Grid Game

Given a $N \times N$ grid of integers, we can choose a combination of $N$ numbers where no two in the same row and no two in the same column. We aim to find a combination of $N$ numbers whose minimum is maximized.

The first line of input consists of an integer $N$, where $1 \leq N \leq 30$. The next $N$ lines each contains $N$ integers, representing the grid. Each integer is in the range $[1..10^6]$.

Output a single integer, representing the maximum possible value of the minimum.

Sample Input 1 | Sample Output 1 |
---|---|

3 3 1 4 1 5 1 2 9 1 |
2 |

Sample Input 2 | Sample Output 2 |
---|---|

5 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 |
21 |