CF1355E.Restorer Distance

You have to restore the wall. The wall consists of $N$ pillars of bricks, the height of the $i$-th pillar is initially equal to $h_{i}$, the height is measured in number of bricks. After the restoration all the $N$ pillars should have equal heights.

You are allowed the following operations:

• put a brick on top of one pillar, the cost of this operation is $A$;
• remove a brick from the top of one non-empty pillar, the cost of this operation is $R$;
• move a brick from the top of one non-empty pillar to the top of another pillar, the cost of this operation is $M$.

You cannot create additional pillars or ignore some of pre-existing pillars even if their height becomes $0$.

What is the minimal total cost of restoration, in other words, what is the minimal total cost to make all the pillars of equal height?

你需要修复这堵墙。这堵墙由 $N$ 根砖柱组成，第 $i$ 根柱子的初始高度为 $h_{i}$（以砖块数量计量）。修复完成后，所有 $N$ 根柱子的高度必须相等。

你被允许执行以下操作：

• 在某一根柱子顶部放置一块砖，该操作花费为 $A$；
• 从一根非空柱子的顶部移除一块砖，该操作花费为 $R$；
• 将一块砖从一根非空柱子的顶部移动到另一根柱子的顶部，该操作花费为 $M$。

你不能新增柱子，也不能忽略任何已存在的柱子（即使其高度变为 $0$）。

修复这堵墙所需的最小总花费是多少？换言之，使所有柱子高度相等所需的最小总花费是多少？

The first line of input contains four integers $N$, $A$, $R$, $M$ ($1 \le N \le 10^{5}$, $0 \le A, R, M \le 10^{4}$) — the number of pillars and the costs of operations.

The second line contains $N$ integers $h_{i}$ ($0 \le h_{i} \le 10^{9}$) — initial heights of pillars.

输入的第一行包含四个整数 $N$、$A$、$R$、$M$（$1 \le N \le 10^{5}$，$0 \le A, R, M \le 10^{4}$）——分别表示柱子的数量以及各操作的代价。

第二行包含 $N$ 个整数 $h_{i}$（$0 \le h_{i} \le 10^{9}$）——表示各柱子的初始高度。

Print one integer — the minimal cost of restoration.

输出一个整数——修复的最小代价。