#include <iostream>
#include <vector>

using namespace std;

const int MOD = 998244353;

class P2 {
public:
	explicit P2(int x = 0, int y = 0) : x(x), y(y) {}
	int x, y;
};

int cross(const P2& a, const P2& b, const P2& c){
	int dx1 = b.x - a.x;
	int dy1 = b.y - a.y;
	int dx2 = c.x - a.x;
	int dy2 = c.y - a.y;
	return dx1 * dy2 - dx2 * dy1;
}

int main(){
	vector<int> pow2(300);
	pow2[0] = 1;
	for(int i=1;i<pow2.size();i++) pow2[i] = 2 * pow2[i-1] % MOD;
	int N;
	while(cin >> N){
		vector<P2> vp(N);
		for(auto& p : vp) cin >> p.x >> p.y;
		int res = pow2[N];
		res = (res + MOD - (1+N)) % MOD;
		vector<vector<int>> checked(N, vector<int>(N, 0));
		for(int i=0;i<N;i++){
			for(int j=i+1;j<N;j++){
				if(checked[i][j]) continue;
				vector<int> idx;
				for(int k=0;k<N;k++){
					if(!cross(vp[i], vp[j], vp[k])) idx.push_back(k);
				}
				int sub = pow2[idx.size()] - idx.size() - 1;
				res = (res + MOD - sub) % MOD;
				for(int k=0;k<idx.size();k++){
					for(int l=k+1;l<idx.size();l++){
						checked[idx[k]][idx[l]] = 1;
					}
				}
			}
		}
		cout << res << endl;
	}
}
### 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 <iostream>
#include <vector>

using namespace std;

const int MOD = 998244353;

class P2 {
public:
	explicit P2(int x = 0, int y = 0) : x(x), y(y) {}
	int x, y;
};

int cross(const P2& a, const P2& b, const P2& c){
	int dx1 = b.x - a.x;
	int dy1 = b.y - a.y;
	int dx2 = c.x - a.x;
	int dy2 = c.y - a.y;
	return dx1 * dy2 - dx2 * dy1;
}

int main(){
	vector<int> pow2(300);
	pow2[0] = 1;
	for(int i=1;i<pow2.size();i++) pow2[i] = 2 * pow2[i-1] % MOD;
	int N;
	while(cin >> N){
		vector<P2> vp(N);
		for(auto& p : vp) cin >> p.x >> p.y;
		int res = pow2[N];
		res = (res + MOD - (1+N)) % MOD;
		vector<vector<int>> checked(N, vector<int>(N, 0));
		for(int i=0;i<N;i++){
			for(int j=i+1;j<N;j++){
				if(checked[i][j]) continue;
				vector<int> idx;
				for(int k=0;k<N;k++){
					if(!cross(vp[i], vp[j], vp[k])) idx.push_back(k);
				}
				int sub = pow2[idx.size()] - idx.size() - 1;
				res = (res + MOD - sub) % MOD;
				for(int k=0;k<idx.size();k++){
					for(int l=k+1;l<idx.size();l++){
						checked[idx[k]][idx[l]] = 1;
					}
				}
			}
		}
		cout << res << endl;
	}
}
```