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
- $1 \le n \le 20$
- $0 \le A_{i, j} \le 1000$
### Example
Input:
```
8
0 5 0 6 0 4 0 7
5 0 2 4 3 0 0 0
0 2 0 1 0 0 0 0
6 4 1 0 7 0 0 0
0 3 0 7 0 0 6 4
4 0 0 0 0 0 3 0
0 0 0 0 6 3 0 2
7 0 0 0 4 0 2 0
```
Output:
```
0
```
