#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
#define int ll
typedef double db;
const db eps=1e-8,V=3003;
int dcmp(db x){return x>eps?1:x<-eps?-1:0;}
struct Point
{
    db x,y;
    void In(){cin>>x>>y;x+=1001;y+=1001;}
    void Out(){cout<<x<<" "<<y<<endl;}
};
bool operator ==(Point A,Point B){return !dcmp(A.x-B.x)&&!dcmp(A.y-B.y);}
typedef Point Vec;
Vec operator +(Vec A,Vec B){return {A.x+B.x,A.y+B.y};}
Vec operator -(Vec A,Vec B){return {A.x-B.x,A.y-B.y};}
Vec operator *(Vec A,db d){return {A.x*d,A.y*d};}
db Cro(Vec A,Vec B){return A.x*B.y-A.y*B.x;}
db Dot(Vec A,Vec B){return A.x*B.x+A.y*B.y;}
Point Cross_LL(Point a,Point b,Point c,Point d)
{
    Vec x=b-a,y=d-c,z=a-c;
    return a+x*(Cro(y,z)/Cro(x,y));
}
bool Pan(Point a,Point b,Point c,Point d)
{
    db c1=Cro(b-a,c-a),c2=Cro(b-a,d-a);
    db d1=Cro(d-c,a-c),d2=Cro(d-c,b-c);
    return dcmp(c1)*dcmp(c2)<0&&dcmp(d1)*dcmp(d2)<0;
}
bool On(Point p,Point a,Point b){return a.x<=p.x&&p.x<=b.x&&a.y<=p.y&&p.y<=b.y;}
db Atan(Vec a){return atan2(a.y,a.x);}
struct Line
{
    Point a,b;db arg;
    void Init(Point _a,Point _b){a=_a;b=_b;arg=Atan(b-a);}
    void Init(db _a,db _b,db _c,db _d){a={_a,_b};b={_c,_d};arg=Atan(b-a);}
    void Out(){cout<<a.x<<" "<<a.y<<" "<<b.x<<" "<<b.y<<endl;}
};
bool operator ==(Line A,Line B){return A.a==B.a&&A.b==B.b;}
Point Cross(Line L1,Line L2){return Cross_LL(L1.a,L1.b,L2.a,L2.b);}
int Chk(Line L,Point a){return dcmp(Cro(a-L.a,L.b-L.a))>0;}
bool Cmp(Line L1,Line L2)
{
	if(dcmp(L1.arg-L2.arg)!=0)return L1.arg<L2.arg;
	return dcmp(Cro(L2.a-L1.a,L1.b-L1.a))>0;
}
int Halfcut(Line *L,int n)
{
	sort(L+1,L+n+1,Cmp);int m=n,h=1,t=0;Line Q[n+1];n=0;
    for(int i=1;i<=m;i++)if(i==1||dcmp(L[i].arg-L[i-1].arg))L[++n]=L[i];
    for(int i=1;i<=n;i++)
	{
        while(h<t&&Chk(L[i],Cross(Q[t],Q[t-1])))t--;
        while(h<t&&Chk(L[i],Cross(Q[h],Q[h+1])))h++;
        Q[++t]=L[i];
    }
    while(h<t&&Chk(Q[h],Cross(Q[t],Q[t-1])))t--;
    while(h<t&&Chk(Q[t],Cross(Q[h],Q[h+1])))h++;
	for(int i=h;i<=t;i++)L[i-h+1]=Q[i];
	return t-h+1;
}
ll F(ll a,ll b,ll c,ll n)
{
    ll ac=a/c,bc=b/c,m=(a*n+b)/c;
    if(!a)return bc*(n+1);
    if(a>=c||b>=c)return n*(n+1)/2*ac+(n+1)*bc+F(a%c,b%c,c,n);
    return n*m-F(c,c-b-1,a,m-1);
}
ll _F(ll a,ll b,ll c,ll n)
{
	ll d=__gcd(__gcd(a,b),c);
	return F(a/d,b/d,c/d,n);
}
ll Sol(ll a,ll b,ll c,ll n)
{
	ll s=0;
	if(b<0)s+=(-b+c-1)/c*(n+1),b=(b%c+c)%c;
	if(a<0)s+=(-a+c-1)/c*n*(n+1)/2,a=(a%c+c)%c;
	return _F(a,b,c,n)-s; 
}
bool Ok(Point a,Point b,Point c,Point d,Point e,Point f)
{
