#include <bits/stdc++.h>

using namespace std;

const int mod = 998244353;

int main()
{
  int fact[501];
  fact[0] = 1;
  for(int i = 1; i < 501; i++) (fact[i] = fact[i - 1] * 2) %= mod;

  int N, X[500], Y[500];
  cin >> N;
  for(int i = 0; i < N; i++) cin >> X[i] >> Y[i];

  int ret = fact[N];

  for(int i = 0; i < N; i++) {
    for(int j = i + 1; j < N; j++) {
      int sum = 0;
      for(int k = j + 1; k < N; k++) {
        sum += (X[j] - X[i]) * (Y[k] - Y[i]) == (X[k] - X[i]) * (Y[j] - Y[i]);
      }
      (ret += mod - fact[sum]) %= mod;
    }
  }

  (ret += mod - 1) %= mod;
  (ret += mod - N) %= mod;

  cout << ret << endl;
}
### Prompt

Please create a solution in cpp to the following problem:

You are given N points (x_i,y_i) located on a two-dimensional plane. Consider a subset S of the N points that forms a convex polygon. Here, we say a set of points S forms a convex polygon when there exists a convex polygon with a positive area that has the same set of vertices as S. All the interior angles of the polygon must be strictly less than 180°.

cddb0c267926c2add885ca153c47ad8a.png

For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons; {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.

For a given set S, let n be the number of the points among the N points that are inside the convex hull of S (including the boundary and vertices). Then, we will define the score of S as 2^{n-|S|}.

Compute the scores of all possible sets S that form convex polygons, and find the sum of all those scores.

However, since the sum can be extremely large, print the sum modulo 998244353.

Constraints

* 1≤N≤200
* 0≤x_i,y_i<10^4 (1≤i≤N)
* If i≠j, x_i≠x_j or y_i≠y_j.
* x_i and y_i are integers.

Input

The input is given from Standard Input in the following format:


N
x_1 y_1
x_2 y_2
:
x_N y_N


Output

Print the sum of all the scores modulo 998244353.

Examples

Input

4
0 0
0 1
1 0
1 1


Output

5


Input

5
0 0
0 1
0 2
0 3
1 1


Output

11


Input

1
3141 2718


Output

0

### Response

```cpp
#include <bits/stdc++.h>

using namespace std;

const int mod = 998244353;

int main()
{
  int fact[501];
  fact[0] = 1;
  for(int i = 1; i < 501; i++) (fact[i] = fact[i - 1] * 2) %= mod;

  int N, X[500], Y[500];
  cin >> N;
  for(int i = 0; i < N; i++) cin >> X[i] >> Y[i];

  int ret = fact[N];

  for(int i = 0; i < N; i++) {
    for(int j = i + 1; j < N; j++) {
      int sum = 0;
      for(int k = j + 1; k < N; k++) {
        sum += (X[j] - X[i]) * (Y[k] - Y[i]) == (X[k] - X[i]) * (Y[j] - Y[i]);
      }
      (ret += mod - fact[sum]) %= mod;
    }
  }

  (ret += mod - 1) %= mod;
  (ret += mod - N) %= mod;

  cout << ret << endl;
}
```