Migrated from Lutece 2323 Help Fat_Dog Kill Bugs

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Description

As you know, dogs are very cute and lovely. However, dogs are usually bugged by ants or other small insects. Fat_Dog is one of them who is bugged. His proper name suggests that he is heavy, but he's still very cute. I believe you are willing to help him solve this problem.

Let's simplify this problem. Fat_Dog has two abilities, valued $X$ and $Y$. What's more, he has $N$ magic books, and the $i$-th book has a value $a_i$. For each book, Fat_Dog can either increase $Y$ by $a_i$ or decrease $X$ by $a_i$. Fat_Dog wants to maximize $Y^2 - X^2$ so that he can kill bugs as many as possible. Please tell him the maximum value.

Input

The first line contains three integers $N$, $X$ and $Y$ ($0 < N \leq 10^4, 0 < X \leq  Y \leq 100$).

The second line contains $N$ integers. The $i$-th number means the value of the $i$-th book $a_i$ ($0 < a_i \leq 100$).

Output

Print the maximum value of $Y^2 - X^2$.

Samples

3 1 1
1 1 1

15

Resources

电子科技大学第十一届 ACM 趣味程序设计竞赛