A two$-$level memory system has eight virtual pages on a disk to be mapped into four page frames $($PFs$)$ in the main memory. A certain program generated the following page trace:

$1,0,2,2,1,7,6,7,0,1,2,0,3,0,4,5,1,5,2,4,5,6,7,6,7,2,4,2,7,3,3,2,3$

$($a$)$ Show the successive virtual pages residing in the four page frames with respect to Optimal Page replacement algorithm.