#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
typedef long long ll;
const int mod=998244353;
int n;
ll pw[210],ans=0;
struct node{int x,y;
}p[210];
bool check(node a,node b,node c)
{ return (b.x-a.x)*(c.y-a.y)==(b.y-a.y)*(c.x-a.x);}
void link(int x,int y){x+=y;}
int main()
{
    link(0,1);
    scanf("%d",&n);
    pw[0]=1;
    for (int i=1;i<=n;i++) pw[i]=(pw[i-1]<<1)%mod;    
    for (int i=1;i<=n;i++) scanf("%d%d",&p[i].x,&p[i].y);
    
    ans=(pw[n]-n-1+mod)%mod;bool _is;int cnt;
    for (int i=1;i<n;i++) 
        for (int j=i+1;j<=n;j++)
        {
            _is=1;
            for (int k=1;k<i;k++) if (check(p[k],p[i],p[j])) {_is=0;break;}
            for (int k=i+1;k<j;k++) if (check(p[k],p[i],p[j])) {_is=0;break;}
            if (!_is) continue;
            cnt=2;
            for (int k=j+1;k<=n;k++) if (check(p[k],p[i],p[j])) cnt++;
            ans=(ans-pw[cnt]+cnt+1+mod)%mod;
        }
    cout<<ans;
}
### 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
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
typedef long long ll;
const int mod=998244353;
int n;
ll pw[210],ans=0;
struct node{int x,y;
}p[210];
bool check(node a,node b,node c)
{ return (b.x-a.x)*(c.y-a.y)==(b.y-a.y)*(c.x-a.x);}
void link(int x,int y){x+=y;}
int main()
{
    link(0,1);
    scanf("%d",&n);
    pw[0]=1;
    for (int i=1;i<=n;i++) pw[i]=(pw[i-1]<<1)%mod;    
    for (int i=1;i<=n;i++) scanf("%d%d",&p[i].x,&p[i].y);
    
    ans=(pw[n]-n-1+mod)%mod;bool _is;int cnt;
    for (int i=1;i<n;i++) 
        for (int j=i+1;j<=n;j++)
        {
            _is=1;
            for (int k=1;k<i;k++) if (check(p[k],p[i],p[j])) {_is=0;break;}
            for (int k=i+1;k<j;k++) if (check(p[k],p[i],p[j])) {_is=0;break;}
            if (!_is) continue;
            cnt=2;
            for (int k=j+1;k<=n;k++) if (check(p[k],p[i],p[j])) cnt++;
            ans=(ans-pw[cnt]+cnt+1+mod)%mod;
        }
    cout<<ans;
}
```