#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

int n;
const int maxn = 205;

int x[maxn],y[maxn];

long long ans[maxn];

const int mod = 998244353;

int qpow(int x,int n){
	int ret = 1;
	while(n > 0){
		if(n & 1){
			ret = 1LL * ret * x % mod;
		}
		x = 1LL * x * x % mod;
		n >>= 1;
	}
	return ret;
}

void upd(long long &a,int b){
	a += b;
	if(a >= mod) a -= mod;
	if(a < 0) a += mod;
}

int main(){
	cin >> n;
	for(int i = 1;i <= n;i++){
		scanf("%d%d",x + i,y + i);
	}
	for(int i = 1;i <= n;i++){
		for(int j = 1;j <= n;j++) if(j != i){
			int num = 2;
			for(int k = 1;k <= n;k++) if(k != i && k != j){
				if((x[k] - x[i]) * (y[j] - y[i]) - (x[j] - x[i]) * (y[k] - y[i]) == 0) num++;	
			}
			upd(ans[num],(qpow(2,num) - 1 - num + mod) % mod);
		}
	}
	long long res = 0;
	upd(res,qpow(2,n));
	upd(res,-n-1);
	for(int i = 1;i <= n;i++){
		int tmp = ans[i] * qpow(i,mod - 2) % mod * qpow(i - 1,mod - 2) % mod;
		upd(res,-tmp);
	}
	cout << res << endl;
	return 0;
}

### Prompt

Your task is to create 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 <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

int n;
const int maxn = 205;

int x[maxn],y[maxn];

long long ans[maxn];

const int mod = 998244353;

int qpow(int x,int n){
	int ret = 1;
	while(n > 0){
		if(n & 1){
			ret = 1LL * ret * x % mod;
		}
		x = 1LL * x * x % mod;
		n >>= 1;
	}
	return ret;
}

void upd(long long &a,int b){
	a += b;
	if(a >= mod) a -= mod;
	if(a < 0) a += mod;
}

int main(){
	cin >> n;
	for(int i = 1;i <= n;i++){
		scanf("%d%d",x + i,y + i);
	}
	for(int i = 1;i <= n;i++){
		for(int j = 1;j <= n;j++) if(j != i){
			int num = 2;
			for(int k = 1;k <= n;k++) if(k != i && k != j){
				if((x[k] - x[i]) * (y[j] - y[i]) - (x[j] - x[i]) * (y[k] - y[i]) == 0) num++;	
			}
			upd(ans[num],(qpow(2,num) - 1 - num + mod) % mod);
		}
	}
	long long res = 0;
	upd(res,qpow(2,n));
	upd(res,-n-1);
	for(int i = 1;i <= n;i++){
		int tmp = ans[i] * qpow(i,mod - 2) % mod * qpow(i - 1,mod - 2) % mod;
		upd(res,-tmp);
	}
	cout << res << endl;
	return 0;
}

```