Library Prefix Pairs

Count ordered index pairs i≠j such that title i is a prefix of title j; different indices with identical titles also count.

输入格式

n (1≤n≤200000), followed by n lines of non-empty lowercase strings, each of length ≤1000, with total length ≤200000; the ranges are site-added to bound Trie memory.

输出格式

Output the number of ordered pairs.

样例 1

输入：

3
ab
abc
ab

输出：

4

样例 2

输入：

1
a

输出：

0

样例 3

输入：

4
car
cart
cat
car

输出：

4