A border outpost has n sentry towers standing in a row, each with a current height. Certain towers are marked as command towers -- each command tower must be strictly taller than every immediate neighbor tower next to it in the row, so that its watch commander always has the clearest sightline. Heights may only be raised (never lowered), and raising any single tower by one unit costs exactly 1 unit of construction material.

Given the tower heights and the list of command tower positions, determine the minimum total units of material needed to raise towers so that every command tower ends up strictly taller than each of its immediate neighbors. If no amount of raising can achieve this (which happens when two command towers are directly next to each other, since neither can ever be simultaneously strictly taller than the other), report that it is impossible.

Input format

• Line 1: a single integer n, the number of sentry towers.
• Line 2: n space-separated integers, the current height of each tower, indexed 0 to n-1 left to right.
• Line 3: a single integer m, the number of command towers.
• Line 4: m space-separated integers in strictly increasing order, the 0-indexed positions of the command towers (this line is empty when m is 0).

Output format

A single integer: the minimum total units of height that must be added across all towers, or -1 if it is impossible.

Constraints

• 1 <= n <= 2*10^5
• 0 <= tower height <= 10^9
• 0 <= m <= n
• command tower positions are distinct, strictly increasing, and within [0, n-1]

5
3 1 4 1 5
2
1 3

9

4
10 10 10 10
2
0 1

-1