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.math.BigInteger;
import java.util.*;


public class B {

    void solve() throws IOException {
        int k=nextInt();
        int n=1000;
        boolean[][] g=new boolean[n][n];
        int v=2;
        int x=1;
        while(x<k)x*=10;
        if(x>k)x/=10;
        int maxl=0;
        while(k>0){
            int[] cv=new int[10];
            int y=x;
            int l=0;
            while(y>=10){
                l++;
                for(int i=0;i<10;i++)
                    for(int j=0;j<10;j++)
                        g[v+i][cv[j]]=g[cv[j]][v+i]=true;
                for(int i=0;i<10;i++)
                    cv[i]=v+i;
                v+=10;
                y/=10;
            }
            y=k/x;
            int m=10;
            if(y!=1){
                l++;
                for(int i=0;i<y;i++)
                    for(int j=0;j<10;j++)
                        g[v+i][cv[j]]=g[cv[j]][v+i]=true;
                for(int i=0;i<y;i++)
                    cv[i]=v+i;
                v+=y;
                m=y;
            }
            for(int i=l;i<maxl;i++){
                for(int j=0;j<m;j++)
                    g[cv[j]][v]=g[v][cv[j]]=true;
                m=1;
                cv[0]=v;
                v++;
            }
            if(l>maxl)maxl=l;
            for(int i=0;i<m;i++)
                g[cv[i]][1]=g[1][cv[i]]=true;
            k%=x;
            x/=10;
        }
        n=v;
        out.println(n);
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++)
                if(g[i][j])
                    out.print('Y');
                else
                    out.print('N');
            out.println();
        }

    }

    public static void main(String[] args) throws IOException {
        new B().run();
    }

    void run() throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));
//      reader = new BufferedReader(new FileReader("input.txt"));
        tokenizer = null;
        out = new PrintWriter(new OutputStreamWriter(System.out));
//      out = new PrintWriter(new FileWriter("output.txt"));
        solve();
        reader.close();
        out.flush();

    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter out;

    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 nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}