## 3 - Obstacle Course

You are working on the team assisting with programming for
the Mars rover. To conserve energy, the rover needs to find
optimal paths across the rugged terrain to get from its
starting location to its final location. The following is
the first approximation for the problem.

**N x N** square matrices contain the expenses for
traversing each individual cell. For each of them, your
task is to find the minimum-cost traversal from the top
left cell [0][0] to the bottom right cell [N-1][N-1].
Legal moves are up, down, left, and right; that is,
either the row index changes by one or the column
index changes by one, but not both.

### Input

Each problem is specified by a single integer between
2 and 125 giving the number of rows and columns in
the N x N square matrix. The file is terminated by
the case N = 0.

Following the specification of N you will find N lines,
each containing N numbers. These numbers will be given
as single digits, zero through nine, separated by
single blanks.

### Output

Each problem set will be numbered (beginning at one)
and will generate a single line giving the problem
set and the expense of the minimum-cost path from
the top left to the bottom right corner, exactly as
shown in the sample output (with only a single space
after “Problem” and after the colon).

Sample Input | Sample Output |

3
5 5 4
3 9 1
3 2 7
5
3 7 2 0 1
2 8 0 9 1
1 2 1 8 1
9 8 9 2 0
3 6 5 1 5
7
9 0 5 1 1 5 3
4 1 2 1 6 5 3
0 7 6 1 6 8 5
1 1 7 8 3 2 3
9 4 0 7 6 4 1
5 8 3 2 4 8 3
7 4 8 4 8 3 4
0 |
Problem 1: 20
Problem 2: 19
Problem 3: 36 |