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.lang.reflect.Array;
import java.math.BigDecimal;
import java.sql.Time;
import java.util.*;

import java.math.BigInteger;

import static java.lang.Math.*;
import static java.math.BigInteger.*;
import static java.util.Arrays.*;


public class Main{

    void run(){
        Locale.setDefault(Locale.US);
        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
//        boolean oj = true;
        try{
            if( oj ){
                sc  = new FastScanner( new InputStreamReader(System.in  ) );
                out = new PrintWriter(   new OutputStreamWriter(System.out) );
            } else{
                sc  = new FastScanner(new FileReader("in.txt") );
//                sc  = new FastScanner(new FileReader("D:\\JavaOlymp\\FatalError\\output.txt") );
                out = new PrintWriter(   new FileWriter("out.txt") );
            }
        } catch (Exception e) {
            System.exit(-1);
        }
        long tB = System.currentTimeMillis();
        solve();
        if( !oj ) System.err.println( "Time: " + (System.currentTimeMillis()-tB)/1e3 );
        out.flush();
    }


    class FastScanner{
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");
        FastScanner( InputStreamReader a ){
            br = new BufferedReader(a);
        }
        FastScanner( FileReader a ){
            br = new BufferedReader(a);
        }
        String next(){
            while( !st.hasMoreTokens() )
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    return null;
                }
            return st.nextToken();
        }
        String readLine(){
            try {
                return br.readLine();
            } catch (Exception e) {
                return null;
            }
        }
        int nextInt(){ return Integer.parseInt(next()); }
        long nextLong(){ return Long.parseLong(next()); }
    }

    FastScanner sc;
    PrintWriter out;



    public static void main(String[] args){
        new Main().run();
//        new Thread( null, new Runnable() {
//            @Override
//            public void run() {
//                new Main().run();
//            }
//            }, "LOL", 256L * 1024 * 1024 / 2 ).run();
//        }, "LOL", 2000 * 1024 * 1024 ).run();
    }



    void TLE(){ for(;;); }

    void MLE(){
        int[][] adj = new int[1024*1024][];
        for( int i = 0; i < adj.length; ++i )
            adj[i] = new int[1024*1024];
    }

    void exit( int val ){
        out.flush();
        System.exit(val);
    }
    //////////////////////////////////////////////////////////////////////////////////////////


    int k, maxPow2;
    boolean[][] grid = new boolean[1005][1005];
    int n;

    void add( int a, int b ){
        grid[a][b] = grid[b][a] = true;
//        out.printf( "%d %d\n", a, b );
    }

    void solve(){
        k = sc.nextInt();

        for( int i = 0; i <= 30; ++i )
            if( 0 < (k & (1<<i)) )
                maxPow2 = i;


        add( 1, 3 );
        add( 1, 4 );
        n = 5;
        for( int i = 1; i <= maxPow2; ++i ){
            add( n-2, n );
            add( n-1, n );
            add( n-2, n+1 );
            add( n-1, n+1 );
            n += 2;
        }

        for( int i = 0; i <= maxPow2; ++i )
            if( 0 < (k & (1<<i)) ){
                int last = 3 + i * 2;
                for( int l = i+1; l <= maxPow2; ++l ){
                    add( last, n );
                    //
                    last = n;
                    ++n;
                }
                add( last, 2 );
            }

        --n;
        out.println( n );
        for( int i = 1; i <= n; ++i ){
            for( int j = 1; j <= n; ++j )
                out.print( grid[i][j]? 'Y' : 'N' );
            out.println();
        }
    }



}