Problem Statement

You are given positive integers $N, K$ and a permutation $P = (P_{1}, P_{2}, \dots, P_{NK})$ of $(1, 2, \dots, NK)$.

Alice repeatedly performs the following operation to sort $P$ in ascending order.

• Choose integers $i$ and $j$ $(i\neq j)$ where $1 \leq i, j \leq NK$, and swap $P_{i}$ and $P_{j}$. If $|i - j|$ is a multiple of $N$, Alice gets $1$ point.

Alice sorts $P$ in ascending order with the minimum number of operations, and under that condition, she maximizes the sum of points she gets.

Output the sum of points Alice gets.

Constraints

• $1\leq N\leq 500$
• $1\leq K\leq 10$
• $(P_{1}, P_{2}, \dots , P_{NK})$ is a permutation of $(1, 2, \dots, NK)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N K
P_{1} P_{2} \dots P_{NK}

Output

Output the answer.