#include<bits/stdc++.h>
using namespace std;
#define maxn 205
#define mod 998244353
int x[maxn],y[maxn];
inline int mul(int a, int b) {
  return (long long) a * b % mod;
}

inline int pow(int a, int b) {
  int res = 1;
  while (b > 0) {
    if (b & 1) {
      res = mul(res, a);
    }
    a = mul(a, a);
    b >>= 1;
  }
  return res;
}

void add(int &a,int b)
{
    a+=b;
    if(a>=mod)a-=mod;
}
int main()
{
    int n;scanf("%d",&n);
    for(int i=0;i<n;i++)scanf("%d%d",&x[i],&y[i]);
    int ans=pow(2,n);
    add(ans,mod-1);
    add(ans,mod-n);
    add(ans,mod-n*(n-1)/2);
    for(int i=0;i<n;i++)for(int j=i+1;j<n;j++)
    {
        int a=y[j]-y[i];
        int b=x[i]-x[j];
        int c=-a*x[i]-b*y[i];
        int cnt=2;
        for(int k=0;k<n;k++)
        {
            if (k==i || k==j)continue;
            int z=a*x[k]+b*y[k]+c;
            if(z!=0)continue;
            if(k<j)break;
            cnt++;
        }
        add(ans,mod-pow(2,cnt));
        add(ans,1);
        add(ans,cnt);
        add(ans,cnt*(cnt-1)/2);
    }
    printf("%d\n",ans);
    return 0;
}

### 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<bits/stdc++.h>
using namespace std;
#define maxn 205
#define mod 998244353
int x[maxn],y[maxn];
inline int mul(int a, int b) {
  return (long long) a * b % mod;
}

inline int pow(int a, int b) {
  int res = 1;
  while (b > 0) {
    if (b & 1) {
      res = mul(res, a);
    }
    a = mul(a, a);
    b >>= 1;
  }
  return res;
}

void add(int &a,int b)
{
    a+=b;
    if(a>=mod)a-=mod;
}
int main()
{
    int n;scanf("%d",&n);
    for(int i=0;i<n;i++)scanf("%d%d",&x[i],&y[i]);
    int ans=pow(2,n);
    add(ans,mod-1);
    add(ans,mod-n);
    add(ans,mod-n*(n-1)/2);
    for(int i=0;i<n;i++)for(int j=i+1;j<n;j++)
    {
        int a=y[j]-y[i];
        int b=x[i]-x[j];
        int c=-a*x[i]-b*y[i];
        int cnt=2;
        for(int k=0;k<n;k++)
        {
            if (k==i || k==j)continue;
            int z=a*x[k]+b*y[k]+c;
            if(z!=0)continue;
            if(k<j)break;
            cnt++;
        }
        add(ans,mod-pow(2,cnt));
        add(ans,1);
        add(ans,cnt);
        add(ans,cnt*(cnt-1)/2);
    }
    printf("%d\n",ans);
    return 0;
}

```