NIMCET 2024 Paper

Consider the program below which uses six temporary variables $\mathit{a},\mathit{b},\mathit{c},\mathit{d},\mathit{e}$ and $\mathit{f}$.
$\mathit{a}=10$
$\mathit{b}=20$
$\mathit{c}=30$
$\mathit{d}=\mathit{a}+\mathit{c}$
$\mathit{e}=\mathit{b}+\mathit{d}$
$\mathit{f}=\mathit{c}+\mathit{e}$
$\mathit{b}=\mathit{c}+\mathit{e}$
$\mathit{e}=\mathit{b}+\mathit{f}$
$\mathit{d}=5+\mathit{e}$
Assuming that all the above operations take their operands from registers, the minimum number of registers needed to execute this program without spilling is $\_\_\_\_$ .