Let \{x\}=x-\lfloor x\rfloor. Consider a function f from the set \{1,2, \ldots, 2020\} to the half-open interval \left[0,1\right) . Suppose that for all x, y, there exists a z so that \{f(x)+f(y)\}=f(z). We say that a pair of integers m, n is valid if 1 \leq m, n, \leq 2020 and there exists a function f satisfying the above so f(1)=\frac{m}{n}. Determine the sum over all valid pairs m, n of \frac{m}{n}.