You are given n strings t_i. Each string has cost c_i.

Let's define the function of string $\text{[math]}$ , where p_s, i is the number of occurrences of s in t_i, |s| is the length of the string s. Find the maximal value of function f(s) over all strings.

Note that the string s is not necessarily some string from t.

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.

Expensive Strings

Examples