For each cow ~i~ from ~1~ to ~N~, we'll need to compute the number of matches ~m_i~ that they won. To do so, we can iterate over all cows ~j~ from ~1~ to ~N~ such that ~i \ne j~, and increment ~m_i~ whenever ~S_{i,j} > S_{j,i}~. Overall, we'll be looking for the cow ~i~ with the largest ~m_i~ value. To find that cow, we can keep track of the largest ~m_i~ value seen so far (as well as the value of its associated index ~i~), and replace it whenever we come across a new maximum. At the end, we can output that associated cow index ~i~.