Finding a Grayscale Image

A grayscale image has no color. Each pixel of a grayscale image therefore records one number, the brightness of that pixel. In this problem the brightness of a pixel is an integer between $0$ and $65535$.

A grayscale image $I$ of size $H \times W$ is $H \times W$ pixels arranged in $H$ rows and $W$ columns. Write $I[i, j]$ for the brightness of the pixel in row $i$ and column $j$. ($1 \le i \le H$, $1 \le j \le W$)

Gyeonggeun has a grayscale image $A$ of size $N \times M$ and a grayscale image $B$ of size $R \times C$. Here $N \ge R$ and $M \ge C$, so $A$ is no shorter and no narrower than $B$. Gyeonggeun believes that $A$ plagiarized $B$, and wants to count how many parts of $A$ resemble $B$.

The counting works like this. First choose one rectangle of $R \times C$ pixels inside the grayscale image $A$. The rectangle is determined by the position $(x, y)$ of the pixel at its top left corner. ($1 \le x \le N - R + 1$, $1 \le y \le M - C + 1$)

The size is fixed, so moving the top left corner moves the whole rectangle with it. For example, take the grayscale image above as $A$ and choose a $4 \times 6$ rectangle whose top left corner is $(4, 4)$. The bottom right corner of that rectangle is $(4 + 4 - 1, 4 + 6 - 1) = (7, 9)$.

Whether the chosen rectangle resembles the image $B$ is decided by the following rule.

If there are real numbers $p$ and $q$ such that $p \times A[x + i - 1, y + j - 1] + q = B[i, j]$ holds for every $i$ and $j$ with $1 \le i \le R$ and $1 \le j \le C$, then the rectangle chosen in $A$ and the image $B$ are similar.

Apply this rule to every rectangle of size $R \times C$ in $A$ and count the rectangles that are similar to $B$. In other words, apply the rule to every $(x, y)$ with $1 \le x \le N - R + 1$ and $1 \le y \le M - C + 1$, then count the pairs $(x, y)$ judged similar. Two rectangles of the same size are different when the coordinates of their top left corners differ, no matter what the brightness inside them is.

Help Gyeonggeun and write a program that counts the parts of $A$ that are similar to $B$.

The first line contains the number of rows $N$ and the number of columns $M$ of the grayscale image $A$, separated by a space. ($1 \le N, M \le 1000$)

The next $N$ lines describe the pixels of $A$. The $i$-th of those lines contains $M$ integers $A[i, 1], A[i, 2], \dots, A[i, M]$ separated by spaces. The $j$-th integer on the $i$-th line is the brightness of the pixel in row $i$ and column $j$ of $A$. ($1 \le i \le N$)

The next line contains the number of rows $R$ and the number of columns $C$ of the grayscale image $B$, separated by a space. ($1 \le R \le N$, $1 \le C \le M$)

The next $R$ lines describe the pixels of $B$. The $i$-th of those lines contains $C$ integers $B[i, 1], B[i, 2], \dots, B[i, C]$ separated by spaces. ($1 \le i \le R$)

Every given pixel brightness is an integer between $0$ and $65535$.

Print the number of parts of $A$ that are similar to $B$.

When every pixel of $B$ has the same brightness, you can take $p = 0$ and let $q$ be that brightness, so every rectangle of $A$ is judged similar.