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Neka su m i n prirodni brojevi takvi da \log_2(\log_{2^m}(\log_{2^n} 2^{1000})) = 0. Koliki je zbroj svih mogućih vrijednosti broja m + n?


Let m and n be two positive integers that satisfy the equation \log_2(\log_{2^m}(\log_{2^n} 2^{1000})) = 0. Find the sum of all possible values of m +n.