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.OutputStream;
import java.io.IOException;
import java.util.Arrays;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author George Marcus
 */
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();
        int N = 1000;
        char[][] A = new char[N][N];
        for(int i = 0; i < N; i++)
            Arrays.fill(A[i], 'N');

        int bmax = Integer.bitCount(Integer.highestOneBit(K) - 1);
        int crt = 2;
        int last = 0;
        int len = 0;
        int[] P = new int[100];
        for(int i = 0; i < bmax; i++) {
            int a1 = crt++;
            int a2 = crt++;
            unite(A, last, a1);
            unite(A, last, a2);
            int to = crt++;
            last = crt - 1;
            unite(A, a1, to);
            unite(A, a2, to);
            len += 2;
            P[len] = to;
        }
        unite(A, last, 1);

        int[] L = new int[100];
        last = 0;
        for(int i = 1; i <= len; i++) {
            L[i] = crt++;
            unite(A, L[i], last);
            last = L[i];
        }

        for(int bit = 0; bit < bmax; bit++)
            if((K & (1 << bit)) > 0) {
                int q = (bmax - bit) * 2;
                unite(A, L[q - 1], P[q]);
            }

        out.println(N);
        for(int i = 0; i < N; i++) {
            out.println(A[i]);
        }
    }

    private void unite(char[][] A, int a, int b) {
        A[a][b] = 'Y';
        A[b][a] = 'Y';
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

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

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));

        return res.toString();
    }

    private boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    }