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 P388B
{
    public static StringTokenizer st;
    public static void nextLine(BufferedReader br) throws IOException
    {
        st = new StringTokenizer(br.readLine());
    }
    
    public static String next()
    {
        return st.nextToken();
    }
    
    public static int nextInt()
    {
        return Integer.parseInt(st.nextToken());
    }
    
    public static long nextLong()
    {
        return Long.parseLong(st.nextToken());
    }
    
    public static double nextDouble()
    {
        return Double.parseDouble(st.nextToken());
    }
    
    static int[] dp;
    
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        nextLine(br);
        int k = nextInt();
        if (k == 1)
        {
            System.out.println(2);
            System.out.println("NY");
            System.out.println("YN");
            return;
        }
        int[] a = new int[10];
        int copy = k;
        for (int i = 0; i < 10; i++)
        {
            a[i] = k % 8;
            k /= 8;
        }
        int chains = 10;
        for (int i = 9; i >= 0; i--)
        {
            if (a[i] == 0)
            {
                chains--;
            }
            else
            {
                break;
            }
        }
        int[][] adj = new int[chains*100][chains*100];
        for (int i = 0; i < chains; i++)
        {
            int startn = 2 + i * 100;
            int[] nodes = new int[10];
            for (int j = 0; j < 10; j++)
            {
                if (j < i)
                {
                    nodes[j] = 8;
                }
                else if (j == i)
                {
                    nodes[j] = a[i];
                }
                else 
                {
                    nodes[j] = 1;
                }
            }
            for (int j = 0; j < nodes[0]; j++)
            {
                connect(adj, 0, startn + j);
            }
            for (int st = 1; st < 10; st++)
            {
                for (int j1 = 0; j1 < nodes[st-1]; j1++)
                {
                    for (int j2 = 0; j2 < nodes[st]; j2++)
                    {
                        connect(adj, startn + ((st-1)*10) + j1, startn + (st*10) + j2);
                    }
                }
            }
            for (int j = 0; j < nodes[9]; j++)
            {
                connect(adj, 1, startn + 90 + j);
            }
        }
        StringBuffer sb = new StringBuffer();
        sb.append(adj.length);
        sb.append('\n');
        for (int i = 0; i < adj.length; i++)
        {
            for (int j = 0; j < adj.length; j++)
            {
                sb.append(adj[i][j] == 0 ? 'N' : 'Y');
            }
            sb.append('\n');
        }
        System.out.print(sb.toString());
    }
    
    private static void connect(int[][] adj, int n1, int n2)
    {
        adj[n1][n2] = 1;
        adj[n2][n1] = 1;
    }
}