One day, Apollo and Avery find a collection T of n spells, each of which can be obtained by repeating some section infinitely.
For example, by repeating the section 'abc', we can get the spell 'abcabcabc...'.
The two kids learnt how to count common substrings of many strings in Mr.Calabash's string course yesterday. However, they find it hard to count that of these spells. Can you help the two poor kids?
Let F(s) be the set of all substrings of spell s. You should tell the two kids .

The first line contains one integer , the number of spells two kids found.
Then next n lines, each line contains a string , which represents the i-th spell repeated by .  consists of lowercase English letters.
Note that .

One integer in one line, representing the number of common substrings of these n spells, or -1 instead if the number of common substrings is infinite.

3
bcbcbc
bbbccc
cbcbcb

4

In the first example, there are three spells:  , , . They have four common substrings: , , , .

5
abacbc
abacabac
ccaccb
cbcaba
cbccac

5