Rocky Mountain Road Trip

Adeline and Byron are on a road trip through the mountains. Interestingly, the roads through the mountains can be modeled as a grid of size $n \times m$, where each cell has an integer altitude. The grid follows standard Cartesian coordinates, with the top-left corner being $(1,1)$ and the bottom-right corner being $(n, m)$.

Adeline, an adrenaline junkie, loves the ups and downs of the mountains, while Byron gets motion sick easily. After some debate, they agreed on a compromise: they must find a route from their starting position $(x\_0, y\_0)$ to their destination $(x\_f, y\_f)$ that minimizes the total distance traveled, but to make it fun for Adeline, they must alternate between gaining and losing altitude with every move. If they take a longer path than necessary, Byron will get sick.

Adeline and Byron's car can move in any of the 8 cardinal directions: North, Northeast, East, Southeast, South, Southwest, West, and Northwest. Each movement to an adjacent cell counts as a distance of 1, regardless of direction.

Help Adeline and Byron determine the minimum number of moves required to reach their destination.

The first line contains two integers $n$ and $m$ $(1 \leq n, m \leq 500)$—the dimensions of the grid.

The next $n$ lines each contain $m$ integers $h\_{i,j}$ $(0 \leq h\_{i,j} \leq 10^9)$, representing the altitude of each cell in the grid.

The next line contains four integers $x\_0, y\_0, x\_f, y\_f$ $(1 \leq x\_0, x\_f \leq n, 1 \leq y\_0, y\_f \leq m)$—the starting and destination positions.

It is guaranteed that the starting and destination positions are distinct.

Print a single integer—the minimum number of moves required to reach $(x\_f, y\_f)$ from $(x\_0, y\_0)$, or print $-1$ if it is impossible to reach the destination.