F. Sweetest Piece
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Zeynep has been craving baklava to satisfy her major sweet tooth. As she's pouring the syrup over the baklava, she wonders: given the locations where she has poured syrup, which piece ends up the sweetest?

Formally, each baklava piece is located at some index $$$(i,j)$$$ on a $$$n \times m$$$ grid, and has some height $$$h_{i,j}$$$. Due to the way the baklava is sliced, the syrup flows at an angle; the syrup can either flow directly up or down to $$$(i \pm 1, j)$$$, or it can flow at a diagonal to either $$$(i-1, j-1)$$$ or $$$(i+1, j+1)$$$. The syrup can only flow to a piece with the same or lower height.

Zeynep pours the syrup on $$$q$$$ locations, and lets the syrup flow completely before pouring again. Can you identify which piece is covered by syrup the most number of times?

Input

The first line contains $$$n, m$$$ and $$$q$$$ ($$$1 \leq n,m \leq 100$$$, $$$1 \leq q \leq 1000$$$), the dimensions of the baklava grid and the number of syrup pours.

The next $$$n$$$ lines each contain $$$m$$$ integers, where the $$$i$$$th line contains the heights $$$h_{i,1}, \ldots, h_{i,m}$$$ ($$$0 \leq h_{i,j} \leq 10^9$$$) of each baklava piece.

The next $$$q$$$ lines contain two integers $$$i$$$ and $$$j$$$ ($$$1 \leq i \leq n, 1 \leq j \leq m$$$), the coordinates of the piece where the $$$i$$$th syrup pour starts.

Output

Output three integers, the coordinates of the sweetest piece $$$(i,j)$$$, as well as the number of times that piece gets covered by syrup. If there are multiple sweetest pieces, pick the one with the smallest row coordinate $$$i$$$, and break further ties with the smallest column $$$j$$$.

Example
Input
5 5 3
7 9 9 9 9
6 6 9 2 8
5 9 5 2 8
4 3 5 2 8
3 9 5 2 8
1 1
3 3
1 5
Output
2 4 3