An antichain in a partially ordered set is a set of elements no two of which are comparable to each other, and a chain is a set of elements every two of which are comparable.
A maximum or longest chain is one which is of the greatest size possible. The size of the longest chain is known as a poset’s height.The following gives an example of such a chain
{1, 2, . . . , 50} ⊂ {1, 2, . . . , 51} ⊂ · · · ⊂ {1, 2, . . . , 100}
which is the maximum size of chain i.e. 51.Hence, the answer is 51.