Leon has created a cute little robot spider pet! //$(::$w$::)$\
Instead of generating an intricate pattern for its web, it simply interweaves $R$ rows with $C$ columns of silk. It starts with an empty web; a full web consists of $R+C$ strands of silk forming a grid-like pattern.
Please help implement some of its functions, and you might be rewarded (with points)!

F1: Robo-Spider generates silk somehow (don't ask me, I'm just the programmer). It weaves in consecutive rows of silk, filling in all rows from $A$ to $B$ (inclusive), if they don't already exist.
F2: Same as F1, but for columns.
F3: Consecutive rows of silk snap (blame the chemist)! Only existing strands of silk that make up rows $A$ to $B$ (inclusive) are affected.
F4: Same as F3, but for columns.
F5: How much of the web is exposed? Please determine the total area not covered by the web.
F6: How optimal is the web? Please determine the area of the hole with the maximum area in the web.

Input Specification

The first line contains three integers: $R$ (the number of rows), $C$ (the number of columns), and $Q$ (the number of queries).
The following $Q$ lines each begin with a function number, $F$. For just F1 to F4, $A$ and $B$ follow.

Output Specification

For each F5 and F6, output the answer on its own line.

Constraints

$1\le F\le 6$
$1\le A\le B\le R$ or $C$

Subtask	Percentage	Constraints
$1$	$20$	$1\le R,C,Q\le 100$
$2$	$20$	$1\le R,C,Q\le 1000$
$3$	$60$	$1\le R,C,Q\le 200000$

Sample Input

10 10 7
6
1 4 6
5
2 7 8
6
3 5 5
5

Sample Output

100
70
24
64

Diagram

A picture is worth a thousand words.

 \ 1 2 3 4 5 6 7 8 9 10
 1
 2
 3
 4
 5         100
 6
 7
 8
 9
10

 \ 1 2 3 4 5 6 7 8 9 10
 1
 2          30
 3
 4 --------------------
 5 --------------------    = 70
 6 --------------------
 7
 8          40
 9
10

 \ 1 2 3 4 5 6 7 8 9 10
 1             | |
 2             | |
 3             | |
 4 ------------|-------
 5 --------------|-----
 6 ------------|-------
 7             | |
 8      24     | |
 9             | |
10             | |

 \ 1 2 3 4 5 6 7 8 9 10
 1             | |
 2      18     | |  6
 3             | |
 4 ------------|-------
 5       6     | |  2      = 64
 6 ------------|-------
 7             | |
 8      24     | |  8
 9             | |
10             | |