You are given an array of ~N~ integers ~v_1, v_2, \dots, v_N~. You can increase any element by ~1~ at a cost of ~A~ or decrease any element by ~1~ at a cost of ~B~. Determine the minimum cost to make all elements of the array distinct. The values are allowed to be decreased so that they are negative.

Constraints

For all subtasks:

~1 \le N \le 2\,000~

~1 \le A, B \le 1\,000\,000~

Subtask 1 [30%]

~1 \le v_i \le 2\,000~

Subtask 2 [70%]

~1 \le v_i \le 1\,000\,000\,000~

Input Specification

The first line will contain a single integer, ~N~.
The second line will contain two space-separated integers, ~A~ and ~B~ in that order.
The third and final line will contain ~N~ space-separated integers, ~v_1, v_2, \dots, v_N~.

Output Specification

Output a single integer, the minimum cost required.

Sample Input

5
4 2
6 5 6 6 5

Sample Output

12