P9204 Immortal "Firebird − Phoenix Wings Soaring−"

Fujiwara no Mokou, who has gained the power of “immortality”, also obtained the ability to control flames, and became the incarnation of a firebird. Are a firebird and a phoenix the same kind of creature?

Mokou can control a firebird. The firebird can be seen as a piece $A$ placed on an **infinitely large** chessboard, with $A$ located at $(x_1,y_1)$. $A$ moves by the following rules: - On odd-numbered moves, $A$ can only move one square to the upper-right or lower-left, as shown by the red arrows in the figure. - On even-numbered moves, $A$ can only move one square to the lower-right or upper-left, as shown by the blue arrows in the figure.  Because the board is infinite, $x$ and $y$ may be negative. In each step, $A$ cannot stay in place. Now we need to move $A$ to position $B$ with coordinates $(x_2,y_2)$. What is the minimum number of steps? In particular, if no such plan exists, output $-1$. The figure below shows the case $A=(2,7)$ and $B=(5,2)$. One optimal plan is marked in the figure and requires $9$ steps. Red segments represent odd-numbered moves, and blue segments represent even-numbered moves. 

The input consists of one line with four integers $x_1,y_1,x_2,y_2$, describing the coordinates of $A$ and $B$.

Output one line with one integer. If there exists a move sequence from $A$ to $B$, output the minimum number of steps; otherwise output $-1$.

### Constraints and Notes For all testdata, it is guaranteed that $0\le x_1,y_1,x_2,y_2\le 10^9$. Translated by ChatGPT 5