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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