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.

Examples

Input

3
abcxyx
cyx
abc

Output

1

Input

6
b
a
abc
c
d
ab

Output

5

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