OIM 2005 Problem 2

A flea jumps in a straight numbered line. It jumps first from point $0$ to point $1$ . Afterwards, if its last jump was from $A$ to $B$ , then the next jump is from $B$ to one of the points $B + (B - A) - 1$ , $B + (B - A)$ , $B + (B-A) + 1$ .

Prove that if the flea arrived twice at the point $n$ , $n$ positive integer, then it performed at least $\lceil 2\sqrt n\rceil$ jumps.