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?

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.

Constraints

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

Sample Input 1

3
abcxyx
cyx
abc

Sample Output 1

1

The only good pair is (abcxyx, cyx).

Sample Input 2

6
b
a
abc
c
d
ab

Sample Output 2

5

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

见题面 Input 部分

见题面 Output 部分