ARC018-B 格子点と整数

ARC018-B.cpp

#include <bits/stdc++.h>
using namespace std;
 
#define fs first
#define sc second
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define rep(i, n) for (int i = 0; i < n; ++i)
#define pb emplace_back
 
using pii = pair<int, int>;
using vi = vector<int>;
using lint = long long;
 
const int inf = 1001001001;
const lint linf = 1001001001001001001ll;
const int mod = 1e9 + 7;
const int dx[]{0, 1, 0, -1, -1, -1, 1, 1}, dy[]{1, 0, -1, 0, -1, 1, -1, 1};
 
template<typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; } return a > b; }
template<typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; } return a < b; }
template<typename T> inline void print(const T &x, string s = "\n") { cout << x << s; }
template<typename T> inline void print(const vector<T> &v, string s = " ") 
{ rep(i, v.size()) cout << v[i] << (i + 1 == v.size() ? "\n" : s); }
inline bool inside(int y, int x, int H, int W) { return 0 <= y && y < H && 0 <= x && x < W; }
inline lint in() { lint x; std::cin>>x; return x; }
 
lint gcd(lint a, lint b) {
		if (b == 0) return a;
			return gcd(b, a % b);
}
 
int main() {
	int n = in();
	vector<lint> x, y;
 
	rep(i, n) {
		x.pb(in());
		y.pb(in());
	}
 
	lint ans = 0;
 
	for (int i = 0; i < n; ++i) {
		for (int j = i + 1; j < n; ++j) {
			for (int k = j + 1; k < n; ++k) {
				if ((y[i] - y[j]) * (x[j] - x[k]) == (x[i] - x[j]) * (y[j] - y[k])) continue;
 
				lint a = gcd(abs(x[i] - x[j]), abs(y[i] - y[j]));
				lint b = gcd(abs(x[j] - x[k]), abs(y[j] - y[k])); 
				lint c = gcd(abs(x[k] - x[i]), abs(y[k] - y[i]));
				
				if ((a + b + c) % 2 == 0) ans++;
			}
		}
	}
 
	print(ans);
}