A template for an artwork is a white grid of $n \times m$ squares. The artwork will
be created by painting $q$
horizontal and vertical black strokes. A stroke starts from
square $(x_1,y_1)$, ends
at square $(x_2,y_2)$
($x_1=x_2$ or $y_1=y_2$) and changes the color of
all squares $(x,y)$ to
black where $x_1 \le x \le
x_2$ and $y_1 \le y \le
y_2$.
The beauty of an artwork is the number of regions in the
grid. Each region consists of one or more white squares that
are connected to each other using a path of white squares in
the grid, walking horizontally or vertically but not
diagonally. The initial beauty of the artwork is $1$. Your task is to calculate the
beauty after each new stroke. Figure 1 illustrates how the
beauty of the artwork varies in Sample Input 1.
Input
The first line of input contains three integers $n$, $m$ and $q$ ($1
\le n,m \le 1000$, $1 \le
q \le 10^4$).
Then follow $q$ lines
that describe the strokes. Each line consists of four integers
$x_1$, $y_1$, $x_2$ and $y_2$ ($1 \le x_1 \le x_2 \le n$,
$1 \le y_1 \le y_2 \le
m$). Either $x_1 =
x_2$ or $y_1 = y_2$
(or both).
Output
For each of the $q$
strokes, output a line containing the beauty of the artwork
after the stroke.
Sample Input 1 
Sample Output 1 
4 6 5
2 2 2 6
1 3 4 3
2 5 3 5
4 6 4 6
1 6 4 6

1
3
3
4
3
