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.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class ProblemB {
    static int[][] ans;
    static void set(int a, int b) {
        ans[a][b] = ans[b][a] = 1;
    }
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        int L = 30;
        ans = new int[3*L+5][3*L+5];
        set(0,3); set(0,4);
        for (int i=0; i < L; i++) {
            set(3*i+3, 3*i+6);
            set(3*i+3, 3*i+7);
            set(3*i+4, 3*i+6);
            set(3*i+4, 3*i+7);
            set(3*i+2, 3*i+5);
        }
        set(3*L+2, 1);
        for (int pw=L-1; pw>=0; pw--) {
            if (k >= (1<<pw)) {
                k -= (1<<pw);
                set(3*pw+3, 3*pw+5);
            }
        }

        int n = 3*L+5;
        StringBuilder sb = new StringBuilder();
        sb.append(n + "\n");
        for (int i=0; i<n; i++) {
            for (int j=0; j<n; j++)
                sb.append(ans[i][j] == 1 ? 'Y' : 'N');
            sb.append('\n');
        }
        System.out.println(sb.toString());
    }
}