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Let $n$ be any integer greater than $2^{10^6}$. Given any $s\le (\log_2 n)/1000$ integers $1=q_1\le q_2\le \cdots q_{s-1}\le q_s=n$. Prove that $$\min_\ell\left(\sum_{i=1}^\ell q_i\right)\left(\sum_{i=...