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.util.*;
import java.io.*;

public class Main {

	BufferedReader in;
	StringTokenizer str = null;
	PrintWriter out;
	
	private String next() throws Exception{
		if (str == null || !str.hasMoreElements())
			str = new StringTokenizer(in.readLine());
		return str.nextToken();
	}
	
	private int nextInt() throws Exception{
		return Integer.parseInt(next());
	}
	
	private long nextLong() throws Exception{
		return Long.parseLong(next());
	}
	
	private double nextDouble() throws Exception{
		return Double.parseDouble(next());
	}

	int [][]g;
	
	public void run() throws Exception{
		in =  new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);

		int k = nextInt();
		int n = 1000;
		List<Integer> layer = new ArrayList<Integer>();
		int []d = new int[n];	
		d[0] = d[2] = d[3] = 1;

		g = new int[n][n];

		g[0][2] = g[0][3] = g[2][0] = g[3][0] = 1;
		layer.add(2);layer.add(3);
		int last = 3;
		while(true) {
			List<Integer> next = new ArrayList<Integer>();
			for(int i=0;i<layer.size();i++){
				int x = layer.get(i);
				g[x][last + i + 1] = 1;
				g[last + i + 1][x] = 1;
				d[last + i + 1]+=d[x];
				next.add(last + i + 1);
			}
			last+=layer.size() + 1;
			next.add(last);
			for(int i=0;i<layer.size();i++){
				int x = layer.get(i);
				g[x][last] = g[last][x] = 1;
				d[last]+=d[x];
			}

			layer = next;
			if (d[last] >= k) break;
		}

		while(k > 0) {
			if (d[last] <= k) {
				k-=d[last];
				g[last][1] = g[1][last] = 1;
			}
			last--;
		}

		// System.out.println(Arrays.toString(d));

		out.println(n);
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				if (g[i][j] == 1) {
					out.print("Y");
				}else {
					out.print("N");
				}
			}
			out.println();
		}
		out.close();
	}

	public static void main(String[] args) throws Exception{
		new Main().run();
	}
}