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.*;

public class CF389D {
	static int M = 1000, m = 0, n = 2;
	static int[] uu, vv;
	static void add1(int u, int v) {
		uu[m] = u;
		vv[m] = v;
		m++;
	}
	static void add(int l, int r, int k, int h) {
		if (k == 0)
			return;
		if (k % 2 == 1) {
			int l_ = l;
			for (int i = 0; i < h; i++) {
				add1(l_, n);
				add1(n, n + 1);
				l_ = n + 1;
				n += 2;
			}
			add1(l_, n);
			add1(n, r);
			n++;
		}
		if (k >= 2) {
			add1(l, n);
			add1(l, n + 1);
			add1(n, n + 2);
			add1(n + 1, n + 2);
			l = n + 2;
			n += 3;
			add(l, r, k / 2, h - 1);
		}
	}
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int k = Integer.parseInt(br.readLine());
		uu = new int[M];
		vv = new int[M];
		if (k == 1) {
			add1(0, 1);
		} else {
			int h = 0;
			for (int b = 0; b < 30; b++)
				if ((k & 1 << b) > 0)
					h = b;
			add(0, 1, k, h);
		}
		char[][] cc = new char[n][n];
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				cc[i][j] = 'N';
		for (int i = 0; i < m; i++) {
			int u = uu[i];
			int v = vv[i];
			cc[u][v] = cc[v][u] = 'Y';
		}
		PrintWriter pw = new PrintWriter(System.out);
		pw.println(n);
		for (int i = 0; i < n; i++)
			pw.println(cc[i]);
		pw.close();
	}
}