Description

Some $1 \\times 1 \\times 1$ containers are piled up in land of $W \\times H$.
The land is separated into $1 \\times 1$ cells. Each of the containers is on one of the cells.

Figure 1

Figure 2: from The Sky

Figure 3: from The Front

Figure 4: from The Side

Given the photograph from the sky, front, and side respectively, calculate how many containers are piled up in the minimum.

Input

$H$ $W$ $u_{11}$ $u_{12}$ $…$ $u_{1W}$ $u_{21}$ $…$ $:$ $:$ $u_{H1}$ $u_{H2}$ $…$ $u_{HW}$ $f_1$ $f_2$ $…$ $f_W$ $s_1$ $s_2$ $…$ $s_H$ The first line of the input file contains the integers $H$ and $W$ ($1 \\leq H,W \\leq 100$), the number of height and width of the land.
Each of the following $H$ lines gives the photograph from the sky.
The value of $u_{ij}$ means,
0: no containers are piled up in $(i, j)$,
1: some containers are piled up in $(i, j)$.
The next line gives the photograph from the front.
The integer $f_i$ is the number of the containers seen in $i$-th row.($0 \\leq f_i \\leq 100$)
The next line gives the photograph from the side.
The integer $s_i$ is the number of the containers seen in $i$-th column.($0 \\leq s_i \\leq 100$)

Output

Output the minimum number of the containers.
If the photographs are inconsistent, just output -1, instead.

Sample Input

2 3
0 1 0
1 1 1
2 3 2
2 3

Sample Output

9

Sample Input

4 6
1 1 0 1 0 0
0 0 1 0 0 1
0 1 0 0 0 1
0 0 1 0 1 0
1 2 1 2 1 1
2 1 2 1

Sample Output

11

Source Name

The First KMCMonthly Contest