For $k \in \{0, 1, \ldots, 9\}$, let $\epsilon_k \in \{-1, 1\}$. If the minimum possible value of $\sum_{i=1}^9 \sum_{j=0}^{i-1} \epsilon_i \epsilon_j 2^{i+j}$ is $m$, find $|m|$.

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