#include <cstdio>
#include <algorithm>
using namespace std;
typedef long long ll;
int n;
int x[202];
int y[202];
int l[222];

ll mod = 998244353;

ll pow2(ll x){
    ll r = 1;
    ll a = 2;
    while(x){
        if (x & 1){
            r = r*a%mod;
        }
        a = a*a%mod;
        x>>=1;
    }
    return r;
}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d%d",&x[i],&y[i]);
    }

    for(int i=1;i<=n;i++){
        for(int j=i+1;j<=n;j++){
            int cnt = 0;
            int b = x[i] - x[j];
            int a = y[j] - y[i];
            int c = a*x[i] + b*y[i];
            for(int k=1;k<=n;k++){
                if (k == i || k == j || c == a*x[k] + b*y[k])cnt++;
            }
            l[cnt]++;
        }
    }
    ll ans = (pow2(n) - n - 1 + mod)%mod;
    for(int i=2;i<=n;i++){
        l[i] /= i*(i-1)/2;
        ans = (ans - (pow2(i) - i - 1)*l[i]%mod + mod) % mod;
    }
    printf("%lld\n", ans);
}

### 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 <cstdio>
#include <algorithm>
using namespace std;
typedef long long ll;
int n;
int x[202];
int y[202];
int l[222];

ll mod = 998244353;

ll pow2(ll x){
    ll r = 1;
    ll a = 2;
    while(x){
        if (x & 1){
            r = r*a%mod;
        }
        a = a*a%mod;
        x>>=1;
    }
    return r;
}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d%d",&x[i],&y[i]);
    }

    for(int i=1;i<=n;i++){
        for(int j=i+1;j<=n;j++){
            int cnt = 0;
            int b = x[i] - x[j];
            int a = y[j] - y[i];
            int c = a*x[i] + b*y[i];
            for(int k=1;k<=n;k++){
                if (k == i || k == j || c == a*x[k] + b*y[k])cnt++;
            }
            l[cnt]++;
        }
    }
    ll ans = (pow2(n) - n - 1 + mod)%mod;
    for(int i=2;i<=n;i++){
        l[i] /= i*(i-1)/2;
        ans = (ans - (pow2(i) - i - 1)*l[i]%mod + mod) % mod;
    }
    printf("%lld\n", ans);
}

```