You are given n strings ti. Each string has cost ci.

Let's define the function of string , where ps,i is the number of occurrences of s in ti, |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.

The first line contains the only integer n (1 \le n \le 105) - the number of strings in t.

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

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

The last line contains n integers ci (-107 \le ci \le 107) - the cost of the i-th string.

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.