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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author sheep
 */
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);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskB {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int k = in.nextInt();
        boolean[][] answer = new boolean[1000][1000];
        int current = 4;
        answer[0][2] = answer[2][0] = true;
        answer[0][3] = answer[3][0] = true;

        int[] at = new int[32];
        at[0] = 2;
        for (int i = 1; i <= 30; ++i) {
            answer[current][current - 2] = answer[current - 2][current] = true;
            answer[current][current - 1] = answer[current - 1][current] = true;
            at[i] = current;

            ++current;

            answer[current][current - 2] = answer[current - 2][current] = true;
            answer[current][current - 3] = answer[current - 3][current] = true;

            ++current;
        }
        if ((k >> 30) % 2 == 1) throw new RuntimeException();
        for (int i = 29; i >= 0; --i) {
            if ((k >> i) % 2 == 1) {
                for (int j = i; j <= 29; ++j) {
                    int now = (j == i ? at[j] : current - 1);
                    int to = (j == 29 ? 1 : current++);
                    answer[now][to] = answer[to][now] = true;
                }
            }
        }

        if (current > 1000) throw new RuntimeException();
        out.println(current);
        for (int i = 0; i < current; ++i) {
            StringBuilder builder = new StringBuilder();
            for (int j = 0; j < current; ++j) {
                builder.append(answer[i][j] ? 'Y' : 'N');
            }

            out.println(builder.toString());
        }
    }
}

class InputReader {
    BufferedReader reader;
    StringTokenizer tokenizer;

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

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

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

    }