Expensive Strings

Description:

Input:

The first line contains the only integer n (1 ≤ n ≤ 10⁵) — the number of strings in t.

Each of the next n lines contains contains a non-empty string t_i. t_i contains only lowercase English letters.

It is guaranteed that the sum of lengths of all strings in t is not greater than 5·10⁵.

The last line contains n integers c_i ( - 10⁷ ≤ c_i ≤ 10⁷) — the cost of the i-th string.

Output:

Print the only integer a — the maximal value of the function f(s) over all strings s. Note one more time that the string s is not necessarily from t.

Sample Input:

2
aa
bb
2 1

Sample Output:

4

Sample Input:

2
aa
ab
2 1

Sample Output:

5