Hosting the Contest

Yongbeom is writing problems for Boramcup. He made $K$ problems for each of $N$ different algorithm types, so $N \times K$ problems in total. The difficulty of the $j$-th problem of the $i$-th algorithm is $d_{ij}$. The contest does not have time for all of them, so he will use exactly one problem from each of the $N$ algorithm types, $N$ problems in total.

Yongbeom also wants to keep the difficulty curve small so that difficulty does not jump sharply. If the difficulty of the $i$-th problem in the contest is $x_i$, the difficulty curve is $|x_1 - x_2| + |x_2 - x_3| + \cdots + |x_{N-1} - x_N|$. When $N = 1$, the difficulty curve is defined as $0$.

Help Yongbeom. Arrange the $N$ problems in a suitable order and find the minimum possible difficulty curve.

The first line contains two integers $N$ and $K$, the number of algorithm types and the number of problems made for each type, separated by a space. $(1 \le N, K \le 1\,000)$

The next $N$ lines contain the difficulties. On line $i+1$, the integers $d_{i1}, \cdots, d_{iK}$ are given, separated by spaces, where $d_{ij}$ is the difficulty of the $j$-th problem of the $i$-th algorithm. $(1 \le d_{ij} \le 100\,000)$

Print the minimum difficulty curve when the $N$ problems are arranged in a suitable order.