CF1334F Strange Function

Let's denote the following function $ f $ . This function takes an array $ a $ of length $ n $ and returns an array. Initially the result is an empty array. For each integer $ i $ from $ 1 $ to $ n $ we add element $ a_i $ to the end of the resulting array if it is greater than all previous elements (more formally, if $ a_i > \max\limits_{1 \le j < i}a_j $ ). Some examples of the function $ f $ : 1. if $ a = [3, 1, 2, 7, 7, 3, 6, 7, 8] $ then $ f(a) = [3, 7, 8] $ ; 2. if $ a = [1] $ then $ f(a) = [1] $ ; 3. if $ a = [4, 1, 1, 2, 3] $ then $ f(a) = [4] $ ; 4. if $ a = [1, 3, 1, 2, 6, 8, 7, 7, 4, 11, 10] $ then $ f(a) = [1, 3, 6, 8, 11] $ . You are given two arrays: array $ a_1, a_2, \dots , a_n $ and array $ b_1, b_2, \dots , b_m $ . You can delete some elements of array $ a $ (possibly zero). To delete the element $ a_i $ , you have to pay $ p_i $ coins (the value of $ p_i $ can be negative, then you get $ |p_i| $ coins, if you delete this element). Calculate the minimum number of coins (possibly negative) you have to spend for fulfilling equality $ f(a) = b $ .

The first line contains one integer $ n $ $ (1 \le n \le 5 \cdot 10^5) $ — the length of array $ a $ . The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ $ (1 \le a_i \le n) $ — the array $ a $ . The third line contains $ n $ integers $ p_1, p_2, \dots, p_n $ $ (|p_i| \le 10^9) $ — the array $ p $ . The fourth line contains one integer $ m $ $ (1 \le m \le n) $ — the length of array $ b $ . The fifth line contains $ m $ integers $ b_1, b_2, \dots, b_m $ $ (1 \le b_i \le n, b_{i-1} < b_i) $ — the array $ b $ .

If the answer exists, in the first line print YES. In the second line, print the minimum number of coins you have to spend for fulfilling equality $ f(a) = b $ . Otherwise in only line print NO.