The function f(x,y) satisfies the conditions \(\begin{align} f(0,y) &= y+1\\ f(x+1,0) &= f(x,1)\\ f(x+1,y+1) &= f(x,f(x+1,y)) \end{align}\)
for all non-negative integers x,y. Given that f(4,2016) can be written as \(2^{2\cdot ^{ . \cdot 2}} - 3\), determine the number of 2's that appear in this expression.
