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.util.Scanner;
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskB {
    char[][] ret;
    int[] chain;
    void addEdge(int s, int t) {
        ret[s][t] = 'Y';
        ret[t][s] = 'Y';
    }
    public void solve(int testNumber, Scanner in, PrintWriter out) {
        int k = in.nextInt();
        int tot = 2;
        int last = 1;
        ret = new char[200][200];
        chain = new int[200];
        for(int i = 40; i >= 0; -- i) {
            addEdge(last, tot);
            addEdge(tot, tot + 1);
            chain[i] = tot + 1;
            last = chain[i];
            tot += 2;
        }
        last = 0;
        for(int cur = 0; k != 0; k >>= 1, ++ cur) {
            if (k % 2 != 0) {
                addEdge(last, chain[cur]);
            }
            addEdge(last, tot);
            addEdge(tot, tot + 2);
            addEdge(last, tot + 1);
            addEdge(tot + 1, tot + 2);
            tot += 3;
            last = tot - 1;
        }
        out.println(tot);
        for(int i = 0; i < tot; ++ i) {
            for(int j = 0; j < tot; ++ j) {
                if (ret[i][j] == 'Y')
                    out.print('Y');
                else
                    out.print('N');
            }
            out.println();
        }
    }
}