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.*;

public class cf388b {
  static FastIO in = new FastIO(), out = in;

  public static void main(String[] args) {
    int k = in.nextInt();
    int n = 95;
    char[][] g = new char[n][n];
    for(char[] x : g) Arrays.fill(x, 'N');
    int cur = 4;
    g[0][2] = g[2][0] = g[0][3] = g[3][0] = 'Y';
    ArrayList<Integer> powers = new ArrayList<Integer>();
    ArrayList<Integer> ladder = new ArrayList<Integer>();
    powers.add(2);
    for(int i=0; i<30; i++) {
      int x = cur++;
      int y = cur++;
      int a = x-2;
      int b = x-1;
      g[a][x] = g[x][a] = 'Y';
      g[a][y] = g[y][a] = 'Y';
      g[b][x] = g[x][b] = 'Y';
      g[b][y] = g[y][b] = 'Y';
      powers.add(x);
    }
    ladder.add(cur++);
    for(int i=0; i<30; i++) {
      int x = cur++;
      int a = x-1;
      g[x][a] = g[a][x] = 'Y';
      ladder.add(x);
    }
    g[cur-1][1] = g[1][cur-1] = 'Y';
    for(int i=0; i<30; i++)
      if((k&(1<<i)) != 0) {
        int x = powers.get(i);
        int y = ladder.get(i);
        g[x][y] = g[y][x] = 'Y';
      }
    out.println(n);
    for(char[] x : g) out.println(new String(x));
    out.close();
  }

  static class FastIO extends PrintWriter {
    BufferedReader br;
    StringTokenizer st;

    public FastIO() {
      this(System.in, System.out);
    }

    public FastIO(InputStream in, OutputStream out) {
      super(new BufferedWriter(new OutputStreamWriter(out)));
      br = new BufferedReader(new InputStreamReader(in));
      scanLine();
    }

    public void scanLine() {
      try {
        st = new StringTokenizer(br.readLine().trim());
      } catch (Exception e) {
        throw new RuntimeException(e.getMessage());
      }
    }

    public int numTokens() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return numTokens();
      }
      return st.countTokens();
    }

    public String next() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return next();
      }
      return st.nextToken();
    }

    public double nextDouble() {
      return Double.parseDouble(next());
    }

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

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