You are managing a hall. There are $n$ registration requests to use the hall, the $i$-th request is $[l_i, r_i]$, requesting to use the hall from time $l_i$ to $r_i$, with the total usage time being $r_i - l_i + 1$.
At any given time, only one request can be accepted. For example, two requests $[3, 5]$ and $[5, 7]$ cannot be accommodated simultaneously due to the overlap at time $5$. Your task is to select a subset of registration requests such that no two requests overlap in time and the total usage time of the hall is maximized.
### Input
- The first line contains an integer $n$.
- The next $n$ lines each contain two integers $l_i$ and $r_i$.
### Output
- Output a single integer representing the maximum total usage time of the hall.
### Constraints
- $1 \le n \le 10^5$
- $1 \le l_i, r_i \le 10^5$
### Example
Input:
```
4
1 3
2 5
4 6
6 8
```
Output:
```
7
```
Explanation: Choose $[2,5]$ and $[6,8]$.
