For every real number $x$, let $\lfloor x\rfloor$ denote the greatest integer not exceeding $x$, and let  
$$f(x)=\lfloor x\rfloor(2014^{x-\lfloor x\rfloor}-1).$$  
The set of all numbers $x$ such that $1\leq x<2014$ and $f(x)\leq 1$ is a union of disjoint intervals. What is the sum of the lengths of those intervals?

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