Get Minimum Time

The time spent at school on a day is the difference in hours between the latest and earliest classes attended that day, plus 1; it is 0 if no class is attended. You may skip at most K classes in total. Find the minimum total time at school over all days.

输入格式

The first line contains N M K (each 1..200), followed by N lines, each a 01 string of length M.

输出格式

Output a single integer, the answer.

样例 1

输入：

1 5 1
10001

输出：

1

样例 2

输入：

2 2 1
11
01

输出：

2

样例 3

输入：

1 3 1
000

输出：

0

样例说明

Example 1: skip either class and attend only the other, spending 1 hour at school.

Example 2: skip the only class on the second day; the first day takes 2 hours, for a total of 2.

Example 3: there are no classes, so there is no need to go to school; the answer is 0.