#include <bits/stdc++.h>
using namespace std;
const int mod=998244353;
const int maxn=300;
struct node{
    int x,y;
    node operator-(const node&p)const {
        return (node){x-p.x,y-p.y};
    }
    int operator*(const node&p)const {
        return x*p.y-y*p.x;
    }
}d[maxn];
int n,p[maxn];
bool check(node a,node b,node c){
    return ((b-a)*(c-a)==0);
}

int main(){
    scanf("%d",&n);
    if(n<=2) return puts("0"),0;
    
    for (int i=1; i<=n; i++)
        scanf("%d%d",&d[i].x,&d[i].y);
        
    p[0]=1;
    for (int i=1; i<=n; i++)
        p[i]=(p[i-1]*2)%mod;
    int cnt;
    long long ans=0;
    
    for (int i=1; i<n; i++)
        for (int j=i+1; j<n; j++){
            cnt=n-j;
            for (int k=j+1; k<=n; k++)
                if(check(d[i],d[j],d[k]))
                    cnt--;
            (ans+=1ll*p[n-j-cnt]*(p[cnt]-1)%mod)%=mod;
        }
    
    printf("%lld\n",ans);
    return 0;
}

### Prompt

Please provide a cpp coded solution 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 <bits/stdc++.h>
using namespace std;
const int mod=998244353;
const int maxn=300;
struct node{
    int x,y;
    node operator-(const node&p)const {
        return (node){x-p.x,y-p.y};
    }
    int operator*(const node&p)const {
        return x*p.y-y*p.x;
    }
}d[maxn];
int n,p[maxn];
bool check(node a,node b,node c){
    return ((b-a)*(c-a)==0);
}

int main(){
    scanf("%d",&n);
    if(n<=2) return puts("0"),0;
    
    for (int i=1; i<=n; i++)
        scanf("%d%d",&d[i].x,&d[i].y);
        
    p[0]=1;
    for (int i=1; i<=n; i++)
        p[i]=(p[i-1]*2)%mod;
    int cnt;
    long long ans=0;
    
    for (int i=1; i<n; i++)
        for (int j=i+1; j<n; j++){
            cnt=n-j;
            for (int k=j+1; k<=n; k++)
                if(check(d[i],d[j],d[k]))
                    cnt--;
            (ans+=1ll*p[n-j-cnt]*(p[cnt]-1)%mod)%=mod;
        }
    
    printf("%lld\n",ans);
    return 0;
}

```