You are given a set of \(N\) strings. Your task is to determine the minimum possible size of set \(S\) (\(S\) is a subset of \(N\) strings) such that it meets the following conditions:

• All \(N\) strings must be covered by set \(S\)
• A string \(P\) is said to be covered by the set \(S\) if either \(P\) exists in \(S\) or any substring of \(P\) exists in \(S\).

Input Format:

• First line contains an integer \(N\)
• Next \(N\) lines contains a string \(P\)

Output Format:

Print the minimum possible size of set \(S\) , which covers all the \(N\) strings.

Constraints:

\(1 \le N \le 500 \\ 1 \le |P| \le 500\)