Water Spreading

You are a graduate student studying how water flows over an $N \times N$ grid of land. Your goal is to find how many of the $N^2$ cells, each with a given height, receive water. After years of research, you found that water spreads according to the following rules.

• Each cell holds a water state, which is one of the $(X+1)$ integers $0, 1, 2, \cdots, X$. State $0$ means no water, and states $1, \cdots, X$ mean water is present.
• The cell where water is first poured has state $X$.
• When water spreads from a cell $(x,y)$ to an adjacent cell, the state of $(x,y)$ is unchanged.
• For an integer $l$ greater than $1$, water in a cell with state $l$ spreads by the following rules.
  • Every second, water spreads to each adjacent cell with the same height as the current cell. The spread water has state $(l-1)$. Water does not spread to a cell whose state is $(l-1)$ or higher.
  • Every second, water spreads to each adjacent cell lower than the current cell. The spread water has state $X$.
• Water can spread from one cell many times. Spreading happens at all cells at the same time.
• If several cells spread water into the same cell at once, its state is the maximum of the spread states.
• If a cell $(x,y)$ has state $0$ and no cell spreads water into $(x,y)$, its state stays $0$.

Two cells $(a,b)$ and $(x,y)$ are adjacent when $|a-x|+|b-y| = 1$. $(i,j)$ denotes row $i$, column $j$. Given the height of each cell in the $N \times N$ grid and the cell where water is first poured, find the number of cells with water, that is, cells with state $1, \cdots, X$, after enough time has passed that water no longer spreads.

The first line contains four integers $N$, $X$, $x$, and $y$, separated by spaces. ($1 \le N \le 2\,000$, $1 \le X \le 2N$, $1 \le x, y \le N$)

$N$ is the side length of the grid, $X$ is the state of the water poured first, and $(x,y)$ is the cell where water is first poured.

The next $N$ lines describe the grid. The $j$-th integer $h_{ij}$ on the $i$-th line is the height of cell $(i,j)$. ($0 \le h_{ij} \le 100\,000$)

Print the number of cells with water, meaning cells with state $1, \cdots, X$, after enough time has passed that water no longer spreads, on the first line.