You are given an array $A$ of size $N$. You have to find out number of ordered triplet $(i,j,k)$ such that $abs(A[i]-A[j])=abs(A[j]-A[k])$ where $abs$ represents absolute value.

Input:

First Line contains $N$ representing size of array.

Next line contains $N$ space separated integers representing array $A$.

Output:

Print the number of ordered triplets satisfying above conditioned modulo $10^9+7$ as answer will be large.

Constraints:

$1<=N<=10^5$

$1<=A[i]<=10^3$