Prove that there exists a number $\alpha$ such that for any triangle $ABC$ the inequality \[ \max(h_A,h_B,h_C)\le \alpha\cdot\min(m_A,m_B,m_C)\] where $h_A,h_B,h_C$ denote the lengths of the altitudes and $m_A,m_B,m_C$ denote the lengths of the medians. Find the smallest possible value of $\alpha$.