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.