Increasing

You are given a list of integers. Your task is to count how many sublists are increasing, i.e., where each number is greater than the preceding number. Sublists of length one are counted too.

For example, if the list is $[2, 1, 3, 4]$, the increasing sublists are $[1]$, $[2]$, $[3]$, $[4]$, $[1,3]$, $[3,4]$ and $[1,3,4]$. Thus the desired answer is $7$.

In a file increasing.py, implement the function count_sublists that takes a list of numbers as a parameter and returns the count of increasing sublists.

You must implement an efficient solution with a time complexity $O(n)$. You cannot afford to go through all sublists separately. Your solution should go through the input list only once.

In the last test case of the following code template, the list is $[1,2,\dots,10^5]$ and thus all sublists are increasing. Your function should finish quickly in this test case too.

def count_sublists(numbers):
    # TODO

if __name__ == "__main__":
    print(count_sublists([2, 1, 3, 4])) # 7
    print(count_sublists([1, 2, 3, 4])) # 10
    print(count_sublists([4, 3, 2, 1])) # 4
    print(count_sublists([1, 1, 1, 1])) # 4
    print(count_sublists([1, 2, 1, 2])) # 6

    numbers = list(range(1, 10**5+1))
    print(count_sublists(numbers)) # 5000050000