#include<iostream>
#include<cstdio>
#include<cmath>
#include<set>
#include<algorithm>
#define N 2000
#define eps 1e-9
#define inf 1e9
using namespace std;
int read()
{
    char c=0;
    int sum=0,f=1;
    while (c!='-'&&(c<'0'||c>'9')) c=getchar();
    if (c=='-') c=getchar(),f=-1;
    while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
    return sum*f;
}
__float128 abs(__float128 x)
{
    return (x>0)?x:-x;
}
struct reads
{
    int x,y;
};
reads st[N+1],tong[N+1];
__float128 get(__float128 a,__float128 b)
{
    if (abs(a)<eps) return -inf;
    return b/a;
}
struct rds
{
    __float128 a,b;
    bool operator < (const rds &t)const
    {
        return get(a,b)<get(t.a,t.b);
    }
};
set<rds>s;
int n,length;
bool used[N+1];
__float128 sx,sy,delta[N+1];
int main()
{
    bool op;
    __float128 a,b,ds;
    n=read();
    for (int i=1;i<=n;++i) st[i].x=read(),st[i].y=read(),sx+=st[i].x,sy+=st[i].y;
    sx/=n,sy/=n;
    for (int i=1;i<=n;++i)
	if (!used[i])
	{
	    if (abs(st[i].x-sx)<eps&&abs(st[i].y-sy)<eps)
	    {
		used[i]=1;
		break;
	    }
	    for (int j=i+1;j<=n;++j)
		if (!used[j]&&abs(st[i].x+st[j].x-sx*2)<eps&&abs(st[i].y+st[j].y-sy*2)<eps)
		{
		    used[i]=used[j]=1;
		    break;
		}
	}
    for (int i=1;i<=n;++i)
	if (!used[i])
	    tong[++length]=st[i];
    if (!length)
    {
	puts("-1");
	return 0;
    }
    for (int i=2;i<=length;++i)
    {
	a=tong[1].x+tong[i].x-sx*2,b=tong[1].y+tong[i].y-sy*2;
	for (int j=1;j<=length;++j) delta[j]=tong[j].x*b-tong[j].y*a;
	ds=sx*b-sy*a,sort(delta+1,delta+length+1),op=1;
	for (int j=1;j<=length;++j) op&=(abs(delta[j]+delta[length+1-j]-ds*2)<eps);
	if (op) s.insert((rds){b,-a});
    }
    for (int i=3;i<=length;++i)
    {
	a=tong[2].x+tong[i].x-sx*2,b=tong[2].y+tong[i].y-sy*2;
	for (int j=1;j<=length;++j) delta[j]=tong[j].x*b-tong[j].y*a;
	ds=sx*b-sy*a,sort(delta+1,delta+length+1),op=1;
	for (int j=1;j<=length;++j) op&=(abs(delta[j]+delta[length+1-j]-ds*2)<eps);
	if (op) s.insert((rds){b,-a});
    }
    printf("%d\n",s.size());
    return 0;
}