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.ArrayDeque;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.util.Collection;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Queue;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    final int N = 1000;
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int k = in.nextInt();
        boolean a[][] = new boolean[N][N];
        int kn = 3;

        if (k == 1) {
            set(0, 1, a);
            print(out, a, 2);
            return;
        }

        set(1, 2, a);
        Queue<Integer> prev = new ArrayDeque<>();
        prev.add(2);
        int len = 1;

        String binary = Integer.toBinaryString(k);
        for (int i = 1; i < binary.length(); i++) {
            int t = kn++, b = kn++;
            while (prev.size() > 0) {
                int cur = prev.poll();
                set(cur, t, a);
                set(cur, b, a);
            }
            if (binary.charAt(i) == '1') {
                int pr = b;
                for (int h = 0; h < len; h++) {
                    set(pr, kn++, a);
                    pr = kn - 1;
                }
                set(pr, 1, a);
            }
            len++;
            prev.add(b);
            prev.add(t);
        }

        while (prev.size() > 0) {
            set(0, prev.poll(), a);
        }

        print(out, a, kn);
    }

    public void set(int i, int h, boolean[][] a) {
        a[i][h] = true;
        a[h][i] = true;
    }

    public void print(PrintWriter out, boolean[][] a, int n) {
        out.println(n);
        for (int i = 0; i < n; i++) {
            for (int h = 0; h < n; h++) {
                if (a[i][h]) {
                    out.print('Y');
                } else {
                    out.print('N');
                }
            }
            out.println();
        }
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

}