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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main228B {

    private FastScanner in;
    private PrintWriter out;

    private class Graph {
        int V;
        byte[][] matrix;

        Graph(int V) {
            this.V = V;
            matrix = new byte[V][V];
        }

        void adj(int i, int j) {
            matrix[i][j] = 1;
            matrix[j][i] = 1;
        }
    }

    public void solve() throws IOException {
        int k = in.nextInt();
        if(k == 1) {
            out.println(2);
            out.println("NY");
            out.println("YN");
            return;
        }
        List<Integer> pow = new ArrayList<Integer>();
        int p = 0;
        while(k > 0) {
            if(k % 2 == 1) {
                pow.add(p);
            }
            p++;
            k /= 2;
        }
        int cp = pow.size();
        int maxP = pow.get(cp - 1);
        int count = 3 * maxP + 1;
        for(int i = cp - 2; i >= 0; i--) {
            count += 2 * (maxP - pow.get(i)) - 1;
        }
        out.println(count);
        Graph graph = new Graph(count);
        for(int i = 0; i < maxP; i++) {
            int curr = 3 * i + 1;
            int next = 3 * i + 4;
            if(i == maxP - 1) {
                next = 0;
            }
            graph.adj(curr, curr + 1);
            graph.adj(curr, curr + 2);
            graph.adj(next, curr + 1);
            graph.adj(next, curr + 2);
        }
        int curV = 3 * maxP + 1;
        for(int i = cp - 2; i >= 0; i--) {
            int curP = pow.get(i);
            int ce = 2 * (maxP - curP);
            graph.adj(3 * curP + 1, curV);
            for(int j = 0; j < ce - 2; j++) {
                graph.adj(curV, curV + 1);
                curV++;
            }
            graph.adj(curV, 0);
            curV++;
        }

        for(int i = 0; i < graph.V; i++) {
            for(int j = 0; j < graph.V; j++) {
                out.print(graph.matrix[i][j] == 1 ? 'Y' : 'N');
            }
            out.println();
        }
    }

    public void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {

        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    public static void main(String[] arg) {
        new Main228B().run();
    }
}