CN-LEAGUE 2003 Problem 2

Let the three sides of a triangle be $\ell, m, n$ , respectively, satisfying $\ell>m>n$ and $\left\{\frac{3^\ell}{10^4}\right\}=\left\{\frac{3^m}{10^4}\right\}=\left\{\frac{3^n}{10^4}\right\}$ , where $\{x\}=x-\lfloor{x}\rfloor$ and $\lfloor{x}\rfloor$ denotes the integral part of the number $x$ . Find the minimum perimeter of such a triangle.