```
public class Solution {
public int countArrangement(int N) {
if (N <= 1) return N;
int[] visited = new int[N + 1];
Map<String, Integer> map = new HashMap<>();
return helper(N, visited, 1, map);
}
private int helper(int N, int[] visited, int pos, Map<String, Integer> map) {
if (pos == N + 1) {
return 1;
}
String key = Arrays.toString(visited) + "-" + pos;
if (map.containsKey(key)) return map.get(key);
int count = 0;
for (int i = 1; i <= N; ++i) {
if (visited[i] == 0 && (i % pos == 0 || pos % i == 0)) {
visited[i] = 1;
count += helper(N, visited, pos + 1, map);
visited[i] = 0;
}
}
map.put(key, count);
return count;
}
}
```