#include<bits/stdc++.h>
using namespace std;
#define reg register
#define ll long long
#define mo 998244353
#define maxn 205
inline ll read()
{
	ll x=0,w=0;char ch=getchar();
	while(!isdigit(ch))w|=ch=='-',ch=getchar();
	while(isdigit(ch))x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
	return w?-x:x;
}
int n,x[maxn],y[maxn],po[maxn],ans;
inline bool bd(int i,int j,int k)
{
    int a=x[k]-x[i],b=y[k]-y[i];
    int c=x[j]-x[k],d=y[j]-y[k];
    if(1ll*a*c<0)return false;
    if(1ll*b*d<0)return false;
    if(1ll*a*d!=1ll*b*c)return false;
    return true;
}
int main()
{
    n=read();reg int i,j,k,tot;po[0]=1;
    for(i=1;i<=n;++i)x[i]=read(),y[i]=read();
    for(i=1;i<=n;++i)po[i]=po[i-1]*2%mo;
    ans=po[n]-n-1;
    for(i=2;i<=n;++i)
        for(j=1;j<i;++j)
        {
            tot=0;
            for(k=1;k<=n;++k)
                if(i!=k&&j!=k&&bd(i,j,k))
                    ++tot;
            ans=(ans+mo-po[tot])%mo;
        }
    cout<<ans<<"\n";
	return 0;
}

### Prompt

Your challenge is to write 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<bits/stdc++.h>
using namespace std;
#define reg register
#define ll long long
#define mo 998244353
#define maxn 205
inline ll read()
{
	ll x=0,w=0;char ch=getchar();
	while(!isdigit(ch))w|=ch=='-',ch=getchar();
	while(isdigit(ch))x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
	return w?-x:x;
}
int n,x[maxn],y[maxn],po[maxn],ans;
inline bool bd(int i,int j,int k)
{
    int a=x[k]-x[i],b=y[k]-y[i];
    int c=x[j]-x[k],d=y[j]-y[k];
    if(1ll*a*c<0)return false;
    if(1ll*b*d<0)return false;
    if(1ll*a*d!=1ll*b*c)return false;
    return true;
}
int main()
{
    n=read();reg int i,j,k,tot;po[0]=1;
    for(i=1;i<=n;++i)x[i]=read(),y[i]=read();
    for(i=1;i<=n;++i)po[i]=po[i-1]*2%mo;
    ans=po[n]-n-1;
    for(i=2;i<=n;++i)
        for(j=1;j<i;++j)
        {
            tot=0;
            for(k=1;k<=n;++k)
                if(i!=k&&j!=k&&bd(i,j,k))
                    ++tot;
            ans=(ans+mo-po[tot])%mo;
        }
    cout<<ans<<"\n";
	return 0;
}

```