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 static java.lang.Math.*;
import static java.lang.System.currentTimeMillis;
import static java.lang.System.exit;
import static java.lang.System.arraycopy;
import static java.util.Arrays.sort;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.fill;
import java.util.*;
import java.io.*;

public class Main {

    public static void main(String[] args) throws IOException {
        try {
            if (new File("input.txt").exists())
                System.setIn(new FileInputStream("input.txt"));
        } catch (SecurityException e) {
        }
        new Main().run();
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st = new StringTokenizer("");

    private void run() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

    final int MAXN = 1000;

    void add(int[][] g, int u, int v) {
        g[u][v] = 1;
        g[v][u] = 1;
    }

    private void solve() throws IOException {
        int[][] g = new int[MAXN][MAXN];
        int k = nextInt();
        int n = 2;
        if(k == 1){
            add(g,0,1);
        }else if (k != 0) {
            int deg = 31;
            while (((1 << deg) & k) == 0)
                deg--;
            int lenPath = 2 * deg;
            int lastUnusebleVertex = 2;
            for(int i = 0; i < deg; i++){
                if(i == 0){
                    add(g,0,lastUnusebleVertex);
                    add(g,0,lastUnusebleVertex+1);
                } else {
                    add(g,lastUnusebleVertex-1,lastUnusebleVertex);
                    add(g,lastUnusebleVertex-1,lastUnusebleVertex+1);
                }
                if(i == deg-1){
                    add(g,lastUnusebleVertex,1);
                    add(g,lastUnusebleVertex+1,1);
                    lastUnusebleVertex += 2;
                } else {
                    add(g,lastUnusebleVertex,lastUnusebleVertex+2);
                    add(g,lastUnusebleVertex+1,lastUnusebleVertex+2);
                    lastUnusebleVertex += 3;
                }
            }
            
            add(g,0,lastUnusebleVertex);
            lastUnusebleVertex++;
            int to = 4;
            for(int d = deg-1; d >= 0; d--){
                if(d == 0)
                    to = 1;
                if(((1 << d) & k) != 0){
                    add(g,lastUnusebleVertex-1,to);
                }
                
                add(g,lastUnusebleVertex-1,lastUnusebleVertex);
                lastUnusebleVertex++;

                add(g,lastUnusebleVertex-1,lastUnusebleVertex);
                lastUnusebleVertex++;
                to += 3;
            }
            n = lastUnusebleVertex;
        }
        
        out.println(n);
        for (int i = 0; i < n; i++) {
//          out.print(((i < 10) ? " ":"") + i + ": ");
            for (int j = 0; j < n; j++){
                if (g[i][j] == 1)
                    out.print("Y");
                else
                    out.print("N");
            }
            out.println();
        }
    }

    String nextToken() throws IOException {
        while (!st.hasMoreTokens())
            st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }
    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    String nextLine() throws IOException {
        st = new StringTokenizer("");
        return in.readLine();
    }
    boolean EOF() throws IOException {
        while (!st.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null)
                return true;
            st = new StringTokenizer(s);
        }
        return false;
    }
}