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F. Strange Function
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$f(a) = b$$$.

Input

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 $$$b$$$.

Output

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.

Examples
Input
11
4 1 3 3 7 8 7 9 10 7 11
3 5 0 -2 5 3 6 7 8 2 4
3
3 7 10
Output
YES
20
Input
6
2 1 5 3 6 5
3 -9 0 16 22 -14
4
2 3 5 6
Output
NO