#include <bits/stdc++.h>
#define re(i, n) for(int i = 0; i < n; ++i)
using namespace std;
const int MXN = 210, mol = 998244353;
int n, ans = 0, pow2[MXN] = {1};

struct point {
    int x, y;
}p[MXN];

int multi(point a, point b, point c) {
    return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y);
}

int main() {
    cin >> n;
    re(i, n) cin >> p[i].x >> p[i].y, pow2[i + 1] = pow2[i] * 2 % mol;
    ans = (pow2[n] + mol - n - 1) % mol;
    re(i, n)
        re(j, i) {
            int t = 0;
            re(k, j) {
                if (multi(p[i], p[j], p[k]) == 0) ++t;
            }
            ans = (ans + mol - pow2[t]) % mol;
        }
    cout << ans << endl;
    return 0;
}

### 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>
#define re(i, n) for(int i = 0; i < n; ++i)
using namespace std;
const int MXN = 210, mol = 998244353;
int n, ans = 0, pow2[MXN] = {1};

struct point {
    int x, y;
}p[MXN];

int multi(point a, point b, point c) {
    return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y);
}

int main() {
    cin >> n;
    re(i, n) cin >> p[i].x >> p[i].y, pow2[i + 1] = pow2[i] * 2 % mol;
    ans = (pow2[n] + mol - n - 1) % mol;
    re(i, n)
        re(j, i) {
            int t = 0;
            re(k, j) {
                if (multi(p[i], p[j], p[k]) == 0) ++t;
            }
            ans = (ans + mol - pow2[t]) % mol;
        }
    cout << ans << endl;
    return 0;
}

```