Show that there exits infinitely many functions $f:\mathbb{N}\to\mathbb{N}$

Question

Show that there exits infinitely many functions $f:\mathbb{N}\to\mathbb{N}$ satisfying

(a) $f(2)=4;$

(b) $f(mn)=f(m)f(n)$ for every $m,n\in\mathbb{N};$

(c) $f(m)<f(n)$ whenever $m<n.$