Problem Statement

You are given two length-$N$ sequences of positive integers: $X=(X_1,X_2,\dots,X_N)$ and $Y=(Y_1,Y_2,\dots,Y_N)$.

Additionally, you are given $M$ length-$N$ sequences of positive integers. The $i$-th sequence is $A_i = (A_{i,1},A_{i,2},\dots,A_{i,N})$.

For each $i = 1,2,\dots,M$, you must perform one of the following operations. You can independently choose which operation to perform for each $i$.

• Replace $X_j$ with $\max(X_j,A_{i,j})$ for all integers $j$ such that $1 \le j \le N$.
• Replace $Y_j$ with $\max(Y_j,A_{i,j})$ for all integers $j$ such that $1 \le j \le N$.

Find the minimum possible value of $\sum_{j=1}^{N} (X_j + Y_j)$ after all operations.

Constraints

• $1 \le N \le 10$
• $1 \le M \le 500$
• $1 \le X_j, Y_j, A_{i,j} \le 500$

Input

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

N M
X_1 X_2 \dots X_N
Y_1 Y_2 \dots Y_N
A_{1,1} A_{1,2} \dots A_{1,N}
A_{2,1} A_{2,2} \dots A_{2,N}
\vdots
A_{M,1} A_{M,2} \dots A_{M,N}

Output

Print the answer.