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 {
        new Main().run();       
    }

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

    private void run() throws IOException {
        if (new File("input.txt").exists())
            in = new BufferedReader(new FileReader("input.txt"));
        else
            in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }
    
    final int M = 20000;
    
    private void solve() throws IOException {
        
        long k = nextLong();
        if (k == 1l) {
            out.println(2);
            out.println("NY");
            out.println("YN");
            return;
        }
        long m = 1;
        while (m <= k) {
            m <<= 1;
        }
        m >>= 2;
        int prev = 0;
        int l[] = new int[M];
        int r[] = new int[M];
        int cnt = 2;
        int po = 0;
        int e = 0;
        while (true) {
            int u = cnt++;
            int v = cnt++;
            int s = cnt++;
            int o = cnt++;
            int no = cnt++;
            l[e] = prev;
            r[e++] = u;
            l[e] = prev;
            r[e++] = v;
            l[e] = s;
            r[e++] = u;
            l[e] = s;
            r[e++] = v;
            l[e] = po;
            r[e++] = o;
            l[e] = no;
            r[e++] = o;
            if ((m & k) != 0) {
                l[e] = s;
                r[e++] = o;
            }
            prev = s;
            po = no;
            if (m == 1)
                break;
            m >>= 1;
        }
        l[e] = 1;
        r[e++] = prev;
        boolean g[][] = new boolean[cnt][cnt];
        for (int i = 0; i < e; i++) {
            g[l[i]][r[i]] = true;
            g[r[i]][l[i]] = true;
        }
        out.println(cnt);
        for (int i = 0; i < cnt; i++) {
            for (int j = 0; j < cnt; j++) {
                out.print((g[i][j] ? "Y" : "N"));
            }
            out.println();
        }
    }
    
    void chk(boolean b) {
        if (b)
            return;
        System.out.println(new Error().getStackTrace()[1]);
        exit(999);
    }
    void deb(String fmt, Object... args) {
        System.out.printf(Locale.US, fmt + "%n", args);
    }
    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;
    }
}