#include<bits/stdc++.h>

 #define P pair<int,int>

 using namespace std;

 const int inf=0x3f3f3f3f;

 const double eps=1e-;

 const int N=;

 struct node{double x,y,k;int px,py;}a[N*N];

 double mid_x,mid_y;

 int n,x[N],y[N],ans,k,t,p[N],die[N],X[N],Y[N],cnt,lst,pos;

 bool cmp (const node &A,const node &B) {return A.k<B.k;}

 bool operator == (const node &A,const node &B) {return A.x*B.y==A.y*B.x;}

 bool check(int x,double b1,double b2)//double不要开成int！

 {

     double dx=mid_y-Y[x],dy=-mid_x+X[x];

     return fabs(dy*b1-b2*dx)<eps;

 }

 int main()

 {

     scanf("%d",&n);

     for (int i=;i<=n;i++)

       scanf("%d%d",&x[i],&y[i]),mid_x+=x[i],mid_y+=y[i];

     mid_x/=n;mid_y/=n;

     for (int i=;i<n;i++)

     if (!die[i])

       for (int j=i+;j<=n;j++)

         if (!die[j]&&fabs(x[i]+x[j]-*mid_x)<eps&&fabs(y[i]+y[j]-*mid_y)<eps) {die[i]=die[j]=;break;}

     for (int i=;i<=n;i++) if (!die[i]) X[++t]=x[i],Y[t]=y[i];

     if (t<) return puts("-1"),;

     for (int i=;i<t;i++)

       for (int j=i+;j<=t;j++)

       {

            double dx=mid_y-(Y[i]+Y[j])/2.0,dy=-mid_x+(X[i]+X[j])/2.0;//垂直，斜率负倒数

            if (dx<) dx=-dx,dy=-dy;

            if (dx==) dy=fabs(dy);

            if (dy==) dx=fabs(dx);//!!!

            a[++cnt].x=dx,a[cnt].y=dy;a[cnt].px=i;a[cnt].py=j;a[cnt].k=atan2(dy,dx);

       }

     sort(a+,a+cnt+,cmp);lst=;

     for (int i=;i<=cnt;i++)//check and count

       if (i==cnt||!(a[i]==a[i+]))

       {

             if (i-lst+>=t/)

             {

                 for (int j=;j<=t;j++) p[j]=;

                 for (;lst<=i;lst++)

                   if (p[a[lst].px]&&p[a[lst].py]) p[a[lst].px]=p[a[lst].py]=;//注意重合的两点不能同时和另一点匹配！一配一

                 k=;

                 for (int j=;j<=t;j++) if (p[j]) k++,pos=j;

                 if (k>(t&)) continue;

                 if (!k||check(pos,a[i].x,a[i].y)) ans++;

             }

             lst=i+;

       }

     printf("%d\n",ans);

    return ;

 }