#include <vector>
#include <iostream>
using namespace std;
const int mod = 998244353;
int n, x[209], y[209], pw[209]; bool vis[209][209];
int main() {
	cin >> n;
	for (int i = 0; i < n; i++) cin >> x[i] >> y[i];
	pw[0] = 1;
	for (int i = 0; i < n; i++) pw[i + 1] = pw[i] * 2 % mod;
	int ret = (pw[n] - n - 1 + mod) % mod;
	for (int i = 0; i < n; i++) {
		for (int j = i + 1; j < n; j++) {
			if (!vis[i][j]) {
				vector<int> v;
				int dx = x[j] - x[i], dy = y[j] - y[i];
				for (int k = 0; k < n; k++) {
					int ex = x[k] - x[i], ey = y[k] - y[i];
					if (dx * ey == ex * dy) v.push_back(k);
				}
				ret = (ret - (pw[v.size()] - v.size() - 1 + mod) % mod + mod) % mod;
				for (int k : v) {
					for (int l : v) {
						vis[k][l] = true;
					}
				}
			}
		}
	}
	cout << ret << endl;
	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 <vector>
#include <iostream>
using namespace std;
const int mod = 998244353;
int n, x[209], y[209], pw[209]; bool vis[209][209];
int main() {
	cin >> n;
	for (int i = 0; i < n; i++) cin >> x[i] >> y[i];
	pw[0] = 1;
	for (int i = 0; i < n; i++) pw[i + 1] = pw[i] * 2 % mod;
	int ret = (pw[n] - n - 1 + mod) % mod;
	for (int i = 0; i < n; i++) {
		for (int j = i + 1; j < n; j++) {
			if (!vis[i][j]) {
				vector<int> v;
				int dx = x[j] - x[i], dy = y[j] - y[i];
				for (int k = 0; k < n; k++) {
					int ex = x[k] - x[i], ey = y[k] - y[i];
					if (dx * ey == ex * dy) v.push_back(k);
				}
				ret = (ret - (pw[v.size()] - v.size() - 1 + mod) % mod + mod) % mod;
				for (int k : v) {
					for (int l : v) {
						vis[k][l] = true;
					}
				}
			}
		}
	}
	cout << ret << endl;
	return 0;
}
```