Unfriendly neighbours

Probability Level 5

Find the greatest positive integer NN, such that for any arrangement of the positive integers 1,2,3,,16001, 2, 3, \ldots , 1600 in a 40×40 40 \times 40 table, there exists two numbers located in the same row or in the same column such that the (positive) difference of these numbers is not less than NN.

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