There are $n$ cities. Going from city $i$ to city $j$ cost $A_{i, j}$ coins. Find the minimum cost route that visits each city exactly once and returns to the starting city.
### Input
- The first line contains integers $n$.
- Next $n$ lines, $i^{th}$ line contains $n$ integers $A_{i, j}$.
### Output
- A single integers is the minimum cost.
### Constraints
- $1 \le n \le 10$
- $1 \le A_{i, j} \le 1000$
- $A_{i,i}=0$
### Example
Input:
```
5
0 2 8 5 1
10 0 5 9 9
3 5 0 6 6
2 8 2 0 2
6 3 8 7 0
```
Output:
```
17
```
