CF1042E.Vasya and Magic Matrix

Vasya has got a magic matrix $a$ of size $n \times m$. The rows of the matrix are numbered from $1$ to $n$ from top to bottom, the columns are numbered from $1$ to $m$ from left to right. Let $a_{ij}$ be the element in the intersection of the $i$-th row and the $j$-th column.

Vasya has also got a chip. Initially, the chip is in the intersection of the $r$-th row and the $c$-th column (that is, in the element $a_{rc}$). Vasya performs the following process as long as possible: among all elements of the matrix having their value less than the value of the element with the chip in it, Vasya randomly and equiprobably chooses one element and moves his chip to this element.

After moving the chip, he adds to his score the square of the Euclidean distance between these elements (that is, between the element in which the chip is now and the element the chip was moved from). The process ends when there are no elements having their values less than the value of the element with the chip in it.

Euclidean distance between matrix elements with coordinates $(i_1, j_1)$ and $(i_2, j_2)$ is equal to $\sqrt{(i_1-i_2)^2 + (j_1-j_2)^2}$.

Calculate the expected value of the Vasya's final score.

It can be shown that the answer can be represented as $\frac{P}{Q}$, where $P$ and $Q$ are coprime integer numbers, and $Q \not\equiv 0~(mod ~ 998244353)$. Print the value $P \cdot Q^{-1}$ modulo $998244353$.

瓦西娅得到了一个大小为 $n \times m$ 的魔法矩阵 $a$。矩阵的行从上到下编号为 $1$ 到 $n$，列从左到右编号为 $1$ 到 $m$。令 $a_{ij}$ 表示第 $i$ 行与第 $j$ 列交叉处的元素。

瓦西娅还拥有一枚棋子。初始时，该棋子位于第 $r$ 行与第 $c$ 列的交叉处（即位于元素 $a_{rc}$）。瓦西娅重复执行如下过程，直到无法继续：在所有值严格小于当前棋子所在元素值的矩阵元素中，瓦西娅等概率地随机选择一个，并将棋子移动到该元素。

每次移动棋子后，他将本次移动的欧几里得距离的平方加到自己的得分中（即当前棋子所在位置与移动前位置之间的欧几里得距离的平方）。当不存在任何值严格小于当前棋子所在元素值的矩阵元素时，该过程结束。

坐标为 $(i_1, j_1)$ 与 $(i_2, j_2)$ 的矩阵元素之间的欧几里得距离定义为 $\sqrt{(i_1-i_2)^2 + (j_1-j_2)^2}$。

请计算瓦西娅最终得分的期望值。

可以证明，答案总可表示为 $\frac{P}{Q}$ 的形式，其中 $P$ 与 $Q$ 是互质的整数，且 $Q \not\equiv 0 \pmod{998244353}$。请输出 $P \cdot Q^{-1} \bmod 998244353$。

The first line of the input contains two integers $n$ and $m$ $(1 \le n, m \le 1\,000)$ — the number of rows and the number of columns in the matrix $a$.

The following $n$ lines contain description of the matrix $a$. The $i$-th line contains $m$ integers $a_{i1}, a_{i2}, \dots, a_{im} ~ (0 \le a_{ij} \le 10^9)$.

The following line contains two integers $r$ and $c$ $(1 \le r \le n, 1 \le c \le m)$ — the index of row and the index of column where the chip is now.

输入的第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 1\,000$）—— 分别表示矩阵 $a$ 的行数和列数。

接下来的 $n$ 行描述矩阵 $a$。其中第 $i$ 行包含 $m$ 个整数 $a_{i1}, a_{i2}, \dots, a_{im}$（$0 \le a_{ij} \le 10^9$）。

接下来的一行包含两个整数 $r$ 和 $c$（$1 \le r \le n,\ 1 \le c \le m$）—— 表示芯片当前所在的行号与列号。

Print the expected value of Vasya's final score in the format described in the problem statement.

按题目描述的格式输出瓦西娅最终得分的期望值。

In the first example, Vasya will move his chip exactly once. The expected value of the final score is equal to $\frac{1^2 + 2^2+ 1^2}{3} = 2$.

在第一个例子中，瓦西娅将恰好移动他的棋子一次。最终得分的期望值等于 $\frac{1^2 + 2^2+ 1^2}{3} = 2$。