function countSwap(arr, sortedArr) {
    let swapCount = 0
    const visited = []
    for (let i = 0; i < arr.length; i++) {
        if (arr[i] === sortedArr[i][0]) {
            visited[i] = true
            continue
        }
        let pCount = 0; // permutations
        let j = i;
        while(!visited[j]) {
            pCount ++
            visited[j] = true
            j = sortedArr[j][1]
        }
        if (pCount > 1) swapCount += pCount - 1  // this math based on Permutation Cycle Decomposition
    }
    
    return swapCount
}
function lilysHomework(arr) {
    // Write your code here
    const pArr = arr.map((e, i) => [e, i]) // add position to arr
    const aSorted = mergeSort(pArr, true) // ascending sorting, you can choose any sort algo
    const dSorted = mergeSort(pArr, false) // descending sorting
    
    let aSwapCount = countSwap(arr, aSorted)
    let dSwapCount = countSwap(arr, dSorted)
    
    return Math.min(aSwapCount, dSwapCount)
}