All subsequences

You are given a list of $n$ integers. Your task is to count how many increasing subsequences does the list contain.

You may assume that $1 \le n \le 100$. The algorithm should be efficient in all these cases.

In a file countseq.py, implement a function count that returns the desired answer.

def count(t):
    # TODO

if __name__ == "__main__":
    print(count([1, 1, 2, 2, 3, 3])) # 26
    print(count([1, 1, 1, 1])) # 4
    print(count([5, 4, 3, 2, 1])) # 5
    print(count([4, 1, 5, 6, 3, 4, 1, 8])) # 37

Explanation: The list $[1,1,2,2,3,3]$ contains the increasing subsequences $[1,2,3]$ ($8$ times), $[1,2]$ ($4$ times), $[1,3]$ ($4$ times), $[2,3]$ ($4$ times), $[1]$ ($2$ times), $[2]$ ($2$ times) and $[3]$ ($2$ times).