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.*;
import java.math.BigInteger;
import java.util.*;
import java.util.Map.Entry;

public class Main {
	public static void main(String[] args) throws IOException {
		(new Main()).solve();
	}

	public Main() {
	}
	
	MyReader in = new MyReader();
	PrintWriter out = new PrintWriter(System.out);
	
	void solve() throws IOException {
		//BufferedReader in = new BufferedReader(new
		//InputStreamReader(System.in));
		//Scanner in = new Scanner(System.in);
		//Scanner in = new Scanner(new FileReader("input.txt"));
		int k = in.nextInt();
		int n = 29;
		int d = 0;
		boolean[][] a = new boolean[1000][1000];
		while (k > 0) {
			int t = k % 2;
			if (t == 1) {
				int i1 = 0, i2 = 0;
				for (int i = 0; i < d; i++) {
					int j1 = i * 2 + 2;
					int j2 = i * 2 + 3;
					a[i1][j1] = true;
					a[i1][j2] = true;
					a[j1][i1] = true;
					a[j2][i1] = true;
					a[i2][j1] = true;
					a[i2][j2] = true;
					a[j1][i2] = true;
					a[j2][i2] = true;
					i1 = j1;
					i2 = j2;
				}
				for (int i = d; i < n; i++) {
					int j1 = 100 + i * 2 + 2;
					int j2 = 100 + i * 2 + 3;
					a[i1][j1] = true;
					a[j1][i1] = true;
					if (d != 0) {
						a[i2][j2] = true;
						a[j2][i2] = true;
					}
					i1 = j1;
					i2 = j2;
				}
				a[i1][1] = true;
				a[i2][1] = true;
				a[1][i1] = true;
				a[1][i2] = true;
			}
			k /= 2;
			d++;			
		}
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < 1000; i++) {
			for (int j = 0; j < 1000; j++) {
				sb.append(a[i][j] ? 'Y' : 'N');
			}
			sb.append("\n");
		}
		out.println(1000);
		out.print(sb.toString());
		out.close();
	}
	
	class MyReader {
		private BufferedReader in;
		String[] parsed;
		int index = 0;

		public MyReader() {
			in = new BufferedReader(new InputStreamReader(System.in));
		}

		public int nextInt() throws NumberFormatException, IOException {
			if (parsed == null || parsed.length == index) {
				read();
			}
			return Integer.parseInt(parsed[index++]);
		}

		public long nextLong() throws NumberFormatException, IOException {
			if (parsed == null || parsed.length == index) {
				read();
			}
			return Long.parseLong(parsed[index++]);
		}
		
		public double nextDouble() throws NumberFormatException, IOException {
			if (parsed == null || parsed.length == index) {
				read();
			}
			return Double.parseDouble(parsed[index++]);
		}
		
		public String nextString() throws IOException {
			if (parsed == null || parsed.length == index) {
				read();
			}
			return parsed[index++];
		}

		private void read() throws IOException {
			parsed = in.readLine().split(" ");
			index = 0;
		}

		public String readLine() throws IOException {
			return in.readLine();
		}
	}

};