Marisa wants to prepare a set of $n$ potion bottles. Each bottle requires a certain amount of time to be filled and labeled. The $i$-th bottle takes $A_i$ seconds to be filled and $B_i$ seconds to be labeled. A bottle must be filled before being labeled.
Marisa has two machines, one for filling potions and another one for labeling. However, each machine can process only one bottle at a time. Marisa wants to find the minimum amount of time required to prepare all $n$ potion bottles.
### Input
- The first line contains an integer $n$.
- The next $n$ lines, the $i^{th}$ line contains two integer $A_i,B_i$.
### Output
- Print an integer is the minimum amount of time required.
### Constraints
- $1 \le n \le 10$.
- $1 \le A_i,B_i \le 10^9$.
### Example
Input:
```
2
1 3
2 3
```
Output:
```
7
```
