Consider two relations R and S with B$($R$)=500,000$ and B$($S$)=100,000$

and M $=2,001$ memory pages available. Estimate the minimum number of I$/$O operations needed to join

these two relations using following methods: $(1)$ block$-$nested$-$loop join, $(2)$ merge$-$join $($for both sorted

and not sorted inputs$),$ and $(3)$ hash$-$join $($not considering hybrid hash$-$join and another approach using

pointer$).$ You can assume that the hash function evenly distributes keys across buckets. Calculate the I$/$O

cost estimation for each join method.