HMMT November 2015 U18

A function $f$ satisfies, for all nonnegative integers $x$ and $y$ :

• $f(0, x)=f(x, 0)=x$
• If $x \geq y \geq 0, f(x, y)=f(x-y, y)+1$
• If $y \geq x \geq 0, f(x, y)=f(x, y-x)+1$

Find the maximum value of $f$ over $0 \leq x, y \leq 100$.