Travelling by car - 2
There are n cities. You want to travel from city 1 to city n by car. To do this you have to buy some gasoline. It is known that a liter of gasoline costs cost[k]
in the k-th city. Initially your fuel tank is empty and you spend one liter of gasoline per kilometer. Cities are located on the same line in ascending order with k-th city having coordinate x[k]
. Also you have to pay toll[k]
to enter k-th city. Your task is to make the trip with minimum possible cost.
Input
First line contains number of cities n (1 ≤ n ≤ 10^5
).
Second line contains n coordinates of cities x[1]
, ..., x[n]
. Coordinates are unique and sorted, x[i]
< x[i+1]
for each i = 1, 2, ..., n - 1.
Third line contains n integers - the gasoline costs cost[1]
, ..., cost[n]
.
Fourth line contains n integers - the entrance payments toll[1]
, ..., toll[n]
.
Its is knows that cities coordinates, gasoline costs and entrance payments are nonnegative integers, not greater than 10^9
.
Output
Print the minimum possible cost to make the trip.