#include <cstdio>
#include <algorithm>
#define LL long long
const int maxn = 205;
const LL mo = 998244353;
using namespace std;
int x[maxn], y[maxn], n;
LL ans = 0, pw[maxn];
int main(){
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) scanf("%d%d", x + i, y + i);
	pw[0] = 1; for (int i = 1; i <= n; i++) pw[i] = pw[i - 1] * 2 % mo; 
	ans = (pw[n] - 1 - n + mo) % mo;
	for (int i = 1; i <= n; i++)
		for (int j = i + 1; j <= n; j++){
			int tmp = 0;
			for (int k = 1; k <= n; k++){
				if (x[k] >= min(x[i], x[j]) && x[k] <= max(x[i], x[j]) && y[k] >= min(y[i], y[j]) && y[k] <= max(y[i], y[j])){
					if ((y[k] - y[i]) * (x[j] - x[k]) == (x[k] - x[i]) * (y[j] - y[k])) ++tmp;
				}
			}
			ans = (ans - pw[tmp - 2] + mo) % mo;
		}
	printf("%lld\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 <algorithm>
#define LL long long
const int maxn = 205;
const LL mo = 998244353;
using namespace std;
int x[maxn], y[maxn], n;
LL ans = 0, pw[maxn];
int main(){
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) scanf("%d%d", x + i, y + i);
	pw[0] = 1; for (int i = 1; i <= n; i++) pw[i] = pw[i - 1] * 2 % mo; 
	ans = (pw[n] - 1 - n + mo) % mo;
	for (int i = 1; i <= n; i++)
		for (int j = i + 1; j <= n; j++){
			int tmp = 0;
			for (int k = 1; k <= n; k++){
				if (x[k] >= min(x[i], x[j]) && x[k] <= max(x[i], x[j]) && y[k] >= min(y[i], y[j]) && y[k] <= max(y[i], y[j])){
					if ((y[k] - y[i]) * (x[j] - x[k]) == (x[k] - x[i]) * (y[j] - y[k])) ++tmp;
				}
			}
			ans = (ans - pw[tmp - 2] + mo) % mo;
		}
	printf("%lld\n", ans);
	return 0;
}
```