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Consider a multiset $A = \{ a_1, a_2, a_3,..,a_n\}$, each of which has the form of $2^{t_i}$ and $\leq 2^{11}$ where $1\leq i\leq n$. Now we design an algorithm to prove the above fact. Step 1: If $2^{11} \in A$. We stop. Step 2: Pick two equal elements in $A$ and merge them. But how do we make sure there exists such two elements? Suppose the reverse. If ...

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