AT_arc194_c [ARC194C] Cost to Flip

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 $ .

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 $

Print the answer.

### Sample Explanation 1 Consider the following procedure: - First, flip $ A_4 $ . Now, $ A = (0, 1, 1, 0) $ . The cost of this operation is $ 0 \times 4 + 1 \times 6 + 1 \times 2 + 0 \times 9 = 8 $ yen. - Next, flip $ A_2 $ . Now, $ A = (0, 0, 1, 0) $ . The cost of this operation is $ 0 \times 4 + 0 \times 6 + 1 \times 2 + 0 \times 9 = 2 $ yen. - Finally, flip $ A_1 $ . Now, $ A = (1, 0, 1, 0) $ , which matches $ B $ . The cost of this operation is $ 1 \times 4 + 0 \times 6 + 1 \times 2 + 0 \times 9 = 6 $ yen. In this case, the total cost is $ 8 + 2 + 6 = 16 $ yen, which is the minimum possible. ### Sample Explanation 2 $ A $ and $ B $ are already identical initially, so there is no need to perform any operations. ### 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.