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 FoxMinimalPath{
    private static boolean[][]grid;
    public static void main(String[]args) {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        int l = (int) (Math.log(k) / Math.log(2));
        int n = 2 + 2 * l;
        for (int i = 0; i <= l; i++) {
            if (k / (int) Math.pow(2, i) % 2 == 1)
                n += l - i;
        }
        grid=new boolean[n][n];
        int lastA=0,lastB=0,ind=2;
        for(int i=0;i<l;i++){
            for(int c=0;c<2;c++) {
                connect(ind,lastA);
                connect(ind,lastB);
                ind++;
            }
            lastA=ind-2;
            lastB=ind-1;
        }
        connect(lastA,1);
        connect(lastB,1);
        for(int i=0;i<l;i++)
            if(k / (int) Math.pow(2, i) % 2 == 1){
                connect(ind,2*i);
                if(i>0)
                    connect(ind,2*i+1);
                for(int j=i;j<l-1;j++)
                    connect(++ind,ind-1);
                connect(ind++,1);
            }
        System.out.println(n);
        for(boolean[]arr:grid) {
            for (boolean b : arr)
                System.out.print(b ? "Y" : "N");
            System.out.println();
        }
    }
    public static void connect(int a,int b){
        grid[a][b]=true;
        grid[b][a]=true;
    }
}