Ciel and Gondolas

有一只叫 Ciel 的狐狸正在排队去做摩天轮，队列中有 $n$ 个人。 摩天轮上有 $k$ 个吊舱，我们按照如下方式分配吊舱： 1. 第一个吊舱有 $q_1$ 只狐狸，就是第 $1\sim q_1$ 只狐狸。 2. 第二个吊舱有 $q_2$ 只狐狸，就是第 $q_1+1\sim q_1+q_2$ 只狐狸。 3. 第二个吊舱有 $q_3$ 只狐狸，就是第 $q_1+q_2+1\sim q_1+q_2+q_3$ 只狐狸。 以此类推，最后 $q_k$ 只狐狸坐进第 $k$ 个吊舱。 显然，我们需要保证 $\sum_{i=1}^kq_i=n$。 每只狐狸都不想和陌生狐坐在一起，所以我们给出矩阵 $u_{i,j}$，表示第 $i$ 只狐狸和第 $j$ 只狐狸的陌生值，保证 $u_{i,j}=u_{j,i},u_{i,i}=0$。 我们定义一个吊舱的陌生值为吊舱中每一对人的陌生值之和，总陌生值为每一个吊舱的陌生值之和，输出总陌生值的最小值。

Fox Ciel is in the Amusement Park. And now she is in a queue in front of the Ferris wheel. There are $ n $ people (or foxes more precisely) in the queue: we use first people to refer one at the head of the queue, and $ n $ -th people to refer the last one in the queue. There will be $ k $ gondolas, and the way we allocate gondolas looks like this: - When the first gondolas come, the $ q_{1} $ people in head of the queue go into the gondolas. - Then when the second gondolas come, the $ q_{2} $ people in head of the remain queue go into the gondolas. ... - The remain $ q_{k} $ people go into the last ( $ k $ -th) gondolas. Note that $ q_{1} $ , $ q_{2} $ , ..., $ q_{k} $ must be positive. You can get from the statement that  and $ q_{i}>0 $ . You know, people don't want to stay with strangers in the gondolas, so your task is to find an optimal allocation way (that is find an optimal sequence $ q $ ) to make people happy. For every pair of people $ i $ and $ j $ , there exists a value $ u_{ij} $ denotes a level of unfamiliar. You can assume $ u_{ij}=u_{ji} $ for all $ i,j $ $ (1<=i,j<=n) $ and $ u_{ii}=0 $ for all $ i $ $ (1<=i<=n) $ . Then an unfamiliar value of a gondolas is the sum of the levels of unfamiliar between any pair of people that is into the gondolas. A total unfamiliar value is the sum of unfamiliar values for all gondolas. Help Fox Ciel to find the minimal possible total unfamiliar value for some optimal allocation.

The first line contains two integers $ n $ and $ k $ ( $ 1<=n<=4000 $ and $ 1<=k<=min(n,800) $ ) — the number of people in the queue and the number of gondolas. Each of the following $ n $ lines contains $ n $ integers — matrix $ u $ , ( $ 0<=u_{ij}<=9 $ , $ u_{ij}=u_{ji} $ and $ u_{ii}=0 $ ). Please, use fast input methods (for example, please use BufferedReader instead of Scanner for Java).

Print an integer — the minimal possible total unfamiliar value.

5 2
0 0 1 1 1
0 0 1 1 1
1 1 0 0 0
1 1 0 0 0
1 1 0 0 0

0

8 3
0 1 1 1 1 1 1 1
1 0 1 1 1 1 1 1
1 1 0 1 1 1 1 1
1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1
1 1 1 1 1 0 1 1
1 1 1 1 1 1 0 1
1 1 1 1 1 1 1 0

7

3 2
0 2 0
2 0 3
0 3 0

2

In the first example, we can allocate people like this: {1, 2} goes into a gondolas, {3, 4, 5} goes into another gondolas. In the second example, an optimal solution is : {1, 2, 3} | {4, 5, 6} | {7, 8}.