#include <bits/stdc++.h>
using namespace std;

#define int long long
const double PI = 3.14159265358979323846;
typedef vector<int> vint;
typedef pair<int, int> pint;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};

int N;
int x[220], y[220];
int tw[220];
int mod = 998244353;

signed main() {
    tw[0] = 1;
    for (int i = 1; i < 220; i++) {
        tw[i] = tw[i - 1] * 2 % mod;
    }
    cin >> N;
    for (int i = 0; i < N; i++)cin >> x[i] >> y[i];

    int ans = (tw[N] - N - 1 + mod) % mod;

    for (int i = 0; i < N; i++) {
        for (int j = i + 1; j < N; j++) {
            int cur = 0;
            for (int k = j + 1; k < N; k++) {
                if ((x[i] - x[j]) * (y[i] - y[k]) == (x[i] - x[k]) * (y[i] - y[j])) cur++;
            }
            (ans += mod - tw[cur]) %= mod;
        }
    }
    cout << ans << endl;
}

### Prompt

In CPP, your task is to solve 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>
using namespace std;

#define int long long
const double PI = 3.14159265358979323846;
typedef vector<int> vint;
typedef pair<int, int> pint;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};

int N;
int x[220], y[220];
int tw[220];
int mod = 998244353;

signed main() {
    tw[0] = 1;
    for (int i = 1; i < 220; i++) {
        tw[i] = tw[i - 1] * 2 % mod;
    }
    cin >> N;
    for (int i = 0; i < N; i++)cin >> x[i] >> y[i];

    int ans = (tw[N] - N - 1 + mod) % mod;

    for (int i = 0; i < N; i++) {
        for (int j = i + 1; j < N; j++) {
            int cur = 0;
            for (int k = j + 1; k < N; k++) {
                if ((x[i] - x[j]) * (y[i] - y[k]) == (x[i] - x[k]) * (y[i] - y[j])) cur++;
            }
            (ans += mod - tw[cur]) %= mod;
        }
    }
    cout << ans << endl;
}

```