BALKAN-SL 2010 C2

A grasshopper jumps on the plane from an integer point (point with integer coordinates) to another integer point according to the following rules: His first jump is of length $\sqrt{98}$ , his second jump is of length $\sqrt{149}$ , his next jump is of length $\sqrt{98}$ , and so on, alternatively. What is the least possible odd number of moves in which the grasshopper could return to his starting point?