Alchemy

For many years, alchemists tried to perform transmutation with the Philosopher's Stone. The alchemist Vlachur came very close. Vlachur has a rectangular metal grid made of $(n+1)+(m+1)$ iron rods, sized $n$ by $m$. The horizontal rods are numbered from $0$ to $n$ from bottom to top, and the vertical rods are numbered from $0$ to $m$ from left to right.

To carry out the transmutation, Vlachur performs the following operation: he takes one rod and paints all of it with magic paint. To see how close he is to his goal, he needs to know how many unit-area squares of his grid have exactly $t$ ($0 \le t \le 4$) painted sides. Help him!

The first line contains three integers $n$, $m$, and $q$ ($1 \le n, m \le 10^9$, $1 \le q \le 10^5$), the grid size and the number of operations. Each of the next $q$ lines describes an operation.

If the first character of the line is h, the same line contains an integer $x$ ($0 \le x \le n$), and the operation paints horizontal rod $x$. Similarly, a line starting with v followed by an integer $y$ ($0 \le y \le m$) paints vertical rod $y$.

A line consisting of a single ? means you must output five numbers: for every $t$ from $0$ to $4$, print $a_t$, the number of sub-rectangles of the grid that have exactly $t$ painted sides.

For each ? operation, print five numbers: the required counts $a_0, a_1, a_2, a_3, a_4$.