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public class Solution {
    private int count = 0;
    private void helper(int N, int pos, boolean[] used) {
        if (pos > N) {
            count++;
            return;
        }
        for (int i = 1; i <= N; i++) {
            if (!used[i] && (i % pos == 0 || pos % i == 0)) {
                used[i] = true;
                helper(N, pos + 1, used);
                used[i] = false;
            }
        }
        
        
    }
    public int countArrangement(int N) {
        if (N == 0) return count;
        boolean[] used = new boolean[N + 1];
        helper(N, 1, used);
        return count;
    }
}

public class Solution {
    private int count = 0;
    private void swap(int[] nums, int i, int j) {
        int tmp = nums[i];
        nums[i] = nums[j];
        nums[j] = tmp;
    }
    private void helper(int[] nums, int start) {
        if (start == 0) {
            count++;
            return;
        }
        for (int i = start; i > 0; i--) {
            swap(nums, start, i);
            if (nums[start] % start == 0 || start % nums[start] == 0) helper(nums, start-1);
            swap(nums,i, start);
        }
    }
    public int countArrangement(int N) {
        if (N == 0) return 0;
        int[] nums = new int[N+1];
        for (int i = 0; i <= N; i++) nums[i] = i;
        helper(nums, N);
        return count;
    }
}