Solution.java

class Solution {
    private int n;
    private int ans;
    private boolean[] vis;
    private Map<Integer, List<Integer>> match;

    public int countArrangement(int n) {
        this.n = n;
        ans = 0;
        vis = new boolean[n + 1];
        match = new HashMap<>();
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (i % j == 0 || j % i == 0) {
                    match.computeIfAbsent(i, k -> new ArrayList<>()).add(j);
                }
            }
        }
        dfs(1);
        return ans;
    }

    private void dfs(int i) {
        if (i == n + 1) {
            ++ans;
            return;
        }
        if (!match.containsKey(i)) {
            return;
        }
        for (int j : match.get(i)) {
            if (!vis[j]) {
                vis[j] = true;
                dfs(i + 1);
                vis[j] = false;
            }
        }
    }
}