First Second

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

inputFormat

Input

Input is given from Standard Input in the following format.

N S_1 S_2 \vdots S_N

outputFormat

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

样例

6
b
a
abc
c
d
ab

5