#abc159e. [abc159_e]Dividing Chocolate
[abc159_e]Dividing Chocolate
Problem Statement
We have a chocolate bar partitioned into horizontal rows and vertical columns of squares.
The square at the -th row from the top and the -th column from the left is dark if is 0
, and white if is 1
.
We will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.
How many times do we need to cut the bar so that every block after the cuts has or less white squares?
Constraints
- is
0
or1
.
Input
Input is given from Standard Input in the following format:
Output
Print the number of minimum times the bar needs to be cut so that every block after the cuts has or less white squares.
Sample Input 1
Sample Output 1
For example, cutting between the -st and -nd rows and between the -rd and -th columns - as shown in the figure to the left - works.
Note that we cannot cut the bar in the ways shown in the two figures to the right.
Sample Input 2
Sample Output 2
No cut is needed.