Problem Statement

We have a bipartite graph with $L$ vertices to the left and $R$ vertices to the right. Takahashi will install surveillance cameras in these vertices. Installing cameras incurs the following cost.

• $A_i$ yen (the Japanese currency) for each camera installed in the $i$-th $(1 \le i \le L)$ vertex to the left;
• $B_j$ yen (the Japanese currency) for each camera installed in the $j$-th $(1 \le j \le R)$ vertex to the right.

It is allowed to install multiple cameras on the same vertex.

Find the minimum amount of money needed to install cameras to satisfy the following condition.

• For every pair of integers $(i, j)$ such that $1 \le i \le L, 1 \le j \le R$, there is a total of $C_{i,j}$ or more cameras installed in the $i$-th vertex to the left and $j$-th vertex to the right.

Constraints

• All values in input are integers.
• $1 \le L,R \le 100$
• $1 \le A_i,B_i \le 10$
• $0 \le C_{i,j} \le 100$

Input

Input is given from Standard Input in the following format:

L R
A_1 A_2 \dots A_L
B_1 B_2 \dots B_R
C_{1,1} C_{1,2} \dots C_{1,R}
C_{2,1} C_{2,2} \dots C_{2,R}
\vdots
C_{L,1} C_{L,2} \dots C_{L,R}

Output

Print the answer as an integer.