Japan Alumni Group Summer Camp 2013 Warming Up

C - Containers


Time limit時間制限 : 1.5sec / Memory limitメモリ制限 : 96MB

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

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