Book Title Catalog — Count Titles That Are Prefix of Another

Given a list of book titles titles, count the ordered index pairs (i,j) such that i≠j and titles[i] is a prefix of titles[j]. Identical titles at different indices also count as prefixes.

输入格式

The first line contains n (1≤n≤200000), followed by n lines, each a non-empty title consisting only of lowercase English letters, with length 1..1000; the total length of all titles is ≤2×10^6. The character set and constraints are site supplements.

输出格式

Output the number of ordered index pairs that satisfy the condition.

样例 1

输入：

6
wall
wallpaper
science
wallet
philosophy
phil

输出：

3

样例 2

输入：

1
a

输出：

0

样例 3

输入：

4
ab
ab
abc
b

输出：

4