Garden Soil Adjustment

Farmer John is planning to build a new garden which has $N$ flowerbeds. In the $i$-th flowerbed, there are currently $A_i$ units of soil, but he needs exactly $B_i$ units. To achieve this, he can perform the following operations:

• Buy one unit of soil and add it to a specified flowerbed at a cost of $X$.
• Remove one unit of soil from any flowerbed at a cost of $Y$.
• Move one unit of soil from flowerbed $i$ to flowerbed $j$ at a cost of $Z|i-j|$.

It is guaranteed that $1\le N \le 10^5$ and $0 \le A_i, B_i \le 10$. Note that moving soil might be cheaper than removing soil from one bed and buying soil for another if $Z|i-j|

Your task is to compute the minimum total cost needed to adjust the amounts of soil in all flowerbeds to meet the desired configuration.

A useful approach is to calculate the difference $D_i = A_i - B_i$ for each flowerbed. Positive values mean extra soil that may be removed or transported to other flowerbeds, while negative values indicate a deficit that may be compensated by buying soil. One can then consider the prefix sums $f_i = \sum_{j=1}^{i} D_j$ and derive the cost of transporting soil along the line. In particular, one strategy is:

$$cost_1 = \sum_{i=1}^{N-1} Z|f_i| + \begin{cases} f_N \cdot Y, & \text{if } f_N \ge 0\\ -f_N \cdot X, & \text{if } f_N < 0 \end{cases} $$

Alternatively, if transferring is too expensive, one can handle each flowerbed independently:

$$cost_2 = \sum_{i=1}^{N}\begin{cases} (A_i - B_i)\cdot Y, & \text{if } A_i > B_i\\ (B_i - A_i)\cdot X, & \text{if } A_i < B_i \end{cases} $$

The answer is the minimum of these two costs.

inputFormat

The first line contains four integers $N$, $X$, $Y$, and $Z$, where $1\le N\le10^5$.
The second line contains $N$ integers $A_1, A_2, \dots, A_N$ representing the current soil units in each flowerbed.
The third line contains $N$ integers $B_1, B_2, \dots, B_N$ representing the desired soil units.

outputFormat

Output a single integer representing the minimum cost required to adjust the soil levels to the desired configuration.

sample

2 1 1 1
5 0
0 5

5