Physical memory consists of $4$ page frames, initially all empty. The following reference string is processed: $01402301023423$

$($a$)$ Using a table $($use the same format we used in class$)$ show which pages are resident under the optimal page replacement algorithm. Indicate when page faults happen. $(10$ points$)$

$($b$)$ Using a table $($use the same format we used in class$)$ show which pages are resident under the FIFO page replacement algorithm. Indicate when page faults happen. $(10$ points$)$

$($c$)$ Using a table $($use the same format we used in class$)$ show which pages are resident under the LRU page replacement algorithm. Indicate when page faults happen. $(10$ points$)$