For every positive integer $n$, let ${\text{mod}}_5(n)$ be the remainder obtained when $n$ is divided by 5. Define a function $h:0,1,2,3,\dots \times 0,1,2,3,4\to 0,1,2,3,4$ recursively as follows:
$h(i,j)=\{\begin{array}{ll}{\text{mod}}_5(j+3)& \text{if }i=0\text{ and }0\le j\le 4,\\ h(i-1,0)& \text{if }i\ge 1\text{ and }j=0,\\ h(i-1,h(i,j-1))& \text{if }i\ge 1\text{ and }1\le j\le 4.\end{array}$
What is $h(2020,3)$?