School Friends Triad

There are three schools, each with exactly 2017 students. Every student is friends with at least 2018 students from the other two schools.

Does there exist a group of 3 students--one from each of the three schools--that are all pairwise friends?

Note: If \(A\) is friends with \(B,\) then \(B\) is friends with \(A.\)

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