\(n\) six-sided dice are rolled. It is given that the probability of obtaining the sum of \(2014\) is non-zero and is the same as the probability of obtaining a sum of \(S\). What is the minimum value of \(S\)?

This problem is from the AHSME.

This problem is from the set "Olympiads and Contests Around the World -3". You can see the rest of the problems here.

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