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.util.*;

public class B {
    public static void main(String[] args) throws Exception {
        new B().solve();
        // new FileInputStream(new File("input.txt")),
        // new PrintStream(new FileOutputStream(new File("output.txt"))));
    }
    void solve() throws IOException {
        BufferedReader in = new BufferedReader(new
                InputStreamReader(System.in));
        Scanner sc = new Scanner(System.in);
        String[] sp;

        // input
        int k = sc.nextInt();
        int hk = Integer.highestOneBit(k);

        boolean[][] g = new boolean[1000][1000];
        int len = 0;
        int s = 2, e = 3;
        int n = 4;

        while (hk != 0) {
            // 0
            int a = n++;
            int b = n++;
            int ee = n++;
            g[e][a] = true;
            g[a][ee] = true;
            g[e][b] = true;
            g[b][ee] = true;
            e = ee;
            len += 2;

            // 1
            if ((k & hk) != 0) {
                int cur = s;
                for (int i = 0; i < len; i++) {
                    int p = n++;
                    g[cur][p] = true;
                    cur = p;
                }
                g[cur][e] = true;
            }

            hk >>= 1;
        }
        g[0][s] = true;
        g[e][1] = true;

        for (int i = 0; i < g.length; i++) {
            for (int jj = 0; jj < g.length; jj++) {
                g[i][jj] |= g[jj][i];
            }
        }

        System.out.println(n);
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            for (int jj = 0; jj < n; jj++) {
                sb.append(g[i][jj] ? 'Y' : 'N');
            }
            sb.append("\n");
        }
        System.out.println(sb);

    }
}
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//
//