Farmer John is building a nicely-landscaped garden, and needs to move a large
amount of dirt in the process.

The garden consists of a sequence of \(N\) flowerbeds (\(1 \leq N \leq 100,000\)),
where flowerbed \(i\) initially contains \(A_i\) units of dirt. Farmer John would
like to re-landscape the garden so that each flowerbed \(i\) instead contains
\(B_i\) units of dirt. The \(A_i\)'s and \(B_i\)'s are all integers in the range
\(0 \ldots 10\).

To landscape the garden, Farmer John has several options: he can purchase one
unit of dirt and place it in a flowerbed of his choice for \(X\) units of money.
He can remove one unit of dirt from a flowerbed of his choice and have it
shipped away for \(Y\) units of money. He can also transport one unit of dirt
from flowerbed \(i\) to flowerbed \(j\) at a cost of \(Z\) times \(|i-j|\). Please
compute the minimum total cost for Farmer John to complete his landscaping
project.

Problem credits: Brian Dean

Problem credits: Brian Dean

The first line of input contains \(N\), \(X\), \(Y\), and \(Z\)
(\(0 \leq X, Y \le 10^8; 0 \le Z \leq 1000\)). Line \(i+1\) contains the integers \(A_i\) and \(B_i\).

Please print the minimum total cost FJ needs to spend on landscaping.

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출처 올림피아드 > USACO > 2015-2016 > US Open > Platinum