#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;

#define ri register int
#define de double
#define mod 998244353
#define sid 205

int n, ans;
de x[sid], y[sid];

inline int fp(int a, int k) {
    int ret = 1;
    for( ; k; k >>= 1, a = 1ll * a * a % mod)
    if(k & 1) ret = 1ll * ret * a % mod;
    return ret;
}

inline bool in(int a, int b, int o) {
    de p1 = (y[o] - y[a]) * (x[o] - x[b]);
    de p2 = (y[o] - y[b]) * (x[o] - x[a]);
    return fabs(p1 - p2) < 1e-9;
}

int main() {
    cin >> n;
    for(ri i = 1; i <= n; i ++) cin >> x[i] >> y[i];
    ans = fp(2, n);
    ans = (ans - 1 + mod) % mod;
    ans = (ans - n + mod) % mod;
    for(ri i = 1; i <= n; i ++)
    for(ri j = i + 1;  j <= n; j ++) {
        int ret = 0;
        for(ri k = j + 1; k <= n; k ++)
        if(in(i, j, k)) ret ++;
        ans = (ans - fp(2, ret) + mod) % mod;
    }
    printf("%d\n", ans);
    return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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 <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;

#define ri register int
#define de double
#define mod 998244353
#define sid 205

int n, ans;
de x[sid], y[sid];

inline int fp(int a, int k) {
    int ret = 1;
    for( ; k; k >>= 1, a = 1ll * a * a % mod)
    if(k & 1) ret = 1ll * ret * a % mod;
    return ret;
}

inline bool in(int a, int b, int o) {
    de p1 = (y[o] - y[a]) * (x[o] - x[b]);
    de p2 = (y[o] - y[b]) * (x[o] - x[a]);
    return fabs(p1 - p2) < 1e-9;
}

int main() {
    cin >> n;
    for(ri i = 1; i <= n; i ++) cin >> x[i] >> y[i];
    ans = fp(2, n);
    ans = (ans - 1 + mod) % mod;
    ans = (ans - n + mod) % mod;
    for(ri i = 1; i <= n; i ++)
    for(ri j = i + 1;  j <= n; j ++) {
        int ret = 0;
        for(ri k = j + 1; k <= n; k ++)
        if(in(i, j, k)) ret ++;
        ans = (ans - fp(2, ret) + mod) % mod;
    }
    printf("%d\n", ans);
    return 0;
}
```