Beautiful Arrangement LeetCode solution in Java

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class Solution {
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  int N;
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  Integer[][] memo;
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  public int countArrangement(int n) {
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    this.N = n;
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    memo = new Integer[n + 1][1 << N];
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    return permute(1, 0);
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  }
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  private int permute(int index, int mask) {
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    if (mask == (1 << N) - 1) return 1;
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    if (memo[index][mask] != null) return memo[index][mask];
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    int res = 0;
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    for (int i = 1; i <= N; i++) {
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      if ((mask & (1 << (i - 1))) == 0 && (index % i == 0 || i % index == 0)) {
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        mask |= (1 << (i - 1));
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        res += permute(index + 1, mask);
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        mask ^= (1 << (i - 1));
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      }
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    }
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    return memo[index][mask] = res;
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  }
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}