P13421 [COCI 2012/2013 #6] DOBRI

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 $N$ ($1 \leq N \leq 5000$), the length of the sequence A. The second line of input contains $N$ space-separated integers representing the sequence A ($-100\,000 \leq A_i \leq 100\,000$).

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

In test data worth at least $40\%$ of total points, $N \leq 50$. In test data worth at least $70\%$ of total points, $N \leq 500$.