#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <math.h>
using namespace std;

typedef long long ll;
const int MAXN = 200 + 10;
const int Mod = 998244353;
int N;
int stk[MAXN], top;
bool vis[MAXN][MAXN];
int fc[MAXN];
int ans;
#define x first
#define y second
pair<int, int> A[MAXN];

inline bool check(int i, int j, int k) {
	return (A[i].y - A[j].y) * (A[i].x - A[k].x) == (A[i].y - A[k].y) * (A[i].x - A[j].x);
}

int main() {
	register int i, j, k;
	scanf("%d", &N);
	for(i = 1; i <= N; ++i)
		scanf("%d%d", &A[i].x, &A[i].y);
	for(*fc = i = 1; i <= N; ++i)
		fc[i] = 1ll * fc[i - 1] * 2 % Mod;
	ans = fc[N] - N - 1;
	for(i = 1; i <= N; ++i)
		for(j = i + 1; j <= N; ++j) {
			int res = 0;
			for(k = j + 1; k <= N; ++k)
				res += check(i, j, k);
			ans = (ans - fc[res] + Mod) % Mod;
		}
	printf("%d\n", ans);
	return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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 <algorithm>
#include <math.h>
using namespace std;

typedef long long ll;
const int MAXN = 200 + 10;
const int Mod = 998244353;
int N;
int stk[MAXN], top;
bool vis[MAXN][MAXN];
int fc[MAXN];
int ans;
#define x first
#define y second
pair<int, int> A[MAXN];

inline bool check(int i, int j, int k) {
	return (A[i].y - A[j].y) * (A[i].x - A[k].x) == (A[i].y - A[k].y) * (A[i].x - A[j].x);
}

int main() {
	register int i, j, k;
	scanf("%d", &N);
	for(i = 1; i <= N; ++i)
		scanf("%d%d", &A[i].x, &A[i].y);
	for(*fc = i = 1; i <= N; ++i)
		fc[i] = 1ll * fc[i - 1] * 2 % Mod;
	ans = fc[N] - N - 1;
	for(i = 1; i <= N; ++i)
		for(j = i + 1; j <= N; ++j) {
			int res = 0;
			for(k = j + 1; k <= N; ++k)
				res += check(i, j, k);
			ans = (ans - fc[res] + Mod) % Mod;
		}
	printf("%d\n", ans);
	return 0;
}
```