There are n bits. Each bit i has a value a_i (0 or 1) and an associated cost c_i. We can change the value of bit i with a cost computed as the sum of all the costs c_j of the bits j such that a_j = 1 AFTER bit i is changed. What is the minimum amount that should be paid to set each bit i to a specified value b_i.

입력 형식

The first line contains the integer n (1 ≤ n ≤ 5 x 10³) - the number of bits</p>

The second line contains n integers c_i (1 ≤ c_i ≤ 10⁹) - the costs associated with the bits

The third line contains the original n values of the bits a_i - the original values of the bits

The fourth line contains the required n values of the bits b_i - the required values of the bits 

출력 형식

Print one number - the minimum cost.

예제 입력

5
5 2 6 1 5
01110
10011

예제 출력

21