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.*;
import java.io.*;
public class Maximus {
public static void main(String [] args)throws Exception{
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	int k = Integer.parseInt(br.readLine());
	boolean array[] = new boolean[32];
	boolean flag = true;
	int highest = 0;
	int nodes = 2;
	//System.out.println((1 << 30));
	for(int i = 30;i >= 0;i--){
		int t = (1 << i);
		if(t <= k){
		   k -= t;
		   array[i] = true;
		   if(flag)nodes += i*2;
		   else nodes += (highest - i);
		if(flag){
			highest = i;
			flag = false;
		}
	}
	}
	System.out.println(nodes);
	StringBuilder sb = new StringBuilder();
	if(highest == 0){
		sb.append("NY");
		sb.append('\n');
		sb.append("YN");
		System.out.print(sb);
		return;
	}
	//System.out.println(highest + " " + nodes + " " + k);
	boolean matrix[][] = new boolean[nodes + 1][nodes + 1];
	for(int i = 1;i <= highest;i++){
		if(i == 1){
			matrix[1][3] = matrix[1][4] = true;
		}
		if(i == highest){
			matrix[2*highest + 1][2] = matrix[2*highest + 2][2] = true;
		}
		else{
			for(int j = 2*i + 1;j <= 2*i + 2;j++){
				matrix[j][2*(i + 1) + 1] = true;
				matrix[j][2*(i + 1) + 2] = true;
			}
		}
	}
	int curr = 2*highest + 2;
	for(int i = highest - 1;i >= 0;i--){
		if(!array[i])continue;
		//System.out.println(i + " 1");
		++curr;
		matrix[2*i + 1][curr] = true;
		if(i != 0)matrix[2*i + 2][curr] = true;
		int level = i + 1;
		while(level < highest){
			matrix[curr][++curr] = true;
			++level;
		}
		matrix[curr][2] = true;
	}
	for(int i = 1;i <= nodes;i++){
		for(int j = 1;j <= nodes;j++){
			if(matrix[i][j])matrix[j][i] = true;
			if(matrix[j][i])matrix[i][j] = true;
		}
	}
	for(int i = 1;i <= nodes;i++){
		for(int j = 1;j <= nodes;j++){
			if(matrix[i][j])sb.append('Y');
			else sb.append('N');
		}
	    sb.append('\n');
	}
	System.out.print(sb);
}
}