#include <iostream>

#define NMAX 100005

using namespace std;

typedef long long ll;

struct elem {
    int x, y;
} a[NMAX];

int n;

inline int cmmdc(int x, int y) {
    while(y) {
        int z = x % y;
        x = y, y = z;
    }
    return x;
}

inline int vabs(const int x) {
    return x > 0 ? x : -x;
}

ll calcArie() {
    /*
    |x1 y1|
    |x2 y2|
    */
    ll ans = 0;
    for(int i = 1; i <= n; ++i)
        ans += 1ll * a[i - 1].x * a[i].y - 1ll * a[i].x * a[i - 1].y;
    return ans;
}

ll calcP() {
    ll ans = 0;
    for(int i = 1; i <= n; ++i)
        ans += cmmdc(vabs(a[i].x - a[i - 1].x), vabs(a[i].y - a[i - 1].y));
    return ans;
}

int main()
{
    freopen("copaci.in", "r", stdin);
    freopen("copaci.out", "w", stdout);
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i)
        scanf("%d%d", &a[i].x, &a[i].y);
    a[0] = a[n];
    cout << (calcArie() - calcP()) / 2 + 1;
    return 0;
}