A thin circular coin of mass 5 gm and radius $4 / 3 \mathrm{~cm}$ is initially in a horizontal $x y$-plane. The coin is tossed vertically up ( $+z$ direction) by applying an impulse of $\sqrt{\frac{\pi}{2}} \times 10^{-2} \mathrm{~N}$-s at a distance $2 / 3 \mathrm{~cm}$ from its center. The coin spins about its diameter and moves along the $+_z$ direction. By the time the coin reaches back to its initial position, it completes $n$ rotations. The value of $n$ is $\_\_\_\_$ .
[Given: The acceleration due to gravity $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ ]