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.*;

public class B {
    private static final int S = 31;
    private static final int D = S * 3 + 2;

    public static void main(String... args) {
        final int k = new Scanner(System.in).nextInt();
        final boolean[][] map = new boolean[D][D];
        map[0][2] = map[0][3] = map[D - 1][1] = true;
        for (int i = 1; i < S; i++)
            map[3 * i - 1][3 * i + 2] = map[3 * i][3 * i + 2] =
                    map[3 * i - 1][3 * i + 3] = map[3 * i][3 * i + 3] = true;
        for (int i = 1; i < S; i++)
            map[3 * i + 1][3 * i + 4] = true;
        for (int i = 0, j = 1; j <= k; i++, j <<= 1)
            if ((k & j) > 0)
                map[3 * i + 2][3 * i + 4] = true;
        for (int i = 0; i < D; i++)
            for (int j = 0; j < i; j++)
                if (map[i][j] | map[j][i])
                    map[i][j] = map[j][i] = true;
        System.out.println(D);
        final StringBuilder sb = new StringBuilder();
        for (int i = 0; i < D; i++) {
            for (int j = 0; j < D; j++)
                sb.append(map[i][j] ? 'Y' : 'N');
            sb.append('\n');
        }
        System.out.println(sb);
    }
}