KVPY SA Exam 2016 Question Paper

Let ${\mathit{A}}_1{\mathit{A}}_2,...,{\mathit{A}}_{\mathit{m}}$ be non-empty subsets of {1,2,3...... 100} satisfying the following conditions:
(1) the numbers $\left|{\mathit{A}}_1\right|,|{\mathit{A}}_2|,...|{\mathit{A}}_{\mathit{m}}|$ are distinct:
(2) ${\mathit{A}}_1,{\mathit{A}}_2,...,{\mathit{A}}_{\mathit{m}}$ are pairwise disjoint.
(Here |A| denotes the number of elements in the set A)
Then the maximum possible value of m is