	if(On(a,c,e)||On(b,c,e))return 1;
	return Pan(a,b,c,d)||Pan(a,b,d,e)||Pan(a,b,e,f)||Pan(a,b,f,c);
}
ll Get(ll a,ll b,ll c,ll l,ll r)
{
	ll s=0;
	for(ll i=l;i<=r;i++)s+=(a*i+b)%c==0;
	return s;
}
const int N=23;
int n,m;
ll ans=0;
Point p[N];
Line L[N],c[N],d[N];
bool In(Point v)
{
	for(int i=1;i<=n;i++)if(dcmp(Cro(p[i]-v,p[i+1]-v))<=0)return 0;
	return 1;
}
ll Calc(Point a,Point b,int l,int r,int op)
{
	if(op==0)a.y-=0.0001,b.y-=0.0001;
	if(a.x>b.x)swap(a,b);
	db dt=b.x-a.x,k=b.y-a.y,w=a.y*dt-a.x*k;
	dt*=40000;k*=40000;w*=40000;
	//cout<<fixed<<setprecision(10)<<k<<" "<<w<<" "<<dt<<endl;
	return Sol(k,w,dt,r)-Sol(k,w,dt,l-1);//(op==0)*Get(k,w,dt,l,r);
}
signed main()
{
	cin>>n;
	for(int i=1;i<=n;i++)p[i].In();
	reverse(p+2,p+n+1);p[n+1]=p[1];
	for(int i=1;i<=n;i++)L[i].Init(p[i],p[i+1]);
	for(db x=1000;x<=V;x+=0.5)for(db y=dcmp(x-floor(x))*0.5+1000;y<=V;y+=1.0)if(In({x,y}))
	{
		if(dcmp(x-floor(x))!=dcmp(y-floor(y)))continue;
		Point v={x,y};m=0;
		for(int i=1;i<=n;i++)if(Ok(p[i],p[i+1],v,{x,V},{V,V},{V,y}))L[++m].Init(p[i],p[i+1]);
		//cout<<endl;
		for(int i=1;i<=n;i++)if(Ok(p[i],p[i+1],{0,0},{0,y},v,{x,0}))L[++m].Init(v*2-p[i],v*2-p[i+1]);
		//cout<<endl;
		for(int i=1;i<=n;i++)if(Ok(p[i],p[i+1],{0,y},{0,V},{x,V},v))
		    L[++m].Init(x+p[i].y-y,y+x-p[i].x,x+p[i+1].y-y,y+x-p[i+1].x);
		//cout<<endl;
		for(int i=1;i<=n;i++)if(Ok(p[i],p[i+1],{x,0},v,{V,y},{0,y}))
		    L[++m].Init(x+y-p[i].y,y+p[i].x-x,x+y-p[i+1].y,y+p[i+1].x-x);
		//cout<<endl;
		L[++m].Init(v,{V,y});L[++m].Init({x,V},v);Line las=L[m];
		//cout<<m<<endl;
		m=Halfcut(L,m);L[0]=L[m];L[m+1]=L[1];
		//cerr<<666<<endl;
		int C=0,D=0,st=0,dst=ceil(x+eps),ded=0,cst=0,ced=dst;
		//cout<<m<<endl;
//		cout<<"Line: "<<endl;
//		for(int i=1;i<=m;i++)L[i].Out();
//		cout<<endl;
		for(int i=1;i<=m;i++)if(L[i]==las)st=i;
		for(int i=st%m+1;i!=st;i=i%m+1)
		{
			//cout<<i<<" "<<L[i].b.x<<" "<<L[i].a.x<<endl;
			if(L[i].b.x>L[i].a.x)d[++D]=L[i];
			if(L[i].b.x<L[i].a.x)c[++C]=L[i];
			if(C==1)cst=ded=floor(Cross(L[i],L[i-1]).x);
		}
		//cout<<ded<<endl;
		//for(int i=1;i<=D;i++)d[i].Out();
		//cout<<endl;
		//for(int i=1;i<=C;i++)c[i].Out(); 
		//cout<<endl;
		for(int i=1;i<=D;i++)
		{
			int l=dst,r=i==D?ded:floor(Cross(d[i],d[i+1]).x);
			//cout<<l<<" "<<r<<endl;
			if(l<=r)ans-=Calc(d[i].a,d[i].b,l,r,0),dst=r+1;
		}
		//cout<<ans<<endl;
		for(int i=1;i<=C;i++)
		{
			int r=cst,l=i==C?ced:ceil(Cross(c[i],c[i+1]).x+eps);
			//cout<<l<<" "<<r<<endl;
			if(l<=r)ans+=Calc(c[i].a,c[i].b,l,r,1),cst=l-1;
		}
		//cout<<ans<<endl;
	}
	cout<<ans;
}