Look like horse steps

Discrete Mathematics Level pending

Two chessman at lattice points (a,b) and (c,d) form a "pseudohorse pair" if and only if one of abs(a-b) and abs(c-d) is 1 and the other is an integer greater than 1. For example, (2,5) forms a "pseudohorse pair" with (3,8) but not with (10,5) nor (3,4). Now, Hermes place k chessman such that any 2 of them form a "pseudohorse pair".

Find the maximum possible value of k.

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