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

#define mod 998244353

long long X[300], Y[300], P[300];
int N;

int main() {
    // freopen("input.in","r",stdin);
    // freopen("output.out","w",stdout);

    cin>>N;
    for(int i = 0;i < N;i++) cin>>X[i]>>Y[i];
    P[0] = 1;
    for(int i = 1;i <= N;i++) P[i] = (2*P[i-1]) % mod;

    long long answer = (P[N]-1-N+mod) % mod;
    // cout << answer << endl;

    for(int i = 0;i < N;i++) {
        for(int j = i+1;j < N;j++) {
            int counter = 0;
            for(int k = j+1;k < N;k++) {
                if((Y[j]-Y[i])*(X[k]-X[i]) == (Y[k]-Y[i])*(X[j]-X[i])) {
                    counter += 1;
                }
            }

            answer = (answer - P[counter] + mod) % mod;
        }
    }

    cout << answer << endl;

    return 0;
}

### Prompt

Please create a solution in CPP to 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 mod 998244353

long long X[300], Y[300], P[300];
int N;

int main() {
    // freopen("input.in","r",stdin);
    // freopen("output.out","w",stdout);

    cin>>N;
    for(int i = 0;i < N;i++) cin>>X[i]>>Y[i];
    P[0] = 1;
    for(int i = 1;i <= N;i++) P[i] = (2*P[i-1]) % mod;

    long long answer = (P[N]-1-N+mod) % mod;
    // cout << answer << endl;

    for(int i = 0;i < N;i++) {
        for(int j = i+1;j < N;j++) {
            int counter = 0;
            for(int k = j+1;k < N;k++) {
                if((Y[j]-Y[i])*(X[k]-X[i]) == (Y[k]-Y[i])*(X[j]-X[i])) {
                    counter += 1;
                }
            }

            answer = (answer - P[counter] + mod) % mod;
        }
    }

    cout << answer << endl;

    return 0;
}

```