#include<bits/stdc++.h>

#define MOD (998244353)
#define N (300)

using namespace std;

int x[N],y[N],p[N];

inline long long myPow(long long a,long long b)
{
    long long c = 1;

    for(;b > 0;b >>=1,a = a * a % MOD)
	if(b & 1)
	    c = c * a % MOD;

    return c;
}

inline bool det(int i,int j,int l)
{
    return (x[l]-x[j])*(y[j] - y[i]) - (x[j] - x[i])*(y[l]-y[j]) == 0;
}

int main(void)
{
    int n;
    long long ans = 0;
    
    cin>>n;

    for(int i = 0;i <= n;i++)
    {
	p[i] = myPow(2,i);
    }

    for(int i = 1;i <= n;i++)
    {
	cin>>x[i]>>y[i];
    }

    for(int i = 1;i <= n;i++) {
	for(int j = i+1;j <= n;j++) {
	    int k = 0;
	    for(int l = j+1;l <= n;l++)
		if(det(i,j,l))
		    k++;
	    ans = (ans + p[k]) % MOD;
	}
    }

    ans = (p[n] - ans - n - 1) % MOD;
    
    cout<<ans<<endl;

    return 0;
}


### Prompt

Please formulate 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>

#define MOD (998244353)
#define N (300)

using namespace std;

int x[N],y[N],p[N];

inline long long myPow(long long a,long long b)
{
    long long c = 1;

    for(;b > 0;b >>=1,a = a * a % MOD)
	if(b & 1)
	    c = c * a % MOD;

    return c;
}

inline bool det(int i,int j,int l)
{
    return (x[l]-x[j])*(y[j] - y[i]) - (x[j] - x[i])*(y[l]-y[j]) == 0;
}

int main(void)
{
    int n;
    long long ans = 0;
    
    cin>>n;

    for(int i = 0;i <= n;i++)
    {
	p[i] = myPow(2,i);
    }

    for(int i = 1;i <= n;i++)
    {
	cin>>x[i]>>y[i];
    }

    for(int i = 1;i <= n;i++) {
	for(int j = i+1;j <= n;j++) {
	    int k = 0;
	    for(int l = j+1;l <= n;l++)
		if(det(i,j,l))
		    k++;
	    ans = (ans + p[k]) % MOD;
	}
    }

    ans = (p[n] - ans - n - 1) % MOD;
    
    cout<<ans<<endl;

    return 0;
}


```