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.*;
import java.util.List;
import java.util.StringTokenizer;

public class B {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void solve() throws IOException {
		int k = readInt();
		int pow = Integer.toString(k).length();

		boolean[][] res = new boolean[1000][1000];
		int curNotUsed = 2;
		int start = 0;
		int end = 1;
		for(int i = 0; i < pow; i++) {
			int z = k % 10;
			k /= 10;
			if(z == 0) {
				continue;
			}
			int sB = curNotUsed;
			int sE = curNotUsed + z - 1;
			for(int j = 0; j < z; j++) {
				res[start][curNotUsed] = true;
				res[curNotUsed][start] = true;
				curNotUsed++;
			}
			for(int j = 0; j < i; j++) {
				int nB = sE + 1;
				int nE = nB + 10-1;
				for(int p = sB; p <= sE; p++) {
					for(int q = nB; q <= nE; q++) {
						res[p][q] = true;
						res[q][p] = true;
					}
				}
				sB = nB;
				sE = nE;
			}

			curNotUsed = sE+1;
			for(int j = sB; j <= sE; j++) {
				res[j][curNotUsed] = true;
				res[curNotUsed][j] = true;
			}
			for(int j = i+2; j < pow+1; j++) {
				res[curNotUsed][curNotUsed+1] = true;
				res[curNotUsed+1][curNotUsed] = true;
				curNotUsed++;
			}

			res[curNotUsed][end] = true;
			res[end][curNotUsed] = true;
			curNotUsed++;
		}

		out.println(curNotUsed);
		for(int i = 0; i < curNotUsed; i++) {
			for(int j = 0; j < curNotUsed; j++) {
				out.print(res[i][j] ? "Y" : "N");
			}
			out.println();
		}

    }

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

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

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    int[] readArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long[] readArrL(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = readLong();
        }
        return res;
    }

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

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }
}