AMO-Bench 2025 Problem 12

Space vectors $\overrightarrow{A_n}(x_{n}, y_{n}, z_{n}) (1 \leq n \leq 2052)$ satisfy that $\sqrt{1+x_{n}}, \sqrt{1+y_{n}}, \sqrt{1+z_{n}} (1 \leq n \leq 2052)$ are all real numbers, and $$\sum_{n=1}^{2052} x_{n}^{3} = \sum_{n=1}^{2052} z_{n}^{3} = \sum_{n=1}^{2052} y_{n} - 2052 = 0,$$ $$\sum_{n=1}^{2052} 4z_{n} = \sum_{n=1}^{2052} x_{n}^{2} = 2736, \sum_{n=1}^{2052} y_{n}^{2} = 4210703, \sum_{n=1}^{2052} y_{n}^{3} = 8640361530.$$

Find the maximum value of $$\frac{\lvert \overrightarrow{A}_{1234}\rvert}{\lvert \overrightarrow{A}_{432}\rvert}.$$