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.*;

import static java.lang.Double.parseDouble;
import static java.lang.Integer.bitCount;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;

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

class Solver {
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;

    void run() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        //in = new BufferedReader(new FileReader("input.txt"));
        //out = new PrintWriter(new File("output.txt"));
        solve();
        out.close();
    }

    int cur = 3;
    ArrayList<Integer>[] G = new ArrayList[570];

    public void solve() throws IOException {
        for (int i = 0; i < 570; ++i) {
            G[i] = new ArrayList<Integer>();
        }
        int k = nextInt();
        int maxi = -1;
        for (int i = 0; i < 30; ++i) {
            if (((k >> i) & 1) == 1) maxi = i;
        }
        G[cur++].add(2);
        for (int i = 0; i < 14; ++i) {
            G[cur - 1].add(cur);
            G[cur - 1].add(cur + 1);
            G[cur - 1].add(cur + 2);
            G[cur - 1].add(cur + 3);
            G[cur].add(cur + 4);
            G[cur + 1].add(cur + 4);
            G[cur + 2].add(cur + 4);
            G[cur + 3].add(cur + 4);
            cur += 5;
        }
        for (int i = 0; i < 30; ++i) {
            if (((k >> i) & 1) == 0) continue;
            int pos = 3 + i / 2 * 5;
            int last = pos;
            if (i % 2 == 1) {
                G[cur++].add(pos);
                G[cur++].add(pos);
                G[cur].add(cur - 1);
                G[cur].add(cur - 2);
                last = cur++;
            }
            int now = (i + 1) / 2 * 2;
            while(now != 30) {
                G[cur].add(last);
                last = cur++;
                ++now;
            }
            G[1].add(cur - 1);
        }
        boolean[][] g = new boolean[570][570];
        for (int i = 1; i < cur; ++i) {
            for (int to : G[i]) {
                g[i][to] = g[to][i] = true;
            }
        }
        out.println(cur - 1);
        for (int i = 1; i < cur; ++i) {
            for (int j = 1; j < cur; ++j) {
                if (g[i][j]) out.print('Y');
                else out.print('N');
            }
            out.println();
        }
    }

    String next() throws IOException {
        if (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }

    int nextInt() throws IOException {
        return parseInt(next());
    }

    long nextLong() throws IOException {
        return parseLong(next());
    }

    double nextDouble() throws IOException {
        return parseDouble(next());
    }
}