#include <cstdio>
#include <cmath>

using namespace std;

const int mod=998244353;
const double eps=0.00000001;

struct punct
{
    int x,y;
};

punct v[210];
int put[210];

int egal(double a,double b)
{
    if(abs(a-b)<eps) return 1;
    return 0;
}

int main()
{
    //freopen("file.in","r",stdin);
    //freopen("file.out","w",stdout);
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d%d",&v[i].x,&v[i].y);
    put[0]=1;
    for(int i=1;i<=n;i++) put[i]=(1LL*put[i-1]*2)%mod;
    int sol=put[n];
    sol--;
    sol=(sol-n+mod)%mod;
    for(int i=1;i<n;i++)
        for(int j=i+1;j<=n;j++)
        {
            double a=0;
            int p=0;
            if(v[i].x!=v[j].x) a=1.0*(v[i].y-v[j].y)/(v[i].x-v[j].x);
            else p=1;
            double b=1.0*v[i].y-a*v[i].x;
            int cnt=0;
            for(int k=j+1;k<=n;k++)
                if(p==1) {if(v[k].x==v[i].x) cnt++;}
                else if(egal(1.0*v[k].y,a*v[k].x+b)==1) cnt++;
            sol=(sol-put[cnt]+mod)%mod;
        }
    printf("%d",sol);
    return 0;
}


### Prompt

Generate a Cpp solution 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 <cstdio>
#include <cmath>

using namespace std;

const int mod=998244353;
const double eps=0.00000001;

struct punct
{
    int x,y;
};

punct v[210];
int put[210];

int egal(double a,double b)
{
    if(abs(a-b)<eps) return 1;
    return 0;
}

int main()
{
    //freopen("file.in","r",stdin);
    //freopen("file.out","w",stdout);
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d%d",&v[i].x,&v[i].y);
    put[0]=1;
    for(int i=1;i<=n;i++) put[i]=(1LL*put[i-1]*2)%mod;
    int sol=put[n];
    sol--;
    sol=(sol-n+mod)%mod;
    for(int i=1;i<n;i++)
        for(int j=i+1;j<=n;j++)
        {
            double a=0;
            int p=0;
            if(v[i].x!=v[j].x) a=1.0*(v[i].y-v[j].y)/(v[i].x-v[j].x);
            else p=1;
            double b=1.0*v[i].y-a*v[i].x;
            int cnt=0;
            for(int k=j+1;k<=n;k++)
                if(p==1) {if(v[k].x==v[i].x) cnt++;}
                else if(egal(1.0*v[k].y,a*v[k].x+b)==1) cnt++;
            sol=(sol-put[cnt]+mod)%mod;
        }
    printf("%d",sol);
    return 0;
}


```