 * Reads a double value.
		 * @return
		 * @throws IOException
		 */
		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;
		}
 
		/**
		 * Reads an array of double values.
		 * @return
		 * @throws IOException
		 */
		public double[] nextDoubleArray(int n) throws IOException {
			double arr[] = new double[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextDouble();
			}
			return arr;
		}
		
		/**
		 * Fills the buffer from input stream.
		 * 
		 * @throws IOException
		 */
		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
 
		/**
		 * 
		 * @return
		 * @throws IOException
		 */
		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}
 
		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}
 
}