#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
typedef long long ll ;
#define rep(i, a, b) for (int i = a; i <= b; ++ i) 
const int N = 205, mo = 998244353 ;
using namespace std ;

int n, fac[N], G[N][N] ;
struct poi {
	int x, y ;
} a[N] ;

int cross(poi p0, poi p1, poi p2) {
	return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y) ;
}

int main() {
	scanf("%d", &n) ;
	rep(i, 1, n) scanf("%d%d", &a[i].x, &a[i].y) ;
	fac[0] = 1 ;
	rep(i, 1, n) fac[i] = (ll) fac[i - 1] * 2 % mo ;
	int ans = fac[n] - 1 - n ; ans %= mo ;
	rep(i, 1, n) {
		rep(j, i + 1, n) {
			int cnt = 2, res = 0, w = 1 ;
			rep(k, 1, n) if (!cross(a[i], a[j], a[k]) && k != i && k != j) {
				if (G[k][i] || G[k][j] || G[i][k] || G[j][k]) w = 0 ;
				++ cnt ;
			}
			res = fac[cnt] - 1 - cnt ;
			ans -= res * w, ans %= mo ;
			rep(k, 1, n) if (!cross(a[i], a[j], a[k]) && j != k && i != k) G[i][k] = G[k][i] = G[j][k] = G[k][j] = true ;
		}
	}
	printf("%d\n", (ans + mo) % mo) ;
	return 0 ;
}
### Prompt

Create a solution in Cpp for 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 <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
typedef long long ll ;
#define rep(i, a, b) for (int i = a; i <= b; ++ i) 
const int N = 205, mo = 998244353 ;
using namespace std ;

int n, fac[N], G[N][N] ;
struct poi {
	int x, y ;
} a[N] ;

int cross(poi p0, poi p1, poi p2) {
	return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y) ;
}

int main() {
	scanf("%d", &n) ;
	rep(i, 1, n) scanf("%d%d", &a[i].x, &a[i].y) ;
	fac[0] = 1 ;
	rep(i, 1, n) fac[i] = (ll) fac[i - 1] * 2 % mo ;
	int ans = fac[n] - 1 - n ; ans %= mo ;
	rep(i, 1, n) {
		rep(j, i + 1, n) {
			int cnt = 2, res = 0, w = 1 ;
			rep(k, 1, n) if (!cross(a[i], a[j], a[k]) && k != i && k != j) {
				if (G[k][i] || G[k][j] || G[i][k] || G[j][k]) w = 0 ;
				++ cnt ;
			}
			res = fac[cnt] - 1 - cnt ;
			ans -= res * w, ans %= mo ;
			rep(k, 1, n) if (!cross(a[i], a[j], a[k]) && j != k && i != k) G[i][k] = G[k][i] = G[j][k] = G[k][j] = true ;
		}
	}
	printf("%d\n", (ans + mo) % mo) ;
	return 0 ;
}
```