Shower

Sinchon has a plain of size $N \times M$, called Sinchon Plain. Showers fall on this plain for $Q$ days. The top-left cell of Sinchon Plain has coordinates $(1, 1)$, and the bottom-right cell has coordinates $(N, M)$.

A shower falls on cell $(a, b)$. After it falls, the ground height decreases by $c$ and water remains in that cell. Ground heights can be negative.

If adjacent cells contain water, the water in those cells becomes connected. Two cells are adjacent when they share an edge.

After each shower, the Sinchon Plain Management Headquarters installs a water quality inspection robot at that point. The robot moves freely through the connected water and finishes its inspection at the cell with the lowest height. If several cells have the lowest height, it finishes at the cell that received rain the longest ago.

Given the locations where showers fall over $Q$ days, write a program that prints, for each day, the point where the robot finishes its inspection.

The first line gives $N$ ($1 \le N \le 1\,000$), $M$ ($1 \le M \le 1\,000$), and $Q$ ($1 \le Q \le 100\,000$), separated by spaces.

Lines 2 to $N+1$ give the height $H$ of each cell of Sinchon Plain ($0 \le H_{a, b} \le 1\,000$) as integers.

Lines $N+2$ to $N+Q+1$ give, in order, the coordinates $a$ ($1 \le a \le N$) and $b$ ($1 \le b \le M$) of the cell where rain falls, and the amount $c$ ($1 \le c \le 100$) by which the ground height decreases, as integers.

For each day, print the coordinates of the point where the robot finishes its inspection, one per line, in order.

The following is the figure for Sample 1.