<p>Given an integer array nums, return <em>the number of <strong>AND triples</strong></em>.</p>

<p>An <strong>AND triple</strong> is a triple of indices <code>(i, j, k)</code> such that:</p>

<ul>
	<li><code>0 &lt;= i &lt; nums.length</code></li>
	<li><code>0 &lt;= j &lt; nums.length</code></li>
	<li><code>0 &lt;= k &lt; nums.length</code></li>
	<li><code>nums[i] &amp; nums[j] &amp; nums[k] == 0</code>, where <code>&amp;</code> represents the bitwise-AND operator.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,1,3]
<strong>Output:</strong> 12
<strong>Explanation:</strong> We could choose the following i, j, k triples:
(i=0, j=0, k=1) : 2 &amp; 2 &amp; 1
(i=0, j=1, k=0) : 2 &amp; 1 &amp; 2
(i=0, j=1, k=1) : 2 &amp; 1 &amp; 1
(i=0, j=1, k=2) : 2 &amp; 1 &amp; 3
(i=0, j=2, k=1) : 2 &amp; 3 &amp; 1
(i=1, j=0, k=0) : 1 &amp; 2 &amp; 2
(i=1, j=0, k=1) : 1 &amp; 2 &amp; 1
(i=1, j=0, k=2) : 1 &amp; 2 &amp; 3
(i=1, j=1, k=0) : 1 &amp; 1 &amp; 2
(i=1, j=2, k=0) : 1 &amp; 3 &amp; 2
(i=2, j=0, k=1) : 3 &amp; 2 &amp; 1
(i=2, j=1, k=0) : 3 &amp; 1 &amp; 2
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [0,0,0]
<strong>Output:</strong> 27
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt; 2<sup>16</sup></code></li>
</ul>

class Solution {
public:
    int countTriplets(vector<int>& nums) {
        int res = 0;

        int n = nums.size();
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                for (int k = j; k < n; k++) {
                    if ((nums[i] & nums[j] & nums[k]) == 0) {
                        if (i == j && j == k) {
                            res += 1;
                        } else if (i == j || j == k || k == i) {
                            res += 3;
                        } else {
                            res += 6;
                        }
                    }
                }
            }
        }

        return res;
    }
};
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