Matchmaker Mystery Cache

The posted coordinates are not real. Solve the puzzle below to obtain the correct coordinates.

Tulsa Area Geocachers (TAG) has formed a group of volunteers who will help maintain Tulsa's geocaches and make sure they can be found by the community. When caches need maintenance, for each cache that is disabled, the volunteers must send one member who is familiar with that cache to maintain it. One volunteer can handle at most one cache at a time. TAG wants to evaluate the Coordinated Assistance for Cache Handling and Evaluation (CACHE) level of the volunteers, which is defined as the maximum value k such that any k caches that need maintenance simultaneously can be maintained by the volunteers.

The inputs to solve this puzzle can be found at this link. (Alert: You are about to be given the option to download files that contain details needed to find this geocache. As the geocache owner, I ensure that these files are safe to download. They have not been checked by Geocaching HQ or by the reviewer for possible malicious content. Download these files at your own risk.)

The first line of inputs contains two integers n and m where n is the number of volunteers and m is the number of geocaches.

Each of the next n lines contains a string of binary digits of length m, describing the n volunteers' familiarity with the m caches. The j-th digit on the i-th line is 1 if volunteer i is familiar with cache j, and 0 otherwise. 

It is guaranteed that for each of the m geocaches there exists at least one volunteer who is familiar with it.

The CACHE level of the volunteers is a single integer.

To obtain the correct coordinates, you must solve all 30 of the problems. Then, concatenate your CACHE levels in order into one long number (e.g. '9', '43', '87', '36'  -> '9438736'). Input that number into Certitude.

For your convenience, below are sample inputs and solution CACHE levels.