Merge Sort Big O

def merge_sort(nums: list[int]) -> list[int]:
    if len(nums) < 2:
        return nums
    first = merge_sort(nums[: len(nums) // 2])
    second = merge_sort(nums[len(nums) // 2 :])
    return merge(first, second)


def merge(first: list[int], second: list[int]) -> list[int]:
    final = []
    i = 0
    j = 0
    while i < len(first) and j < len(second):
        if first[i] <= second[j]:
            final.append(first[i])
            i += 1
        else:
            final.append(second[j])
            j += 1
    while i < len(first):
        final.append(first[i])
        i += 1
    while j < len(second):
        final.append(second[j])
        j += 1
    return final