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.

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).