int countSwaps(vector<int> arr, vector<int> sortedArr) {
    int n = arr.size();
    unordered_map<int, int> indexMap;

    // Mapping each value to its index in the sorted array
    for (int i = 0; i < n; i++)
        indexMap[sortedArr[i]] = i;

    vector<bool> visited(n, false);
    int swaps = 0;

    for (int i = 0; i < n; i++) {
        // If already visited or already in the correct position, skip
        if (visited[i] || indexMap[arr[i]] == i)
            continue;

        // Cycle detection
        int cycleSize = 0;
        int j = i;
        while (!visited[j]) {
            visited[j] = true;
            j = indexMap[arr[j]];
            cycleSize++;
        }

        // A cycle of size k requires (k-1) swaps
        if (cycleSize > 1)
            swaps += (cycleSize - 1);
    }

int lilysHomework(vector<int> arr) {
    vector<int> sortedArr = arr;

    // Sort in ascending order and count swaps
    sort(sortedArr.begin(), sortedArr.end());
    int swapsAsc = countSwaps(arr, sortedArr);

    // Sort in descending order and count swaps
    sort(sortedArr.begin(), sortedArr.end(), greater<int>());
    int swapsDesc = countSwaps(arr, sortedArr);

    // Return minimum of the two
    return min(swapsAsc, swapsDesc);
}






    return swaps;
}