        #include <bits/stdc++.h>
        using namespace std;
   #define int long long
const int MAX =2000007;
const int MOD = 998244353;
//
int modpow(int a, int n, int mod) {
    int res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}
     signed main(){
  int n;
  cin>>n;
  int x[n],y[n];for(int i=0;i<n;i++)cin>>x[i]>>y[i];
  bool used[n][n];for(int i=0;i<n;i++)fill(used[i],used[i]+n,false);
  int ans=(modpow(2,n,MOD)+MOD-n-1)%MOD;
  for(int i=0;i<n;i++)for(int j=i+1;j<n;j++){
      if(used[i][j])continue;
      vector<int> v;
      v.push_back(i);v.push_back(j);
      for(int k=j+1;k<n;k++)if((x[i]-x[k])*(y[i]-y[j])==(y[i]-y[k])*(x[i]-x[j]))v.push_back(k);
      ans=(ans+MOD-modpow(2,v.size(),MOD)+v.size()+1)%MOD;
    for(int p=0;p<v.size();p++)for(int q=p+1;q<v.size();q++)used[v[p]][v[q]]=true;
  }
  cout<<ans<<endl;

     }


 


 






    





      

        

### Prompt

Construct a CPP code solution to the problem outlined:

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;
   #define int long long
const int MAX =2000007;
const int MOD = 998244353;
//
int modpow(int a, int n, int mod) {
    int res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}
     signed main(){
  int n;
  cin>>n;
  int x[n],y[n];for(int i=0;i<n;i++)cin>>x[i]>>y[i];
  bool used[n][n];for(int i=0;i<n;i++)fill(used[i],used[i]+n,false);
  int ans=(modpow(2,n,MOD)+MOD-n-1)%MOD;
  for(int i=0;i<n;i++)for(int j=i+1;j<n;j++){
      if(used[i][j])continue;
      vector<int> v;
      v.push_back(i);v.push_back(j);
      for(int k=j+1;k<n;k++)if((x[i]-x[k])*(y[i]-y[j])==(y[i]-y[k])*(x[i]-x[j]))v.push_back(k);
      ans=(ans+MOD-modpow(2,v.size(),MOD)+v.size()+1)%MOD;
    for(int p=0;p<v.size();p++)for(int q=p+1;q<v.size();q++)used[v[p]][v[q]]=true;
  }
  cout<<ans<<endl;

     }


 


 






    





      

        

```