Let $A_0=(0,0)$. Distinct points $A_1,A_2,\dots$ lie on the $x$-axis, and distinct points $B_1,B_2,\dots$ lie on the graph of $y=\sqrt{x}$. For every positive integer $n$, $A_{n-1}{B}_n{A}_n$ is a right isosceles triangle with the right angle at $B_n$. What is the least $n$ for which the length $A_0{A}_n\ge 100$?