#include <bits/stdc++.h>
#define ll long long
#define AwD 998244353
using namespace std;
ll mi(ll a, ll b) {
	ll ret = 1;
    for (; b; b >>= 1, a = a * a % AwD)
	if (b & 1) ret = ret * a % AwD;
    return ret;
}
ll x[250], y[250], ans;
map<ll, int> MAP;
int main() {
    ll n; cin >> n;
    for (int i = 1; i <= n; i ++) cin >> x[i] >> y[i];
	ans = mi(2, n) - n - 1;
	for (int i = 1; i <= n; i ++) {
		MAP.clear();
		for (int j = i + 1; j <= n; j ++) {
            ll k;
            if (x[j] == x[i]) k = -1;
			else k = ((y[j] - y[i]) * mi(x[j] - x[i], AwD - 2) % AwD + AwD)% AwD;
			MAP[k] ++;
		}
		for (auto it = MAP.begin(); it != MAP.end(); it ++) (ans -= mi(2, it -> second) - 1) %= AwD;
	}
	cout << ((ans) % AwD + AwD) % AwD << endl;
	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 <bits/stdc++.h>
#define ll long long
#define AwD 998244353
using namespace std;
ll mi(ll a, ll b) {
	ll ret = 1;
    for (; b; b >>= 1, a = a * a % AwD)
	if (b & 1) ret = ret * a % AwD;
    return ret;
}
ll x[250], y[250], ans;
map<ll, int> MAP;
int main() {
    ll n; cin >> n;
    for (int i = 1; i <= n; i ++) cin >> x[i] >> y[i];
	ans = mi(2, n) - n - 1;
	for (int i = 1; i <= n; i ++) {
		MAP.clear();
		for (int j = i + 1; j <= n; j ++) {
            ll k;
            if (x[j] == x[i]) k = -1;
			else k = ((y[j] - y[i]) * mi(x[j] - x[i], AwD - 2) % AwD + AwD)% AwD;
			MAP[k] ++;
		}
		for (auto it = MAP.begin(); it != MAP.end(); it ++) (ans -= mi(2, it -> second) - 1) %= AwD;
	}
	cout << ((ans) % AwD + AwD) % AwD << endl;
	return 0;
}

```