Mosaic Browsing

The International Center for the Preservation of Ceramics (ICPC) is searching for motifs in some ancient mosaics. According to the ICPC’s definition, a mosaic is a rectangular grid where each grid square contains a colored tile. A motif is similar to a mosaic but some of the grid squares can be empty. Figure 1 shows an example motif and mosaic.

The rows of an $r_ q \times c_ q$ mosaic are numbered $1$ to $r_ q$ from top to bottom, and the columns are numbered $1$ to $c_ q$ from left to right.

A contiguous rectangular subgrid of the mosaic matches the motif if every tile of the motif matches the color of the corresponding tile of the subgrid. Formally, an $r_ p \times c_ p$ motif appears in an $r_ q \times c_ q$ mosaic at position $(r, c)$ if for all $1 \leq i \leq r_ p$, $1 \leq j \leq c_ p$, the tile $(r + i - 1, c + j - 1)$ exists in the mosaic and either the square $(i, j)$ in the motif is empty or the tile at $(i, j)$ in the motif has the same color as the tile at $(r + i - 1, c + j - 1)$ in the mosaic.

Given the full motif and mosaic, find all occurrences of the motif in the mosaic.

Figure 1: Motif (left) and mosaic (right) of Sample Input 1.

Input

The first line of input contains two integers $r_ p$ and $c_ p$, where $r_ p$ and $c_ p$ ($1 \leq r_ p, c_ p \leq 1\, 000$) are the number of rows and columns in the motif. Then $r_ p$ lines follow, each with $c_ p$ integers in the range $[0, 100]$, denoting the color of the motif at that position. A value of $0$ denotes an empty square.

The next line of input contains two integers $r_ q$ and $c_ q$ where $r_ q$ and $c_ q$ ($1 \leq r_ q, c_ q \leq 1\, 000$) are the number of rows and columns in the mosaic. Then $r_ q$ lines follow, each with $c_ q$ integers in the range $[1, 100]$, denoting the color of the mosaic at that position.

Output

On the first line, output $k$, the total number of matches. Then output $k$ lines, each of the form $r$ $c$ where $r$ is the row and $c$ is the column of the top left tile of the match. Sort matches by increasing $r$, breaking ties by increasing $c$.

2 2
1 0
0 1
3 4
1 2 1 2
2 1 1 1
2 2 1 3

3
1 1
1 3
2 2