For every positive integer $n$, let ${mod}_5 (n)$ be the remainder obtained when $n$ is divided by $5$. Define a function $f: \{0,1,2,3,\cdots\} \times \{0,1,2,3,4\} \to \{0,1,2,3,4\}$ recursively as follows:    
$$f(i,j)=\begin{cases}\operatorname{mod}_5(j+1)&\text{if}i=0\text{and}0\le j\le4,\\f(i-1,1)&\text{if}i\ge1\text{and}j=0\text{,and}\\f(i-1,f(i,j-1))&\text{if}i\ge1\text{and}1\le j\le4.\end{cases}$$  
Find the value of $f(2015,2)$.

Let's think step by step and output the final answer within \boxed{}.
user