Let $X$ be a finite set. Suppose that $X=A_1\sqcup\ldots\sqcup A_{10}$ and $X=B_1\sqcup\ldots\sqcup B_{10}$ are partitions of $X$ satisfying the following condition: if $A_i\cap B_j=\varnothing$ for some $1\leqslant i\leqslant j\leqslant 10$, then $|A_i\cup B_j|\geqslant 10$. Determine the smallest possible number of the elements in $X$.