A$33$-gon $p_1$ is drawn in the cartesian plane. the sum of the $x$-coordinates of the $33$ vertices equals $99$. the midpoints of the sides of $p_1$ form a second $33$-gon, $p_2$. finally, the midpoints of the sides of $p_2$ form a third $33$-gon, $p_3$. find the sum of the $x$-coordinates of the vertices of $p_3$.