#include <bits/stdc++.h>

#define MOD 998244353

using namespace std;

int powers2[201], x[200], y[200];

int main() {
  powers2[0] = 1;
  for (int i = 1; i <= 200; i++) powers2[i] = powers2[i - 1] * 2 % MOD;

  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d %d", &x[i], &y[i]);
  
  int res = powers2[n];
  res -= 1 + n + n * (n - 1) / 2;
  res %= MOD;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      int counter = 2;
      int a = y[j] - y[i];
      int b = x[i] - x[j];
      int c = -a * x[i] - b * y[i];
      for (int k = 0; k < n; k++) {
        if (k == i || k == j) continue;
        if (a * x[k] + b * y[k] + c != 0) continue;
        if (k < j) break;
        counter++;
      }
      res -= powers2[counter];
      res += 1 + counter + counter * (counter - 1) / 2;
      res %= MOD;
    }
  }
  printf("%d\n", (res % MOD + MOD) % MOD);
  return 0;
}

### Prompt

Your task is to create a Cpp solution 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>

#define MOD 998244353

using namespace std;

int powers2[201], x[200], y[200];

int main() {
  powers2[0] = 1;
  for (int i = 1; i <= 200; i++) powers2[i] = powers2[i - 1] * 2 % MOD;

  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d %d", &x[i], &y[i]);
  
  int res = powers2[n];
  res -= 1 + n + n * (n - 1) / 2;
  res %= MOD;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      int counter = 2;
      int a = y[j] - y[i];
      int b = x[i] - x[j];
      int c = -a * x[i] - b * y[i];
      for (int k = 0; k < n; k++) {
        if (k == i || k == j) continue;
        if (a * x[k] + b * y[k] + c != 0) continue;
        if (k < j) break;
        counter++;
      }
      res -= powers2[counter];
      res += 1 + counter + counter * (counter - 1) / 2;
      res %= MOD;
    }
  }
  printf("%d\n", (res % MOD + MOD) % MOD);
  return 0;
}

```