P8668 [Lanqiao Cup 2018 NOI Qualifier B] Spiral Polyline.

As shown in the figure, the spiral polyline passes through every integer lattice point on the plane exactly once.  For a lattice point $(X, Y)$, we define its distance to the origin $\text{dis}(X, Y)$ as the length of the spiral polyline segment from the origin to $(X, Y)$. For example, $\text{dis}(0, 1)=3$, and $\text{dis}(-2, -1)=9$. Given the integer coordinates $(X, Y)$, can you compute $\text{dis}(X, Y)$?

$X$ and $Y$.

Output $\text{dis}(X, Y)$.

For $40\%$ of the testdata, $-1000\le X, Y\le 1000$. For $70\%$ of the testdata, $-10^5\le X, Y \le 10^5$. For $100\%$ of the testdata, $-10^9\le X, Y \le 10^9$. Translated by ChatGPT 5