Problem2363--Expensive Strings

2363: Expensive Strings

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
6 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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.

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 ti. ti contains only lowercase English letters.

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

The last line contains n integers ci (-107≤ci≤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.

Examples
Input
2
aa
bb
2 1
Output
4
Input
2
aa
ab
2 1
Output
5

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