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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def left_right_inversions(tab):
 """ Compute left and right inversions of each element of a table. :param tab: list with comparable elements :returns: lists left and right. left[j] = the number of i<j such that tab[i] > tab[j]. right[i] = the number of i<j such that tab[i] > tab[j]. :complexity: `O(n \log n)` """

    n = len(tab)
    left = [0] * n
    right = [0] * n
    tmp = [None] * n      # temporary table
    rank = list(range(n))
    _merge_sort(tab, tmp, rank, left, right, 0, n)
    return left, right