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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~.
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