Let's turn the input into triples T_i = (A_i, B_i, C_i).

Sort the triples into increasing order by C_i.

In addition, we'll make a set of pairs of integers, initially empty. We'll store pairs {A_j, B_j} here, keeping the invariant that there are no two pairs {A_j, B_j} and {A_i, B_i} in the set such that A_j < A_i and B_j < B_i.

Now loop from i = n - 1 to i = 0. At every i, Find from the set the smallest element that is larger than or equal to {A_i, B_i}. Let's say that element is {A_j, B_j}.

Since the pair is larger than equal to {A_i, B_i}, A_j > A_i. Then just check if B_j > B_i. If it is, this i won't be counted, since T_j is larger at all three parts.

Otherwise, we'll increment the result by one, and add {A_i, B_i} to the set. To maintain the invariant, while the largest pair that is smaller than {A_i, B_i} in the set is also smaller in its B-part, we'll remove it. We insert at most n elements into the set, and each element obviously gets removed at most once, so this part doesn't affect the overall complexity.

In the end just output the result. total time complexity is .