Given an array $A$ consisting of $n$ integer elements, check if $A$ is a bitonic sequence.
A sequence is called a bitonic sequence if there exists an index $i$ such that:
- For all $j < i$, $A_j < A_{j + 1}$.
- For all $j > i$, $A_j < A_{j-1}$.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
### Output
- If $A$ is a bitonic sequence, print YES, otherwise print NO.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le A_i \le 10^9$.
### Example
Input:
```
4
1 4 10 2
```
Output:
```
YES
```
