Bingo

Consider the following game. You have an integer matrix of size $N \times M$. Your task is to put $M$ tokens at some cells of the matrix such as:

1. each column contains exactly one token;
2. difference $D\_r$ between the maximum and minimum number of tokens in one row is minimum possible;
3. among all such token placements, select one such that the maximum value in a matrix cell with a token is minimum possible.

The first line of input contains two integers $N$ and $M$ ($1 \le N, M \le 110$). Then matrix $a\_i$ comes: $N$ lines, each containing $M$ integers $a\_{i,j}$ ($1 \le a\_{i,j} \le 10^9$).

Print two integers which describe the placement you found: the minimum possible value of $D\_r$ and the minimum value in a matrix cell with a token.