Three blocks of masses $m_1, m_2$ and $m_3$, with $m_1 \lt m_2 \lt m_3$, are placed in contact with each other on a frictionless, horizontal surface, as shown. A constant horizontal force $F$ is applied to $m_1$ as shown. If the three masses are in the ratio of $1:2:3$, what is the ratio of the contact forces of the two heavier blocks, i.e, $F_2:F_3$?

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