Hiring Chefs

Chef Shahhoud wants to hire new chefs for his restaurant. Shahhoud posted a job offer on Chef Rami's paper "Fast Food Times". $N$ candidates (numbered $1$ through $N$) have applied for the job. There are $M$ traits that define how good a chef is. You are given $N$ strings $S_1, S_2, \ldots, S_N$ describing the traits of the candidates. Each of these strings has length $M$. For each valid $i$ an