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.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Solution {

    void solve() throws Exception {
        int k = nextInt();
        int[] a = new int[40];
        int al = 0;
        while (k > 0) {
            a[al++] = k % 2;
            k /= 2;
        }
        boolean[][] g = new boolean[1001][1001];
        g[1][2] = g[2][1] = true;
        int tv = 2;
        int lv = 2;
        int l = 1;
        for (int i = al - 2; i >= 0; i--) {
            g[lv][tv + 1] = g[tv + 1][lv] = true;
            g[lv][tv + 2] = g[tv + 2][lv] = true;
            g[tv + 1][tv + 3] = g[tv + 3][tv + 1] = true;
            g[tv + 2][tv + 3] = g[tv + 3][tv + 2] = true;
            tv += 3;
            lv = tv;
            l += 2;
            if (a[i] == 1) {
                g[1][tv + 1] = g[tv + 1][1] = true;
                for (int j = 1; j < l - 1; j++) {
                    g[tv + j][tv + j + 1] = g[tv + j + 1][tv + j] = true;
                }
                g[tv + l - 1][lv] = g[lv][tv + l - 1] = true;
                tv += l - 1;
            }
        }
        out.println(tv);
        for (int i = 1; i <= tv; i++) {
            int ii = i;
            if (i == lv) ii = 2;
            if (i == 2) ii = lv;
            for (int j = 1; j <= tv; j++) {
                int jj = j;
                if (j == lv) jj = 2;
                if (j == 2) jj = lv;
                out.print(g[ii][jj]? 'Y' : 'N');
            }
            out.println();
        }
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st;

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

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

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

    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        } finally {
            out.close();
        }
    }

}