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 Round_228_B {

	static BufferedReader br;
	static PrintWriter out;
	static StringTokenizer st;

	static int N, cnt;
	static boolean[][] adj;
	public static void main (String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(new OutputStreamWriter(System.out));
		//br = new BufferedReader(new FileReader("in.txt"));
		//out = new PrintWriter(new FileWriter("out.txt"));

		N = readInt();
		cnt = bitCount(N);
		adj = new boolean[3 * cnt + 2][3 * cnt + 2];
		out.println(3 * cnt + 2);
		// layer
		for (int i = cnt - 1; i >= 0; i--) {
			int index = (cnt - 1 - i) * 3 + 2;
			if (i == cnt - 1) {
//				adj[index][1] = adj[1][index] = true;
				adj[index + 2][1] = adj[1][index + 2] = true;
			} else {
				adj[index][index - 3] = adj[index - 3][index] = true;
				adj[index + 1][index - 3] = adj[index - 3][index + 1] = true;
				adj[index][index - 2] = adj[index - 2][index] = true;
				adj[index + 1][index - 2] = adj[index - 2][index + 1] = true;
				adj[index + 2][index - 1] = adj[index - 1][index + 2] = true;
				if ((N & 1 << (i + 1)) > 0) {
					adj[index][index - 1] = adj[index - 1][index] = true;
					adj[index + 1][index - 1] = adj[index - 1][index + 1] = true;
				}
			}
		}
		
		adj[0][(cnt - 1) * 3 + 2] = adj[(cnt - 1) * 3 + 2][0] = true;
		adj[0][(cnt - 1) * 3 + 3] = adj[(cnt - 1) * 3 + 3][0] = true;
		if ((N & 1) == 1)
			adj[0][(cnt - 1) * 3 + 4] = adj[(cnt - 1) * 3 + 4][0] = true;
		
		for (int i = 0; i < 3 * cnt + 2; i++) {
			for (int j = 0; j < 3 * cnt + 2; j++) {
				out.print(adj[i][j] ? 'Y' : 'N');
			}
			out.println();
		}
//		out.println(check());
		out.close();
	}
	
	static int check () {
		int n = 3 * cnt + 2;
		int[] dp = new int[n];
		dp[1] = 1;
		for (int i = 1; i < n; i++)
			for (int j = 0; j < i; j++)
				if (adj[i][j])
					dp[i] += dp[j];
		int ret = 0;
		for (int j = 1; j < n; j++)
			if (adj[0][j])
				ret += dp[j];
		return ret;
	}
	
	static int bitCount (int n) {
		int ret = 0;
		while (n > 0) {
			n >>= 1;
			ret++;
		}
		return ret;
	}

	static String next () throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine().trim());
		return st.nextToken();
	}

	static long readLong () throws IOException {
		return Long.parseLong(next());
	}

	static int readInt () throws IOException {
		return Integer.parseInt(next());
	}

	static double readDouble () throws IOException {
		return Double.parseDouble(next());
	}

	static char readCharacter () throws IOException {
		return next().charAt(0);
	}

	static String readLine () throws IOException {
		return br.readLine().trim();
	}
}