/*Program from Luvwgyx*/
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=2e2+10;
const int mod=998244353;
int n,x[maxn],y[maxn],power[maxn];
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
void print(int x){
    if(x<0)putchar('-'),x=-x;
    if(x>9)print(x/10);
    putchar(x%10+'0');
}
void write(int x){print(x);puts("");}
void init(){power[0]=1;for(int i=1;i<=n;i++)power[i]=(power[i-1]<<1)%mod;}
bool check(int i,int j,int k){return (x[i]-x[j])*(y[i]-y[k])==(x[i]-x[k])*(y[i]-y[j]);}
int main(){
    n=read();init();int ans;
    for(int i=1;i<=n;i++)x[i]=read(),y[i]=read();
    ans=(power[n]-n-1+mod)%mod;
    for(int i=1;i<=n;i++)
        for(int j=i+1;j<=n;j++){
            int ret=0;
            for(int k=j+1;k<=n;k++)
                if(check(i,j,k))ret++;
            ans=(ans-power[ret]+mod)%mod;
        }
    write(ans);
    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
/*Program from Luvwgyx*/
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=2e2+10;
const int mod=998244353;
int n,x[maxn],y[maxn],power[maxn];
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
void print(int x){
    if(x<0)putchar('-'),x=-x;
    if(x>9)print(x/10);
    putchar(x%10+'0');
}
void write(int x){print(x);puts("");}
void init(){power[0]=1;for(int i=1;i<=n;i++)power[i]=(power[i-1]<<1)%mod;}
bool check(int i,int j,int k){return (x[i]-x[j])*(y[i]-y[k])==(x[i]-x[k])*(y[i]-y[j]);}
int main(){
    n=read();init();int ans;
    for(int i=1;i<=n;i++)x[i]=read(),y[i]=read();
    ans=(power[n]-n-1+mod)%mod;
    for(int i=1;i<=n;i++)
        for(int j=i+1;j<=n;j++){
            int ret=0;
            for(int k=j+1;k<=n;k++)
                if(check(i,j,k))ret++;
            ans=(ans-power[ret]+mod)%mod;
        }
    write(ans);
    return 0;
}

```