Prove that there must exist two adjacent cells with common edge (not including diagonally) whose numbers have an absolute difference of at least 5.

In general with the numbers 1, 2,...., n

^{2}written on the cells of a nxn square grid in a random order such that each number occurs in a cell exactly once, will there always exist two adjacent cells with common edge (not including diagonally) whose numbers have an absolute difference of at least n, for every value of n ≥ 2?