The 2016 Nordic Collegiate Programming Contest


2016-10-08 11:00 CEST

The 2016 Nordic Collegiate Programming Contest


2016-10-08 16:00 CEST
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Problem A

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.

\includegraphics[width=0.9\textwidth ]{sample}
Figure 1: Illustration of Sample Input 1.


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).


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