BALKAN-SL 2007 G4

Points $M,N$ and $P$ on the sides $BC, CA$ and $AB$ of $\vartriangle ABC$ are such that $\vartriangle MNP$ is acute. Denote by $h$ and $H$ the lengths of the shortest altitude of $\vartriangle ABC$ and the longest altitude of $\vartriangle MNP$ . Prove that $h \le 2H$ .