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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    public static long mod = 17352642619633L;

    void run(FastScanner in, PrintWriter out) {
        K = in.nextInt();
        construct();

        out.println(1000);
        for (int i = 0; i < g.length; i++) {
            for (int j = 0; j < g.length; j++) {
                out.print(g[i][j] ? "Y" : "N");
            }
            out.println();
        }

    }

    boolean[] visited = new boolean[1000];

    int K;
    boolean[][] g = new boolean[1000][1000];
    void construct() {

        int sz = 2;
        if (K%2 == 1) {
            g[0][sz] = true;
            g[sz][0] = true;

            for (int k = 2; k < 60; k++) {
                g[sz][sz+1] = true;
                g[sz+1][sz] = true;
                sz++;
            }
            g[sz][1] = true;
            g[1][sz] = true;
            sz++;
        }

        int prevVertex = 0;
        for (int i = 1; i <= 30; i++) {

            g[sz][prevVertex] = true;
            g[prevVertex][sz] = true;

            g[sz][sz+2] = true;
            g[sz+2][sz] = true;

            g[sz+1][prevVertex] = true;
            g[prevVertex][sz+1] = true;

            g[sz+1][sz+2] = true;
            g[sz+2][sz+1] = true;

            prevVertex = sz+2;
            sz += 2;
            if ((K&(1<<i)) > 0) {

                // make path of length 60
                // current length is 2*i+1
                for (int k = 2*i+1; k < 60; k++) {
                    g[sz][sz+1] = true;
                    g[sz+1][sz] = true;
                    sz++;
                }

                g[sz][1] = true;
                g[1][sz] = true;
            }
            sz++;

        }

    }


    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}