There are N stacks of boxes, all boxes have same dimensions as 1 unit. The height of a stack is defined as the number of boxes in it. The initial height of i^th stack is given as h_i We need to equalize the heights of stacks by adding, removing or moving the boxes accross the stacks.

The cost of each operation is defined as following:

1. Add a box on top of a stack costs A

2. Remove a box from top of a non-empty stack costs R

3. Moving a box from top of non-empty stack to top of another stack costs M

Input

First line contains one integer N

Second line contains 3 integers the costs A, R, M

Thrid line contains the N integers as heights  h_i for i^th stack. 

1 <= N <= 10⁵

0 <= A, R, M <= 10⁴

0 <= h_i <= 10⁹

Output

One integer in a line - the minimum cost of equalising the heights of all stack by using above operations

Example

Input:
5 

1 2 2

5 5 3 6 5
Output:
3

(Move 1 box from 4th stack to 3rd stack now height are  (cost - 2) -> 5 5 4 5 5 -> now add one box on 3rd stack (cost -1) , total cost=3