Total Hamming Distance
<p>The <a href="https://en.wikipedia.org/wiki/Hamming_distance" target="_blank">Hamming distance</a> between two integers is the number of positions at which the corresponding bits are different.</p>

<p>Given an integer array <code>nums</code>, return <em>the sum of <strong>Hamming distances</strong> between all the pairs of the integers in</em> <code>nums</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [4,14,2]
<strong>Output:</strong> 6
<strong>Explanation:</strong> In binary representation, the 4 is 0100, 14 is 1110, and 2 is 0010 (just
showing the four bits relevant in this case).
The answer will be:
HammingDistance(4, 14) + HammingDistance(4, 2) + HammingDistance(14, 2) = 2 + 2 + 2 = 6.
</pre>

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

<pre>
<strong>Input:</strong> nums = [4,14,4]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li>The answer for the given input will fit in a <strong>32-bit</strong> integer.</li>
</ul>
Bit Manipulation; Array; Math
impl Solution {
    pub fn total_hamming_distance(nums: Vec<i32>) -> i32 {
        let mut ans = 0;
        for i in 0..32 {
            let mut a = 0;
            for &x in nums.iter() {
                a += (x >> i) & 1;
            }
            let b = (nums.len() as i32) - a;
            ans += a * b;
        }
        ans
    }
}
