#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=998244353;

ll beki[222];
int used[222][222];

int main(){
  beki[0]=1;
  rep(i,202) beki[i+1]=beki[i]*2%MOD;
  ll N; cin>>N;
  ll X[N],Y[N]; rep(i,N) cin>>X[i]>>Y[i];
  ll ans=(beki[N]-1-N-N*(N-1)/2+MOD)%MOD;
  rep(i,N) rep(j,i) if(used[i][j]==0){
    vector<int> V;
    V.push_back(i);
    V.push_back(j);
    rep(k,N) if(k!=i&&k!=j){
      if((X[k]-X[j])*(Y[i]-Y[j])-(X[i]-X[j])*(Y[k]-Y[j])==0) V.push_back(k);
    }
    ll n=V.size();
    rep(k,n) rep(l,n) used[V[k]][V[l]]=1;
    if(n>=3) ans=(ans+MOD-beki[n]+1+n+n*(n-1)/2)%MOD;
  }
  cout<<ans%MOD<<endl;
  return 0;
}

### Prompt

Create a solution in cpp for 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;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=998244353;

ll beki[222];
int used[222][222];

int main(){
  beki[0]=1;
  rep(i,202) beki[i+1]=beki[i]*2%MOD;
  ll N; cin>>N;
  ll X[N],Y[N]; rep(i,N) cin>>X[i]>>Y[i];
  ll ans=(beki[N]-1-N-N*(N-1)/2+MOD)%MOD;
  rep(i,N) rep(j,i) if(used[i][j]==0){
    vector<int> V;
    V.push_back(i);
    V.push_back(j);
    rep(k,N) if(k!=i&&k!=j){
      if((X[k]-X[j])*(Y[i]-Y[j])-(X[i]-X[j])*(Y[k]-Y[j])==0) V.push_back(k);
    }
    ll n=V.size();
    rep(k,n) rep(l,n) used[V[k]][V[l]]=1;
    if(n>=3) ans=(ans+MOD-beki[n]+1+n+n*(n-1)/2)%MOD;
  }
  cout<<ans%MOD<<endl;
  return 0;
}

```