Facility Locations

A company has $n$ clients and must serve all of them by opening $k$ facilities. An open facility serves any number of clients, and every client is assigned to one open facility. There are $m$ candidate locations for the facilities. Serving client $j$ from candidate location $i$ costs a non-negative integer $c_{ij}$, and the costs satisfy a locality condition: for any clients $j$ and $j'$ and any candidate locations $i$ and $i'$, $c_{ij} \le c_{i'j} + c_{i'j'} + c_{ij'}$ holds.

The company eventually wants the cheapest way to open $k$ facilities. Right now it needs the answer to an earlier question. Decide whether it can open $k$ facilities and assign every client at a total cost of zero.

The first line contains the integers $m$, $n$, $k$, separated by spaces. ($1 \le m \le 100$, $1 \le n \le 100$, $1 \le k \le m$)

Line $i$ of the next $m$ lines contains $n$ non-negative integers, the $j$-th of which is $c_{ij}$. ($0 \le c_{ij} \le 10000$)

Print yes if the company can open $k$ facilities and assign every client at a total cost of zero. Otherwise print no.