#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <queue>
#include <cstring>
#include <stack>
#include <algorithm>
#include <string>
#include <vector>
#include <ctime>
#include <bitset>
#include <cmath>
typedef long long LL;
#define INF 0x3f3f3f3f
using namespace std;

struct Edge {
	int u, v, w;
};

struct Point {
	int x, y;
};

template <class T> inline T min(T a, T b) {
	return a > b ? b : a;
}

template <class T> inline T max(T a, T b) {
	return a < b ? b : a;
}

template <class T> inline T abs(T a) {
	return a > 0 ? a : -a;
}

template <class T> inline void CLR(T *a, int num) {
	memset(a, num, sizeof(a));
}

int N;
Point point[1030];
LL ans, T, S;

inline void in() {
	scanf("%d", &N);
	for(int i = 0;i < N;i ++) scanf("%d%d", &point[i].x, &point[i].y);
}

inline void getS() {
	int i;
	Point St = point[0];
	for(i = 1;i < N - 1;i ++) {
		S += ((point[i].x - St.x) * (point[i + 1].y - St.y)) - ((point[i + 1].x - St.x) * (point[i].y - St.y));
	}
	S = abs(S);
}

LL gcd(LL a, LL b) {
	return b == 0 ? a : gcd(b, a % b);
}

inline void getT() {
	int i, j;
	LL c, d, x, y;
	for(i = 0;i < N - 1;i ++) {
		Point p1 = point[i], p2 = point[i + 1];
		T += gcd(abs(p2.x - p1.x), abs(p2.y - p1.y));
	}
	Point p1 = point[N - 1], p2 = point[0];
	T += gcd(abs(p2.x - p1.x), abs(p2.y - p1.y));
}

inline void solve() {
	getS();
	getT();
	ans = (S - T) / 2 + 1;
	cout << ans;
}

int main() {
	freopen("sistercookies.in", "r", stdin);
	freopen("sistercookies.out", "w", stdout);
	in();
	solve();
	//while(1);
	return 0;
}