A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100\; mm$, as shown in the figure. The permissible shear stress of the rivet material is $50$ $\text{MPa}$. If a load $P = 10$ $\text{kN}$ is applied at an eccentricity $e = 3\sqrt{7} a$, the minimum cross-sectional area of each of the rivets to avoid failure is ________________$mm^2$.

1. $800$
2. $25$
3. $100\sqrt{7}$
4. $200$