In the cube

Taja likes to go to the cafe In the cube with her friends, since it has a very convenient ordering system. To place an order, a guest walks to an automated stand and chooses any dishes they like. There are several stands, and each is fixed at a specific place inside the cafe.

Guests sit in front of tables. There are $k$ tables. The $i$th table can serve at most $c_i$ persons. The uncomfortableness of a table is the sum of distances from that table to the $c_i$ stands closest to it.

Formally, the cafe is the grid $(0, 0)$ to $(5000, 5000)$. Each cell $(x, y)$ ($0 \le x, y \le 5000$) can contain either one automated stand, one table, or nothing. The distance between cells $(x_1, y_1)$ and $(x_2, y_2)$ is $|x_2 - x_1| + |y_2 - y_1|$.

Arrange the tables so that the total uncomfortableness of all tables is minimal.

The first line contains two integers $n$ and $k$ ($1 \le n \le 18$, $1 \le k \le 200$), the number of automated stands and the number of tables.

Each of the next $n$ lines contains the coordinates $x_i$ and $y_i$ of the $i$th stand ($0 \le x_i, y_i \le 5000$).

Each of the next $k$ lines contains a single integer $c_j$ ($1 \le c_j \le n$), the number of seats at the $j$th table.

Output one integer, the minimal total uncomfortableness.

A possible arrangement of the tables for the first sample is shown above.