def removeOverlapping(arr, sortedArr):
    numToIdx = {n: idx for n, idx in zip(arr, range(len(arr)))}
    swaps = 0
    
    for sIdx in range(len(sortedArr)):
        if sortedArr[sIdx] == arr[sIdx]:
            continue
        else:
            swappedOutItem = arr[sIdx]
            arr[sIdx] = sortedArr[sIdx]
            arr[numToIdx[sortedArr[sIdx]]] = swappedOutItem
            numToIdx[swappedOutItem] = numToIdx[sortedArr[sIdx]]
            numToIdx[sortedArr[sIdx]] = sIdx
            swaps += 1
    return swaps
        
def lilysHomework(arr):
    sortedArr = sorted(arr, reverse=True)
    return min(removeOverlapping(list(arr), sortedArr) , removeOverlapping(arr, list(reversed(sortedArr))))