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Let $f(x)$ be a function satisfying $f(1) =101$ and

$\begin{aligned} f(x+5) & \geq f(x)+5\\ f(x+1) & \leq f(x)+1, \end{aligned}$

for all positive integers $x$. What are the last three digits of $f(2013)?$

This problem is posed by Indulal G.

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