Description

Input

The first line contains one integer n (1 ≤ n ≤ 200000) — the number of elements in a.

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹) — elements of the array.

Output

Print one integer — the sum of d(a_i, a_j) over all pairs (i, j) such that 1 ≤ i ≤ j ≤ n.

Samples

5
1 2 3 1 3

4

4
6 6 5 5

0

4
6 6 4 4

-8

Note

In the first example:

1. d(a₁, a₂) = 0;
2. d(a₁, a₃) = 2;
3. d(a₁, a₄) = 0;
4. d(a₁, a₅) = 2;
5. d(a₂, a₃) = 0;
6. d(a₂, a₄) = 0;
7. d(a₂, a₅) = 0;
8. d(a₃, a₄) =  - 2;
9. d(a₃, a₅) = 0;
10. d(a₄, a₅) = 2.