2023 IMO Shortlist C2

Determine the maximal length $L$ of a sequence $a_{1}, \ldots, a_{L}$ of positive integers satisfying both the following properties: - every term in the sequence is less than or equal to $2^{2023}$, and - there does not exist a consecutive subsequence $a_{i}, a_{i+1}, \ldots, a_{j}$ (where $1 \leq i \leq j \leq L$ ) with a choice of signs $s_{i}, s_{i+1}, \ldots, s_{j} \in\{1,-1\}$ for which $$s_{i} a_{i}+s_{i+1} a_{i+1}+\cdots+s_{j} a_{j}=0$$ (Czech Republic)

确定满足以下两个属性的正整数序列 $a_{1}, \ldots, a_{L}$ 的最大长度 $L$： - 序列中的每一项都小于或等于 $2^{2023}$，并且 - 不存在连续的子序列 $a_{i}, a_{i+1}, \ldots, a_{j}$ (其中 $1 \leq i \leq j \leq L$ ) 可选择符号 $s_{i}, s_{i+1}, \ldots, s_{j} \in\{1,-1\}$ 其中 $$s_{i} a_{i}+s_{i+1} a_{i+1}+\cdots+s_{j} a_{j}=0$$ (捷克共和国)