Insert an element into a sorted list, and keep the list sorted.

        The major difference from bisect.bisect_left is that this function supports a key method, so user doesn't have
        to create the key array for each insertion.

        :param list lst: The list. Must be pre-ordered.
        :param object element: An element to insert into the list.
        :param func key: A method to get the key for each element in the list.
        :param int lo: Lower bound of the search.
        :param int hi: Upper bound of the search.
        :return: None

def _binary_insert(lst, elem, key, lo=0, hi=None):
        """
        Insert an element into a sorted list, and keep the list sorted.

        The major difference from bisect.bisect_left is that this function supports a key method, so user doesn't have
        to create the key array for each insertion.

        :param list lst: The list. Must be pre-ordered.
        :param object element: An element to insert into the list.
        :param func key: A method to get the key for each element in the list.
        :param int lo: Lower bound of the search.
        :param int hi: Upper bound of the search.
        :return: None
        """

        if lo < 0:
            raise ValueError("lo must be a non-negative number")

        if hi is None:
            hi = len(lst)

        while lo < hi:
            mid = (lo + hi) // 2
            if key(lst[mid]) < key(elem):
                lo = mid + 1
            else:
                hi = mid

        lst.insert(lo, elem)