In a tournament, there are n players. Every pair of players play against each other precisely once, and the rules of the game exclude draws. A vector of nonnegative integers (S₁, S2, ..., Sn) is called a score vector for this tournament if s; is the number of wins recorded by the ith player in this tournament. Given a nonnegative integer vector b = (b₁...., bn), we want to check whether b can be the score vector in such a tournament. How will you solve this problem?