P16232 [Lanqiao Cup 2026 NOI Qualifier B] Youth Constant

All testdata for the Lanqiao Cup 2026 provincial contest on this site are created by Luogu and may differ from the official data. They are for learning reference only.

Xiao Lan’s connection with the Lanqiao Cup has reached its fourth year. From his first steps in 2023, to fighting through 2024 and 2025, and now in 2026, this will be the last time in his college life that he stands on this contest stage. On the eve of retiring, filled with mixed feelings, Xiao Lan wrote down the years of these four contests in reverse order on scratch paper and concatenated them into a huge integer $N = 2026202520242023$. While整理 (zhengli) his competition notes from the past four years, he decided to split this constant $N$ into two non-negative integers $x$ and $y$, representing the accumulation in the first half of his journey and the breakthrough in the second half. According to the splitting rule, the sum of these two parts must be exactly equal to $N$ (that is, $x + y = N$). At the same time, because in the second half Xiao Lan built up a deeper foundation in algorithms, the value of the second part $y$ must be strictly greater than the value of the first part $x$ (that is, $0 \le x < y$). Now, please compute how many integer pairs $(x, y)$ satisfy the above conditions.

N/A

This is an output-only fill-in-the-blank problem. You only need to compute the result and submit it. The result of this problem is an integer. When submitting the answer, only fill in this integer; submitting any extra content will result in no score.

Translated by ChatGPT 5