#include <bits/stdc++.h>
using namespace std;
#define f(i, x, n) for (int i = x; i < (int)(n); ++i)
#define ll long long

int tw[201], md = 998244353;

struct V{
	int x, y;
	V(){}
	V(int a, int b):x(a), y(b) {}
	int operator |(V const o)const { return x * o.y - o.x * y; }
	bool operator <(V const o)const { return (*this | o) < 0; }
	void N() { if (x < 0 || x == 0 && y < 0)x = -x, y = -y; }
	V operator -(V o) { return V(x - o.x, y - o.y); }
}p[200];

int main(){
	tw[0] = 1;
	f(i, 1, 201)if ((tw[i] = tw[i - 1] << 1) >= md)tw[i] -= md;
	int n;
	scanf("%d", &n);
	f(i, 0, n)scanf("%d%d", &p[i].x, &p[i].y);
	int an = tw[n] - 1 - n;
	if (an < 0)an += md;
	f(i, 0, n){
		map<V, int> mp;
		f(j, i + 1, n){
			V v = p[j] - p[i];
			v.N();
			++mp[v];
		}
		for (map<V, int>::iterator it = mp.begin(); it != mp.end(); ++it)if ((an -= tw[it->second] - 1) < 0)an += md;
	}
	printf("%d\n", an);
}
### 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>
using namespace std;
#define f(i, x, n) for (int i = x; i < (int)(n); ++i)
#define ll long long

int tw[201], md = 998244353;

struct V{
	int x, y;
	V(){}
	V(int a, int b):x(a), y(b) {}
	int operator |(V const o)const { return x * o.y - o.x * y; }
	bool operator <(V const o)const { return (*this | o) < 0; }
	void N() { if (x < 0 || x == 0 && y < 0)x = -x, y = -y; }
	V operator -(V o) { return V(x - o.x, y - o.y); }
}p[200];

int main(){
	tw[0] = 1;
	f(i, 1, 201)if ((tw[i] = tw[i - 1] << 1) >= md)tw[i] -= md;
	int n;
	scanf("%d", &n);
	f(i, 0, n)scanf("%d%d", &p[i].x, &p[i].y);
	int an = tw[n] - 1 - n;
	if (an < 0)an += md;
	f(i, 0, n){
		map<V, int> mp;
		f(j, i + 1, n){
			V v = p[j] - p[i];
			v.N();
			++mp[v];
		}
		for (map<V, int>::iterator it = mp.begin(); it != mp.end(); ++it)if ((an -= tw[it->second] - 1) < 0)an += md;
	}
	printf("%d\n", an);
}
```