def merge_sort_and_count_inversions(arr):
if len(arr) <= 1:
return arr, 0
mid = len(arr)
left, inversions_left = merge_sort_and_count_inversions(arr[:mid])
right, inversions_right = merge_sort_and_count_inversions(arr[mid:])
merged, inversions = merge_and_count_inversions(left, right)
total_inversions = inversions + inversions_left + inversions_right
return merged, total_inversions
def merge_and_count_inversions(left, right):
result = []
inversions = 0
i = j = 0
while i < len(left) and j < len(right):
if left[i] <= right[j]:
result.append(left[i])
i += 1
else:
result.append(right[j])
j += 1
inversions += len(left) - i
result.extend(left[i:])
result.extend(right[j:])
return result, inversions