P10414 [Lanqiao Cup 2023 National A] 2023 Power

Find the value of $2^{(3^{(4^{(\ldots ^{2023})})})}$ modulo $2023$. Note: All parts in the expression above are exponents. It can be written as $2** (3**(4**(\ldots 2023\ldots))$, where $**$ denotes exponentiation. This is an output-only fill-in-the-blank problem. You only need to compute the result and submit it. The answer is an integer. When submitting, fill in only this integer; adding extra content will result in no score.

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