$1)$ Consider the input sequence of length $120$ given below:

$22066131359417212621773176250841141872011164102842244871148214428$

$211131251921213417615719721122367199203301545112314017221824927915$

$51202591962402387110021749231226121182332042222203122066173569462$

$126124250218174116233916762204161351521027973868418222924466159$

$1872401671001692011741142328218787175131156301$

$2-$way $4-$way $8-$way

LRU FIFO RAND LRU FIFO RAND LRU FIFO RAND

$8$ blocks

$16$ blocks

$32$ blocks

$64$ blocks

$1.$ Analyze the effectiveness of different block replacement techniques by listing down the miss rate in each case.

$2.$ What other block replacement technique can be used and is proved to be the ideal? Explain.