Algorithm $2\mathrm{.}3\mathrm{.}13($Compute Power$).$ Let a and $n$ be integers and $m$ a

nonnegative integer. This algorithm computes $a^m$ modulo $n.$

$[$Write in Binary$]$ Write $m$ in binary using Algorithm $2\mathrm{.}3\mathrm{.}11,$ so $a^m=$

$pro{d}_{{}_i}=1a^{2^i}(modn)$

$[$Compute Powers$]$ Compute $a,a^2,a^{2^2}=(a^2{)}^2,a^{2^3}=(a^{2^2}{)}^2,$ etc., up

to $a^{2^r},$ where $r+1$ is the number of binary digits of $m.$

$[$Multiply Powers$]$ Multiply together the $a^{2^i}$ such that ${}_i=1,$ always

working modulo $n.$

Use Algorithm $2\mathrm{.}3\mathrm{.}13.$

What is $3^52($mod $100)?$ Please type and show all steps.