Score : $700$ points

Problem Statement

Limak can repeatedly remove one of the first two characters of a string, for example $abcxyx \rightarrow acxyx \rightarrow cxyx \rightarrow cyx$.

You are given $N$ different strings $S_1, S_2, \ldots, S_N$. Among $N \cdot (N-1) / 2$ pairs $(S_i, S_j)$, in how many pairs could Limak obtain one string from the other?

Constraints

• $2 \leq N \leq 200\,000$
• $S_i$ consists of lowercase English letters a-z.
• $S_i \neq S_j$
• $1 \leq |S_i|$
• $|S_1| + |S_2| + \ldots + |S_N| \leq 10^6$

Input

Input is given from Standard Input in the following format.

$N$

$S_1$

$S_2$

$\vdots$

$S_N$

Output

Print the number of unordered pairs $(S_i, S_j)$ where $i \neq j$ and Limak can obtain one string from the other.

3
abcxyx
cyx
abc

1

The only good pair is $(abcxyx, cyx)$.

6
b
a
abc
c
d
ab

5

There are five good pairs: $(b, abc)$, $(a, abc)$, $(abc, c)$, $(b, ab)$, $(a, ab)$.