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$$
\eqalign{
& Let{\text{ }}a_{\text{1}} ,a_{\text{2}} ,...a_{{\text{2023 }}} is{\text{ }}positive{\text{ }}\operatorname{int} eger{\text{ }}and \cr
& a_{\text{1}} ,a_{\text{2}} ,...a_{{\text{2023 }}} is{\text{ a permutation of 1,2,}}...{\text{2023 }}and \cr
& |a_{\text{1}} - a_{\text{2}} |,|a_2 - a_3 |,...|a_{2022} - a_{{\text{2023}}} |{\text{ }}is{\text{ a permutation of 1,2,}}...{\text{2022}} \cr
& {\text{Prove max(}}a_{\text{1}} ,a_{{\text{2023}}} ) \geqslant 507 \cr
& \cr}
$$
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