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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.Comparator;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}
}

class Task {
	
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        
    	int K = in.nextInt();
    	int len=0;
    	while((1<<len)<=K) len++;
    	len--;
    	boolean[][] a = new boolean[1005][1005];
    	int n=2;
    	int[][] d = new int[1005][3];
    	for(int i=1;i<=len;i++) 
    		for(int j=0;j<3;j++) d[i][j]=++n;
    	for(int i=0;i<3;i++) {
    		int x=1,y=d[1][i];
    		a[x][y]=a[y][x]=true;
    	}
    	for(int i=1;i<3;i++) {
    		int x=2,y=d[len][i];
    		a[x][y]=a[y][x]=true;
    	}
    	for(int i=1;i<len;i++) {
    		int x=d[i][0],y=d[i+1][0];
    		a[x][y]=a[y][x]=true;
    		for(int j=1;j<3;j++) {
    			x=d[i][j];
    			for(int k=1;k<3;k++) {
    				y=d[i+1][k];
    				a[x][y]=a[y][x]=true;
    			}
    		}
    	}
    	d[0][0]=1; d[len+1][1]=2;
    	for(int i=0;i<=len;i++) if((K&(1<<i))!=0) {
    		int x=d[len-i][0],y=d[len+1-i][1];
    		a[x][y]=a[y][x]=true;
    		y=d[len+1-i][2];
    		a[x][y]=a[y][x]=true;
    	}
    	out.println(n);
    	for(int i=1;i<=n;i++)
    	{
    		for(int j=1;j<=n;j++) out.print(a[i][j]?"Y":"N");
    		out.println();
    	}
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
    
    public long nextLong() {
    	return Long.parseLong(next());
    }
    
    public double nextDoubel() {
    	return Double.parseDouble(next());
    }
}