A pair of strings is considered good if they have at least one common letter. For example, the pair abc and adc is good because they share the letters a and c. Conversely, the pair bc and def is not good because they have no common letters.
Given $n$ strings, count the number of good string pairs.
### Input
- The first line contains an integer $n$.
- The next $n$ lines each contain a string.
### Output
- Print the number of good string pairs.
### Constraints
- $1 \le n \le 10^5$.
- The strings consist of the first 15 letters of the alphabet and have a length of at most 10 characters.
### Example
Input:
```
4
abc
def
afg
ed
```
Output:
```
3
```
