A process, has been allocated $3$ page frames. Assume that none of the pages of the process are available in the memory initially. The process makes the following sequence of page references (reference string): $1, 2, 1, 3, 7, 4, 5, 6, 3, 1$
Least Recently Used (LRU) page replacement policy is a practical approximation to optimal page replacement. For the above reference string, how many more page faults occur with LRU than with the optimal page replacement policy?