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 static java.lang.Math.*;
import static java.lang.System.currentTimeMillis;
import static java.lang.System.exit;
import static java.lang.System.arraycopy;
import static java.util.Arrays.sort;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.fill;
import java.util.*;
import java.io.*;

public class Main {

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

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

	int length(int temp) {
		int l = 0;
		while ((temp >> 1) > 0) {
			temp >>= 1;
			l++;
		}
		return l;
	}

	int n = 1000;
	char a[][] = new char[n][n];

	void add(int u, int v) {
		a[u][v] = 'Y';
		a[v][u] = 'Y';
//		System.err.println(u + " " + v);
	}

	private void run() throws IOException {
		if (new File("input.txt").exists())
			in = new BufferedReader(new FileReader("input.txt"));
		else
			in = new BufferedReader(new InputStreamReader(System.in));
		if (new File("output.txt").exists())
			out = new PrintWriter("output.txt");
		else
			out = new PrintWriter(System.out);

		for (int i = 0; i < n; i++)
			fill(a[i], 'N');
		int k = nextInt();

		int len = length(k);
		int begin = 2;
		int end = begin + 3 * len;
		add(begin, 0);
		add(end, 1);
		for (int i = 0; i < len; i++) {
			add(begin + 3 * i, begin + 3 * i + 1);
			add(begin + 3 * i, begin + 3 * i + 2);
			add(begin + 3 * i + 1, begin + 3 * (i + 1));
			add(begin + 3 * i + 2, begin + 3 * (i + 1));
		}
		System.err.println("+");
		int begin2 = end + 1;
		add(0, begin2);
		int end2 = begin2 + len * 2;
		for (int i = begin2; i < end2; i++)
			add(i, i + 1);
		k ^= (1 << len);
		while (k > 0) {
			int l = length(k);
			k ^= (1 << l);
			int from = end - 3 * l;
			int to = end2 - 1 - 2 * (l);
			add(from, to);
		}

		out.println(n);
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++)
				out.print(a[i][j]);
			out.println();
		}

		in.close();
		out.close();
	}

	void chk(boolean b) {
		if (b)
			return;
		System.out.println(new Error().getStackTrace()[1]);
		exit(999);
	}

	void deb(String fmt, Object... args) {
		System.out.printf(Locale.US, fmt + "%n", args);
	}

	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}

	boolean EOF() throws IOException {
		while (!st.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null)
				return true;
			st = new StringTokenizer(s);
		}
		return false;
	}
}