#define REP(i,n) for(int i=0; i<(int)(n); i++)

#include <queue>
#include <cstdio>
inline int getInt(){ int s; scanf("%d", &s); return s; }

typedef long long ll;

#include <set>

using namespace std;

const ll mod = 998244353;

ll pow2(int n){
  ll r = 1;
  REP(i,n) r = (r * 2) % mod;
  return r;
}

int main(){
  const int n = getInt();
  vector<int> x(n);
  vector<int> y(n);

  REP(i,n){
    x[i] = getInt();
    y[i] = getInt();
  }

  if(n <= 2) {
    puts("0");
    return 0;
  }

  ll ans = pow2(n) - 1 - n;

  for(int i = 0; i < n; i++){
    for(int j = i + 1; j < n; j++){
      int cnt = 2;
      for(int k = 0; k < n; k++){
	if(k == i || k == j) continue;

	if((x[j] - x[i]) * (y[k] - y[i]) == (y[j] - y[i]) * (x[k] - x[i])){
	  if(k < j) goto bad;
	  cnt++;
	}
      }

      ans = (ans - (pow2(cnt) - cnt - 1) + mod) % mod;
    bad:;
    }
  }

  printf("%lld\n", ans);

  return 0;
}
### 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
#define REP(i,n) for(int i=0; i<(int)(n); i++)

#include <queue>
#include <cstdio>
inline int getInt(){ int s; scanf("%d", &s); return s; }

typedef long long ll;

#include <set>

using namespace std;

const ll mod = 998244353;

ll pow2(int n){
  ll r = 1;
  REP(i,n) r = (r * 2) % mod;
  return r;
}

int main(){
  const int n = getInt();
  vector<int> x(n);
  vector<int> y(n);

  REP(i,n){
    x[i] = getInt();
    y[i] = getInt();
  }

  if(n <= 2) {
    puts("0");
    return 0;
  }

  ll ans = pow2(n) - 1 - n;

  for(int i = 0; i < n; i++){
    for(int j = i + 1; j < n; j++){
      int cnt = 2;
      for(int k = 0; k < n; k++){
	if(k == i || k == j) continue;

	if((x[j] - x[i]) * (y[k] - y[i]) == (y[j] - y[i]) * (x[k] - x[i])){
	  if(k < j) goto bad;
	  cnt++;
	}
      }

      ans = (ans - (pow2(cnt) - cnt - 1) + mod) % mod;
    bad:;
    }
  }

  printf("%lld\n", ans);

  return 0;
}
```