Mountain Peaks After Land Swaps

In Berland Kingdom, the land is represented as an $n \times m$ grid. The cell at row $i$ and column $j$ initially has an altitude of $a_{i,j}$. Over a long period, there are $T$ geological events. In each event, the altitudes of two specified cells are swapped.

A cell is called a mountain peak if its altitude is strictly greater than the altitudes of all its directly adjacent neighbors (up, down, left, and right; if a neighbor does not exist, it is ignored).

After all swaps, you are to determine how many mountain peaks exist and output their coordinates. The cells are indexed starting from 1.

inputFormat

The first line contains three integers $n$, $m$, and $T$ ($1 \le n, m \le 1000$, $0 \le T \le 10^5$), representing the number of rows, columns, and the number of swap events respectively.

The next $n$ lines each contain $m$ integers, where the $j$-th integer in the $i$-th line is $a_{i,j}$, the altitude of the cell at row $i$, column $j$.

Then $T$ lines follow, each containing four integers $x_1$, $y_1$, $x_2$, $y_2$, indicating that the altitudes of the cells at positions $(x_1,y_1)$ and $(x_2,y_2)$ are to be swapped.

outputFormat

Output the total number of mountain peaks in the grid after all swaps. Then, output the coordinates of each mountain peak in separate lines in the format row column. The order of peaks can be arbitrary.

sample

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

2
1 3
2 2