Frederic Edward Xavier runs a very successful delivery company called FredEX. He’s been looking at driving records lately, and is not happy with the costs of delivery.
He has made the following estimations:
Driving from one intersection to the neighboring one costs $B$ dollars
Going straight through an intersection costs $S$ dollars
Turning right in an intersection costs $R$ dollars
Turning left in an intersection costs $L$ dollars
Delivering a package is free, but you still pay the cost for the turn/going straight in that intersection.
FredEX operates in a city where the streets make up an infinite grid of square blocks, with intersections numbered from $(-\infty ,-\infty )$ to $(\infty ,\infty )$. Lower numbers on the $x$ axis are to the left, and lower numbers on the $y$ axis are down. The truck starts at the intersection $(0, 0)$ but you may choose which direction it should face. There are $N$ packages that must be delivered in a specific order. The truck cannot go in reverse, and cannot perform U-turns to go back the way it came. Help Frederic find out the cheapest way to deliver all $N$ packages.
The first line of the input is a line with five space-separated integers $B$, $S$, $R$, $L$ and $N$.
Then follow $N$ lines, each with two space-separated integers $X_ i$ and $Y_ i$, the $x$ and $y$ coordinates of the intersection for delivering package number $i$. The packages are listed in the order they must be delivered.
Output the minimum cost of delivering all packages.
$1 \leq S, R, L, B \leq 100$
$1 \leq N \leq 30\, 000$
$-5 \leq X_ i, Y_ i \leq 5$
|Sample Input 1||Sample Output 1|
1 1 1 10 2 2 2 1 2