Description
Here is a well-known game, ‘ 彈水阿給’（=瘋狂阿給=爆爆王). This is very similar to Bomber Man. The range of explosion of each water-ball is a cross shape on the map, and it will trigger any water-ball on the path of that cross.
Illustrated by following pictures:
, 
Now you are in this intense “Rising Green Pepper Contest”, trying to play this exciting game. We redefined the rule as following:
0. You are playing on an N * M map. There’s no obstacles on that map, only several placed water-balls.
1. Assume that every water-ball have infinite explosion range, that is to say, it would explode until the bound of the map.
2. The horizontal explosion of the water-ball will trigger water-balls on the same row, while doing no damage.
3. The vertical explosion of the water-ball will NOT trigger water-ball on the same column, while bringing damage.
Now things you are trying to do is:
0. Choose several water-balls to make them explode, and the number of choosing water-balls should be a minimum.
1. The total DAMAGE range should cover the whole map.
2. We want to be eco-friendly, so the DAMAGE range cannot be overlapped, or we would waste water.
Input
There are several testcases.
The first line of each testcases indicates N, M, which represents an N * M map.
Following will be N lines, each consists of M number(0 or 1), representing the state of the map. 0 means null, while 1 means water-ball.
1 <= N,M <= 100
Output
Print a positive integer, the minimum number of your choose.
If the goal cannot be achieved, print -1.