6835: ABC168 —— F - . (Single Dot)
[Creator : ]
Description
There is a grass field that stretches infinitely.
In this field, there is a negligibly small cow. Let $(x, y)$ denote the point that is $x\ \mathrm{cm}x$ cm south and $y\ \mathrm{cm}y$ cm east of the point where the cow stands now. The cow itself is standing at $(0,0)$.
There are also $N$ north-south lines and $M$ east-west lines drawn on the field. The $i$-th north-south line is the segment connecting the points $(A_i, C_i)$ and $(B_i, C_i)$, and the $j$-th east-west line is the segment connecting the points $(D_j, E_j)$ and $(D_j, F_j)$.
What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.
In this field, there is a negligibly small cow. Let $(x, y)$ denote the point that is $x\ \mathrm{cm}x$ cm south and $y\ \mathrm{cm}y$ cm east of the point where the cow stands now. The cow itself is standing at $(0,0)$.
There are also $N$ north-south lines and $M$ east-west lines drawn on the field. The $i$-th north-south line is the segment connecting the points $(A_i, C_i)$ and $(B_i, C_i)$, and the $j$-th east-west line is the segment connecting the points $(D_j, E_j)$ and $(D_j, F_j)$.
What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print INF instead.
Input
Input is given from Standard Input in the following format:
$N\ M$
$A_1\ B_1\ C_1$
$\vdots$
$A_N\ B_N\ C_N$
$D_1\ E_1\ F_1$
$\vdots$
$D_M\ E_M\ F_M$
$N\ M$
$A_1\ B_1\ C_1$
$\vdots$
$A_N\ B_N\ C_N$
$D_1\ E_1\ F_1$
$\vdots$
$D_M\ E_M\ F_M$
Output
If the area of the region the cow can reach is infinite, print INF; otherwise, print an integer representing the area in $\mathrm{cm^2}$.
(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)
(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)
Constraints
All values in input are integers between $-10^9$ and $10^9$ (inclusive).
$1 \leq N, M \leq 1000$
$A_i < B_i\ (1 \leq i \leq N)$
$E_j < F_j\ (1 \leq j \leq M)$
The point $(0, 0)$ does not lie on any of the given segments.
$1 \leq N, M \leq 1000$
$A_i < B_i\ (1 \leq i \leq N)$
$E_j < F_j\ (1 \leq j \leq M)$
The point $(0, 0)$ does not lie on any of the given segments.
Sample 1 Input
5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4
Sample 1 Output
13
The area of the region the cow can reach is $13\ \mathrm{cm^2}$.
Sample 2 Input
6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4
Sample 2 Output
INF
The area of the region the cow can reach is infinite.