2022 IMO Shortlist C1

A $\pm 1$-sequence is a sequence of 2022 numbers $a_{1}, \ldots, a_{2022}$, each equal to either +1 or -1 . Determine the largest $C$ so that, for any $\pm 1$-sequence, there exists an integer $k$ and indices $1 \leq t_{1}<\ldots<t_{k} \leq 2022$ so that $t_{i+1}-t_{i} \leq 2$ for all $i$, and $$\left|\sum_{i=1}^{k} a_{t_{i}}\right| \geq C$$ (Czech Republic)

$\pm 1$-序列是 2022 个数字 $a_{1}, \ldots, a_{2022}$ 的序列，每个数字等于 +1 或 -1 。确定最大的 $C$，使得对于任何 $\pm 1$-序列，存在整数 $k$ 和索引 $1 \leq t_{1}<\ldots<t_{k} \leq 2022$，使得所有 $i$ 都为 $t_{i+1}-t_{i} \leq 2$，并且 \left|\sum_{i=1}^{k} a_{t_{i}}\右| \geq C(捷克共和国)