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.BigInteger;
import java.util.*;
public class Makise {
	static PrintWriter out=new PrintWriter(System.out);
	public static void main(String[] args) throws Exception{
		Scanner sc=new Scanner(System.in);
		int tc=sc.nextInt();
		while(tc-->0) {
			int d=sc.nextInt();
			double dis=d*d-4*d;
			if (dis<0) {
				out.println("N");
			}
			else {
				out.print("Y ");
				double one=(d+Math.sqrt(dis))/2.0;
				double two=(d-Math.sqrt(dis))/2.0;

				out.println(one+" "+two);

			}
		}



		out.flush();
	}

	static class UnionFind {                                              
		int[] p, rank, setSize;
		int numSets;

		public UnionFind(int N) 
		{
			p = new int[numSets = N];
			rank = new int[N];
			setSize = new int[N];
			for (int i = 0; i < N; i++) {  p[i] = i; setSize[i] = 1; }
		}

		public int findSet(int i) { return p[i] == i ? i : (p[i] = findSet(p[i])); }

		public boolean isSameSet(int i, int j) { return findSet(i) == findSet(j); }

		public void unionSet(int i, int j) 
		{ 
			if (isSameSet(i, j)) 
				return;
			numSets--; 
			int x = findSet(i), y = findSet(j);
			if(rank[x] > rank[y]) { p[y] = x; setSize[x] += setSize[y]; }
			else
			{	p[x] = y; setSize[y] += setSize[x];
			if(rank[x] == rank[y]) rank[y]++; 
			} 
		}

		public int numDisjointSets() { return numSets; }

		public int sizeOfSet(int i) { return setSize[findSet(i)]; }
	}

	static class Scanner{
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream system) { br = new BufferedReader(new InputStreamReader(system));}
		public Scanner(String file) throws Exception{br = new BufferedReader(new FileReader (file));}
		public String next() throws IOException{
			while (st==null|| !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException{
			return Integer.parseInt(next());
		}
		public long nextLong() throws IOException{
			return Long.parseLong(next());
		}
		public String nextLine() throws IOException{
			return br.readLine();
		}
		public Double nextDouble() throws IOException{
			return Double.parseDouble(next());
		}

	}
}