Given $n$ string $S_1, S_2,...,S_n$. Determine if there exists 2 distinct indices $i, j$ that $S_i$ is a prefix of $S_j$.
### Input
- The first line contains an integer $n$.
- The next $n$ lines, each line contains a string.
### Output
- Print the `YES` if there exists satisfied indices, `NO` otherwise.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le |S_i| \le 20$.
- $S_i$ contain only lowercase letters.
### Example
Input:
```
3
reimu
marisa
mari
```
Output:
```
YES
```