Score : $400$ points
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.
Input is given from Standard Input in the following format:
$N$ $L$ $R$ $A_1$ $A_2$ $\ldots$ $A_N$
Print the answer.
5 4 3 5 5 0 6 3
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.
4 10 10 1 2 3 4
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.
10 -5 -3 9 -6 10 -1 2 10 -1 7 -15 5
-58
$L$, $R$, and $A_i$ may be negative.