# Travelling by car

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 $n(1≤n≤1000)$.

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.