#include<cstdio>
using namespace std;
#define mod 998244353
typedef long long ll;
int main(){
    int n,x[200],y[200],cnt;
    ll c[201]={},two[201],ans;
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d %d",&x[i],&y[i]);
    }
    two[0]=1;
    for(int i=1;i<=n;i++){
        two[i]=2*two[i-1];
        two[i]%=mod;
    }
    for(int i=0;i<n;i++){
        for(int j=i+1;j<n;j++){
            cnt=0;
            for(int k=0;k<n;k++){
                if(x[i]*y[j]-y[i]*x[j]+x[j]*y[k]-y[j]*x[k]+x[k]*y[i]-y[k]*x[i]==0){
                    cnt++;
                }
            }
            c[cnt]++;
        }
    }
    ans=two[n];
    ans-=n+1;
    ans+=mod;
    ans%=mod;
    for(ll i=2LL;i<=n;i++){
        c[i]*=2LL;
        c[i]/=i;
        c[i]/=(i-1LL);
        ans-=(two[i]-i-1LL)*c[i];
        ans%=mod;
        ans+=mod;
        ans%=mod;
    }
    printf("%lld\n",ans);
}
### Prompt

Develop a solution in Cpp to the problem described below:

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<cstdio>
using namespace std;
#define mod 998244353
typedef long long ll;
int main(){
    int n,x[200],y[200],cnt;
    ll c[201]={},two[201],ans;
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d %d",&x[i],&y[i]);
    }
    two[0]=1;
    for(int i=1;i<=n;i++){
        two[i]=2*two[i-1];
        two[i]%=mod;
    }
    for(int i=0;i<n;i++){
        for(int j=i+1;j<n;j++){
            cnt=0;
            for(int k=0;k<n;k++){
                if(x[i]*y[j]-y[i]*x[j]+x[j]*y[k]-y[j]*x[k]+x[k]*y[i]-y[k]*x[i]==0){
                    cnt++;
                }
            }
            c[cnt]++;
        }
    }
    ans=two[n];
    ans-=n+1;
    ans+=mod;
    ans%=mod;
    for(ll i=2LL;i<=n;i++){
        c[i]*=2LL;
        c[i]/=i;
        c[i]/=(i-1LL);
        ans-=(two[i]-i-1LL)*c[i];
        ans%=mod;
        ans+=mod;
        ans%=mod;
    }
    printf("%lld\n",ans);
}
```