Problem Statement

You are given two integer sequences of length $N$, $A = (A_1, A_2, \ldots, A_N)$ and $B = (B_1, B_2, \ldots, B_N)$, each consisting of $0$ and $1$.

You can perform the following operation on $A$ any number of times (possibly zero):

1. First, choose an integer $i$ satisfying $1 \leq i \leq N$, and flip the value of $A_i$ (if the original value is $0$, change it to $1$; if it is $1$, change it to $0$).
2. Then, pay $\sum_{k=1}^N A_k C_k$ yen as the cost of this operation.

Note that the cost calculation in step 2 uses the $A$ after the change in step 1.

Print the minimum total cost required to make $A$ identical to $B$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $A_i, B_i \in {0, 1}$
• $1 \leq C_i \leq 10^6$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_N
C_1 C_2 \ldots C_N

Output

Print the answer.