6288: ABC224 —— C - Triangle?
[Creator : ]
Description
In the $xy$-plane, we have $N$ points numbered $1$ through $N$.
Point ii is at the coordinates $(X_i,Y_i)$. Any two different points are at different positions.
Find the number of ways to choose three of these $N$ points so that connecting the chosen points with segments results in a triangle with a positive area.
Point ii is at the coordinates $(X_i,Y_i)$. Any two different points are at different positions.
Find the number of ways to choose three of these $N$ points so that connecting the chosen points with segments results in a triangle with a positive area.
Input
Input is given from Standard Input in the following format:
$N$
$X_1\ Y_1$
$X_2\ Y_2$
$\dots$
$X_N\ Y_N$
$N$
$X_1\ Y_1$
$X_2\ Y_2$
$\dots$
$X_N\ Y_N$
Output
Print the answer as an integer.
Constraints
All values in input are integers.
$3 \le N \le 300$
$-10^9 \le X_i,Y_i \le 10^9$
$(X_i,Y_i) \neq (X_j,Y_j)$ if $i \neq j$.
$3 \le N \le 300$
$-10^9 \le X_i,Y_i \le 10^9$
$(X_i,Y_i) \neq (X_j,Y_j)$ if $i \neq j$.
Sample 1 Input
4
0 1
1 3
1 1
-1 -1
Sample 1 Output
3
The figure below illustrates the points.
There are three ways to choose points that form a triangle: $\{1,2,3\},\{1,3,4\},\{2,3,4\}$.
Sample 2 Input
20
224 433
987654321 987654321
2 0
6 4
314159265 358979323
0 0
-123456789 123456789
-1000000000 1000000000
124 233
9 -6
-4 0
9 5
-7 3
333333333 -333333333
-9 -1
7 -10
-1 5
324 633
1000000000 -1000000000
20 0
Sample 2 Output
1124