Triangle?

AtCoder

IDabc224_c

Time2000ms

Memory256MB

Difficulty—

In the $xy$\-plane, we have $N$ points numbered $1$ through $N$. Point $i$ 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. ## 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 $i \neq j$. ## Input Input is given from Standard Input in the following format: $N$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\dots$ $X_N$ $Y_N$ [samples]

Samples

Input #1

Output #1

3

The figure below illustrates the points.
![image](https://img.atcoder.jp/ghi/11f8cb446cb2872c9a712c59195a1268.png)
There are three ways to choose points that form a triangle: ${1,2,3},{1,3,4},{2,3,4}$.

Input #2

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

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Triangle?",
    "description": {
      "content": "In the $xy$\\-plane, we have $N$ points numbered $1$ through $N$.   Point $i$ is at the coordinates $(X_i,Y_i)$. Any two different points are at different positions.   Find the number of ways to choose",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc224_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In the $xy$\\-plane, we have $N$ points numbered $1$ through $N$.  \nPoint $i$ is at the coordinates $(X_i,Y_i)$. Any two different points are at different positions.  \nFind the number of ways to choose...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments