1948. Good elements

You are given a sequence `A` consisting of `N` integers (not to be confused with the sequence from the previous task). We will call the `i`th sequence element good if it equals the sum of some three elements in positions strictly smaller than `i` (an element can be used more than once in the sum).

How many good elements does the sequence contain?

The first line of input contains the positive integer `N` (`1\ ≤\ N\ ≤\ 5000`), the length of the sequence `A`. The second line of input contains `N` space-separated integers representing the sequence `A` (`-100\ 000\ ≤\ A_i\ ≤\ 100\ 000`).

The first and only line of output must contain the number of good elements in the sequence.

2
1 3

1

6
1 2 3 5 7 10

4

3
-1 2 0

1