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
- The first line contains a single integers is the minimum cost.
- The second line contains $n$ integers, denoting the journey.
### Constraints
- $1 \le n \le 100$
- $1 \le A_{i, j} \le 10^5$
### 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
3 4 1 5 2
```
### Scoring
- All test cases are scored equally.
- Consider the jury's answer as $Y$ and your answer as $X$.
- If $X$ is less than or equal to $Y$, you receive a score of $100\\%$ for test case.
- If $1 < \frac{X}{Y} \le 2$, your score for the test case is calculated as $\frac{2Y - X}{Y}\times 100 \\%$.
- If $\frac{X}{Y} > 2$, you receive a score of $0\\%$ for the test case.
