AT_abc400_f [ABC400F] Happy Birthday! 3

There is a circular cake that has been cut into $ N $ equal slices by its radii. Each piece is labeled with an integer from $ 1 $ to $ N $ in clockwise order, and for each integer $ i $ with $ 1 \leq i \leq N $ , the piece $ i $ is also referred to as piece $ N + i $ . Initially, every piece’s color is color $ 0 $ . You can perform the following operation any number of times: - Choose integers $ a $ , $ b $ , and $ c $ such that $ 1 \leq a, b, c \leq N $ . For each integer $ i $ with $ 0 \leq i < b $ , change the color of piece $ a + i $ to color $ c $ . The cost of this operation is $ b + X_c $ . You want each piece $ i $ (for $ 1 \leq i \leq N $ ) to have color $ C_i $ . Find the minimum total cost of operations needed to achieve this.

The input is given from Standard Input in the following format: > $ N $ $ C_1 $ $ C_2 $ $ \ldots $ $ C_N $ $ X_1 $ $ X_2 $ $ \ldots $ $ X_N $

Print the answer.

### Sample Explanation 1 Let $ A_i $ denote the color of piece $ i $ . Initially, $ (A_1, A_2, A_3, A_4, A_5, A_6) = (0, 0, 0, 0, 0, 0) $ . Performing an operation with $ (a, b, c) = (2, 1, 4) $ changes $ (A_1, A_2, A_3, A_4, A_5, A_6) $ to $ (0, 4, 0, 0, 0, 0) $ . Performing an operation with $ (a, b, c) = (3, 3, 2) $ changes $ (A_1, A_2, A_3, A_4, A_5, A_6) $ to $ (0, 4, 2, 2, 2, 0) $ . Performing an operation with $ (a, b, c) = (1, 1, 1) $ changes $ (A_1, A_2, A_3, A_4, A_5, A_6) $ to $ (1, 4, 2, 2, 2, 0) $ . Performing an operation with $ (a, b, c) = (4, 1, 1) $ changes $ (A_1, A_2, A_3, A_4, A_5, A_6) $ to $ (1, 4, 2, 1, 2, 0) $ . Performing an operation with $ (a, b, c) = (6, 1, 5) $ changes $ (A_1, A_2, A_3, A_4, A_5, A_6) $ to $ (1, 4, 2, 1, 2, 5) $ . In this case, the total cost is $ 5 + 5 + 2 + 2 + 6 = 20 $ . ### Constraints - $ 1 \leq N \leq 400 $ - $ 1 \leq C_i \leq N $ - $ 1 \leq X_i \leq 10^9 $ - All input values are integers.