102633: [AtCoder]ABC263 D - Left Right Operation

Problem Statement

You are given an integer sequence of length $N$: $A=(A_1,A_2,\ldots,A_N)$.

You will perform the following consecutive operations just once:

• Choose an integer $x$ $(0\leq x \leq N)$. If $x$ is $0$, do nothing. If $x$ is $1$ or greater, replace each of $A_1,A_2,\ldots,A_x$ with $L$.

• Choose an integer $y$ $(0\leq y \leq N)$. If $y$ is $0$, do nothing. If $y$ is $1$ or greater, replace each of $A_{N},A_{N-1},\ldots,A_{N-y+1}$ with $R$.

Print the minimum possible sum of the elements of $A$ after the operations.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $-10^9 \leq L, R\leq 10^9$
• $-10^9 \leq A_i\leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $L$ $R$
$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

5 4 3
5 5 0 6 3

Sample Output 1

14

If you choose $x=2$ and $y=2$, you will get $A = (4,4,0,3,3)$, for the sum of $14$, which is the minimum sum achievable.

Sample Input 2

4 10 10
1 2 3 4

Sample Output 2

10

If you choose $x=0$ and $y=0$, you will get $A = (1,2,3,4)$, for the sum of $10$, which is the minimum sum achievable.

Sample Input 3

10 -5 -3
9 -6 10 -1 2 10 -1 7 -15 5

Sample Output 3

-58

$L$, $R$, and $A_i$ may be negative.

问题描述

给你一个长度为$N$的整数序列$A=(A_1,A_2,\ldots,A_N)$。

你只需执行一次以下连续操作：

• 选择一个整数$x$ $(0\leq x \leq N)$。如果$x$为0，则不做任何操作。如果$x$为1或更大，则将$A_1,A_2,\ldots,A_x$替换为$L$。

• 选择一个整数$y$ $(0\leq y \leq N)$。如果$y$为0，则不做任何操作。如果$y$为1或更大，则将$A_{N},A_{N-1},\ldots,A_{N-y+1}$替换为$R$。

输出操作后$A$的元素和的最小值。

限制条件

• $1 \leq N \leq 2\times 10^5$
• $-10^9 \leq L, R\leq 10^9$
• $-10^9 \leq A_i\leq 10^9$
• 输入中的所有值都是整数。

输入

输入从标准输入中给出以下格式：

$N$ $L$ $R$
$A_1$ $A_2$ $\ldots$ $A_N$

输出

输出答案。

样例输入1

5 4 3
5 5 0 6 3

样例输出1

14

如果选择$x=2$和$y=2$，你将得到$A = (4,4,0,3,3)$，元素和为14，这是可以达到的最小和。

样例输入2

4 10 10
1 2 3 4

样例输出2

10

如果选择$x=0$和$y=0$，你将得到$A = (1,2,3,4)$，元素和为10，这是可以达到的最小和。

样例输入3

10 -5 -3
9 -6 10 -1 2 10 -1 7 -15 5

样例输出3

-58

$L$，$R$和$A_i$可能为负数。