Artifact Excavation

The Hongik University playground is a grid with $R$ rows and $C$ columns. Fragments of artifacts that could shake up the academic world have been found on this playground.

Only one artifact can be excavated at a time. So the artifact with the largest expected size is excavated first. If several artifacts share the largest expected size, the one with the smallest number is excavated first.

Each fragment is $1 \times 1$ in size, and several fragments can be at the same position. The expected size of an artifact is the size of the smallest rectangle that encloses all of its fragments. All sides of the rectangle must be parallel to the sides of the playground.

The first line contains two integers $R$ and $C$, separated by a space. $(1 \leq R, C \leq 100\,000)$

The second line contains the number of fragments $N$. $(1 \leq N \leq 100\,000)$

From the third line, the next $N$ lines each contain three integers $a_i$, $v_i$, and $h_i$, separated by spaces. $(1 \leq a_i \leq N;$ $1 \leq v_i \leq R;$ $1 \leq h_i \leq C)$ This means that a fragment of artifact $a_i$ is at row $v_i$, column $h_i$.

Print the number of the artifact that is excavated first and its expected size, separated by a space.