#include<cstdio>
using namespace std;
int n,neizheng;
double sum;
double x[1500],y[1500];
double fabs(double x)
{return x<0?-x:x;}
int abs(int a)
{return a<0?-a:a;}
int gcd(int a,int b)
{return b==0?a:gcd(b,a%b);}
int main()
{
	freopen("sistercookies.in","r",stdin);freopen("sistercookies.out","w",stdout);
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%lf%lf",&x[i],&y[i]);
    }
    x[n+1]=x[1];y[n+1]=y[1];
    for(int i=1;i<=n;i++)
    {
        sum+=(x[i+1]*y[i]-x[i]*y[i+1]);
    }
    double areas=fabs(sum)/2;
    for(int i=1;i<=n;i++)
    {
		neizheng+=gcd(abs(x[i+1]-x[i]),abs(y[i+1]-y[i]))-1;
    }
    neizheng+=n;
    printf("%d\n",(int)(areas+1.0-neizheng*0.5));
}