<p>Given an integer array <code>nums</code>, return<em> an integer array </em><code>counts</code><em> where </em><code>counts[i]</code><em> is the number of smaller elements to the right of </em><code>nums[i]</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [5,2,6,1]
<strong>Output:</strong> [2,1,1,0]
<strong>Explanation:</strong>
To the right of 5 there are <b>2</b> smaller elements (2 and 1).
To the right of 2 there is only <b>1</b> smaller element (1).
To the right of 6 there is <b>1</b> smaller element (1).
To the right of 1 there is <b>0</b> smaller element.
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1]
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1,-1]
<strong>Output:</strong> [0,0]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    struct ArrayValWithOrigIdx {
    int val;
    int originalIdx;

    ArrayValWithOrigIdx(int v, int idx) : val(v), originalIdx(idx) {}
};

// Function to count smaller numbers after self
vector<int> countSmaller(const std::vector<int>& nums) {
    if (nums.empty()) return std::vector<int>();

    int n = nums.size();
    std::vector<int> result(n, 0);
    std::vector<ArrayValWithOrigIdx> newNums;

    for (int i = 0; i < n; ++i) {
        newNums.emplace_back(nums[i], i);
    }

    mergeSortAndCount(newNums, 0, n - 1, result);

    return result;
}

// Merge sort and count function
void mergeSortAndCount(std::vector<ArrayValWithOrigIdx>& nums, int start, int end, vector<int>& result) {
    if (start >= end) return;

    int mid = (start + end) / 2;
    mergeSortAndCount(nums, start, mid, result);
    mergeSortAndCount(nums, mid + 1, end, result);

    int leftPos = start;
    int rightPos = mid + 1;
    std::deque<ArrayValWithOrigIdx> merged;
    int numElemsRightArrayLessThanLeftArray = 0;

    while (leftPos <= mid && rightPos <= end) {
        if (nums[leftPos].val > nums[rightPos].val) {
            ++numElemsRightArrayLessThanLeftArray;
            merged.push_back(nums[rightPos]);
            ++rightPos;
        } else {
            result[nums[leftPos].originalIdx] += numElemsRightArrayLessThanLeftArray;
            merged.push_back(nums[leftPos]);
            ++leftPos;
        }
    }

    while (leftPos <= mid) {
        result[nums[leftPos].originalIdx] += numElemsRightArrayLessThanLeftArray;
        merged.push_back(nums[leftPos]);
        ++leftPos;
    }

    while (rightPos <= end) {
        merged.push_back(nums[rightPos]);
        ++rightPos;
    }

    int pos = start;
    for (const auto& m : merged) {
        nums[pos++] = m;
    }
}
};
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