Problem Statement

For integers $A, B, C$ ( $A < B < C$ ), if they satisfy $B-A = C-B$, then $(A, B, C)$ is called a fine triplet. You are given a set of $N$ distinct positive integers $S = \{ S_1, S_2, \dots, S_N \}$. Find the number of fine triplets $(A, B, C)$ with $A, B, C \in S$.

Constraints

• All input values are integers.
• $1 \le N \le 10^6$
• $1 \le S_i \le 10^6$
• The elements of $S$ are distinct.

Input

The input is given from Standard Input in the following format:

N
S_1 S_2 \dots S_N

Output

Print the number of fine triplets as an integer.