You have an n by m grid. Each grid square has a certain value associated with it. This is given by the numbers v_i,j.

You can capture grid squares in two different ways.

1. You can directly capture a grid square. This costs c_i,j.
2. You can indirectly capture a grid square. You can only do this if we have already captured all of this squares neighbors. This costs b_i,j ≤ c_i,j.

Two squares are neighbors if they share an edge.

Your score is the sum of values you have captured minus the cost it took to capture those squares. Return the maximum possible score you can achieve.

Input format:

The first line of input will contain two integers n, m.

The next n lines of input will contain m space separated integers each. The j-th number on the i-th line denotes v_i,j.

The next n lines of input will contain m space separated integers each. The j-th number on the i-th line denotes b_i,j.

The next n lines of input will contain m space separated integers each. The j-th number on the i-th line denotes c_i,j.

Output format:

Print a single integer, the answer to the problem.

Constraints

For all subtasks:
0 ≤ v_i,j ≤ 100,000
0 ≤ b_i,j ≤ c_i,j ≤ 100,000
1 ≤ n, m

Subtask 1 (45 pts):
n, m ≤ 3

Subtask 2 (35 pts):
n, m ≤ 7

Subtask 3 (20 pts):
n, m ≤ 25