I$-$Mem$/$D$-$Mem: $250$ps$,$ Register File: $150$ps$,$ Mux: $25$ps$,$ ALU: $200$ps$,$ Adder: $150$ps$,$ Single gate: $5$ps$,$ Register Read: $30$ps$,$ Register Setup: $20$ps$,$ Sign extend: $50$ps$,$ Control: $50$ps$,$ "Register read" is the time needed after the rising clock edge for the new register value to appear on the output. This value applies to the PC only. "Register setup" is the amount of time a register's data input must be stable before the rising edge of the clock. This value applies to both the PC and Register File.

$($a$)$

What is the latency of an R$-$type instruction$($i$.$e$.,$ how long must the clock period be to ensure that this instruction works correctly$)?$