Problem: Fox Ciel wants to write a task for a programming contest. The task is: "You are given a simple undirected graph with n vertexes. Each its edge has unit length. You should calculate the number of shortest paths between vertex 1 and vertex 2."

Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to k?

Input

The first line contains a single integer k (1 ≤ k ≤ 109).

Output

You should output a graph G with n vertexes (2 ≤ n ≤ 1000). There must be exactly k shortest paths between vertex 1 and vertex 2 of the graph.

The first line must contain an integer n. Then adjacency matrix G with n rows and n columns must follow. Each element of the matrix must be 'N' or 'Y'. If Gij is 'Y', then graph G has a edge connecting vertex i and vertex j. Consider the graph vertexes are numbered from 1 to n.

The graph must be undirected and simple: Gii = 'N' and Gij = Gji must hold. And there must be at least one path between vertex 1 and vertex 2. It's guaranteed that the answer exists. If there multiple correct answers, you can output any of them. 

Examples

Input

2

Output

4
NNYY
NNYY
YYNN
YYNN

Input

9

Output

8
NNYYYNNN
NNNNNYYY
YNNNNYYY
YNNNNYYY
YNNNNYYY
NYYYYNNN
NYYYYNNN
NYYYYNNN

Input

1

Output

2
NY
YN

Note

In first example, there are 2 shortest paths: 1-3-2 and 1-4-2.

In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main
{
	public static void main(String[] args) {
		new Thread(null, new Runnable() {
			public void run() {
                solve();
            }
        }, "1", 1 << 26).start();
	}
	static void solve () {
		FastReader fr =new FastReader();	PrintWriter op =new PrintWriter(System.out);
 
 		int K =fr.nextInt() ,i =1<<29 ,j =29 ,k ,sp ,n =2 ,l ;
 		ArrayList<ArrayList<Integer>> g =new ArrayList<>() ;
 		g.add(new ArrayList<>()) ;	g.add(new ArrayList<>()) ;

 		while ((K&i)==0) {
 			i >>= 1 ;	--j ;
 		}
 		sp =j ;

 		if (sp==0) {
 			g.get(0).add(1) ;	g.get(1).add(0) ;
 		}
 		else {
	 		g.add(new ArrayList<>()) ;	g.add(new ArrayList<>()) ;

			g.get(0).add(n) ;	g.get(n++).add(0) ;	g.get(0).add(n) ;	g.get(n++).add(0) ;

			for (k =2 ; k<=sp ; ++k) {
				g.add(new ArrayList<>()) ;	g.add(new ArrayList<>()) ;

				g.get(n-2).add(n) ;	g.get(n-1).add(n) ;	g.get(n).add(n-2) ;	g.get(n).add(n-1) ;
				g.get(n-2).add(n+1) ;	g.get(n-1).add(n+1) ;	g.get(n+1).add(n-2) ;	g.get(n+1).add(n-1) ;
				n +=2 ;
			}

			g.get(1).add(n-1) ;	g.get(1).add(n-2) ;
			g.get(n-1).add(1) ;	g.get(n-2).add(1) ;
		}

		for (--j ; j>0 ; --j) {
			i >>= 1 ;	if ((K&i)==0)	continue;	l =1 ;

			++l ;	g.add(new ArrayList<>()) ;
			g.get(n).add(0) ;	g.get(0).add(n) ;	++n ;

			for (k =sp-1 ; k>j ; --k) {
				++l ;	g.add(new ArrayList<>()) ;
				g.get(n).add(n-1) ;	g.get(n-1).add(n) ;	++n ;
			}

			g.get(n-1).add(2*l) ;	g.get(n-1).add(2*l+1) ;
			g.get(2*l).add(n-1) ;	g.get(2*l+1).add(n-1) ;
		}

		if (j==0 && (K&1)==1) {
			g.add(new ArrayList<>()) ;
			g.get(n).add(0) ;	g.get(0).add(n) ;	++n ;

			for (k =2 ; k<=sp ; ++k) {
				g.add(new ArrayList<>()) ;
				g.get(n).add(n-1) ;	g.get(n-1).add(n) ;	++n ;
			}

			g.get(n-1).add(1) ;	g.get(1).add(n-1) ;
		}

		boolean mrk[][] =new boolean[n][n] ;

 		for (i =0 ; i<n ; ++i) {
 			for (j =0 ; j<g.get(i).size() ; ++j)	mrk[i][g.get(i).get(j)] =true ;
 		}
 		op.println(n) ;
 		for (i =0 ; i<n ; ++i) {
 			for (j =0 ; j<n ; ++j) {
 				if (mrk[i][j])	op.print('Y') ;	else 	op.print('N') ;
 			}
 			op.println() ;
 		}
		op.flush();	op.close();
	}
	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;
		}

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

		long nextLong() {
			return Long.parseLong(next()) ;
		}
	}
}