#include<bits/stdc++.h>

const int N = 210;
const int moder = 998244353;

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

int powermod(int a, int exp){
	int ret = 1;
	for ( ; exp; exp >>= 1){
		if (exp & 1){
			ret = 1ll * ret * a % moder;
		}
		a = 1ll * a * a % moder;
	}
	return ret;
}

int det(int x1, int y1, int x2, int y2){
	return x1 * y2 - y1 * x2;
}

bool onSeg(int x1, int y1, int x2, int y2, int x3, int y3){
	return !det(x2 - x1, y2 - y1, x3 - x1, y3 - y1);
}

int main(){
	scanf("%d", &n);
	for (int i = 0; i < n; ++ i){
		scanf("%d%d", &x[i], &y[i]);
	}
	int ans = 0;
	for (int i = 0; i < n; ++ i){
		for (int j = i + 1; j < n; ++ j){
			int cnt = 0;
			for (int k = 0; k < n; ++ k){
				cnt += onSeg(x[i], y[i], x[j], y[j], x[k], y[k]);
			}
			ans = (ans + 1ll * (powermod(2, cnt) - (cnt + 1) + moder) * powermod(cnt * (cnt - 1) >> 1, moder - 2)) % moder;
		}
	}
	ans = (ans + n + 1) % moder;
	return printf("%d\n", (powermod(2, n) - ans + moder) % moder), 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>

const int N = 210;
const int moder = 998244353;

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

int powermod(int a, int exp){
	int ret = 1;
	for ( ; exp; exp >>= 1){
		if (exp & 1){
			ret = 1ll * ret * a % moder;
		}
		a = 1ll * a * a % moder;
	}
	return ret;
}

int det(int x1, int y1, int x2, int y2){
	return x1 * y2 - y1 * x2;
}

bool onSeg(int x1, int y1, int x2, int y2, int x3, int y3){
	return !det(x2 - x1, y2 - y1, x3 - x1, y3 - y1);
}

int main(){
	scanf("%d", &n);
	for (int i = 0; i < n; ++ i){
		scanf("%d%d", &x[i], &y[i]);
	}
	int ans = 0;
	for (int i = 0; i < n; ++ i){
		for (int j = i + 1; j < n; ++ j){
			int cnt = 0;
			for (int k = 0; k < n; ++ k){
				cnt += onSeg(x[i], y[i], x[j], y[j], x[k], y[k]);
			}
			ans = (ans + 1ll * (powermod(2, cnt) - (cnt + 1) + moder) * powermod(cnt * (cnt - 1) >> 1, moder - 2)) % moder;
		}
	}
	ans = (ans + n + 1) % moder;
	return printf("%d\n", (powermod(2, n) - ans + moder) % moder), 0;
}
```