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.ArrayList;
import java.util.Scanner;

public class R228_Div1_B {
	static int dist = 0;
	static int last = 1;
	static boolean[][] edges = new boolean[200][200];
	static ArrayList<Integer> pass = new ArrayList();
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		solve(n);
		edge(0, last);
		
		boolean started = false;
		for(int i = pass.size()-1; i >= 0; --i) {
			if(pass.get(i) != 0) {
				started = true;
				edge((pass.size()-i-1)*3+1, last+1);
			}
			if(started) {
				edge(last+1, last+2);
				edge(last+2, last+3);
				last += 2;
			}
		}
		edge(0, last);
		
		System.out.println(last+1);
		for(int i = 0; i <= last; ++i) {
			for(int j = 0; j <= last; ++j)
				System.out.print(edges[i][j] ? 'Y' : 'N');
			System.out.println();
		}
	}
	
	static void solve(int k) {
		if(k == 1)
			return;
		solve(k/2);
		edge(last, last+1);
		edge(last, last+2);
		edge(last+1, last+3);
		edge(last+2, last+3);
		last += 3;
		dist += 2;
		pass.add(dist*(k%2));
	}
	
	static void edge(int a, int b) {
		edges[a][b] = true;
		edges[b][a] = true;
	}
}