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:
//package B;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;
    
    public static String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    
    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int k = nextInt();
        boolean[][] a = new boolean[1000][1000];
        int[] pos = new int[2005];
        Arrays.fill(pos, -1);
        int last = 0, n = 2, dist = 0;
        
        while (k > 1) {     
            if (k % 2 == 1) {
                int u = n++;
                int v = n++;
                a[u][last] = a[last][u] = true;
                a[v][last] = a[last][v] = true;
                last = v;
                dist += 1;
                pos[u] = dist;
                --k;
            } else {
                int u = n++;
                int v = n++;
                int w = n++;
                dist += 2;
                a[last][u] = a[u][last] = true;
                a[last][v] = a[v][last] = true;
                a[u][w] = a[w][u] = true;
                a[v][w] = a[w][v] = true;
                last = w;
                k /= 2;
            }           
        }
        
        a[last][1] = a[1][last] = true;
        ++dist;
        int m = n;
        
        int[] g = new int[2005];
        Arrays.fill(g, -1);
        
        for (int u = 2; u < n; ++u) if (pos[u] != -1) {
            int t = dist - pos[u] - 1;
            int w = u;
            boolean conn = false;
            for (int iter = t - 1; iter >= 0; --iter) {
                if (g[iter] != -1) {
                    int z = g[iter];
                    a[w][z] = a[z][w] = true;
                    conn = true;
                    break;
                }
                int v = m++;
                g[iter] = v;
                a[w][v] = a[v][w] = true;
                w = v;
            }
            if (!conn) {
                a[w][1] = a[1][w] = true;
            }
        }
        
        out.println(m);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < m; ++j) {           
                if (a[i][j]) {
                    out.print('Y');
                } else {
                    out.print('N');
                }
            }
            out.println();
        }
        out.close();
    }

}