Problem: A convex polygon consisting of N vertices is given. The coordinates of each vertex are represented counterclockwise by (X1, Y1), (X2, Y2), ……, (XN, YN). No matter what straight line passes through the point P, find the coordinates of the point P so that the areas of the two convex polygons obtained after cutting are equal.

Constraints

* All inputs are integers

* 3 ≤ N ≤ 50

* 0 ≤ | Xi |, | Yi | ≤ 1000000

* The input polygon is a simple convex polygon.

* The output must satisfy max (| X-cX |, | Y-cY |) ≤ 0.0001 when the output coordinates are (X, Y) and the exact solution is (cX, cY).

Input

The input is given in the following format.

> N
> X1 Y1
> X2 Y2
> ……
> XN YN
>

Output

If there is a point that satisfies the condition of the problem statement, the coordinates of that point

> X Y
>

Output in the format of. If the point does not exist, output "NA" on one line.

Examples

Input

4
100 100
0 100
0 0
100 0


Output

50.00000 50.00000


Input

3
100 100
0 100
0 0


Output

NA

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define ll long long
#define rep(i,n) for(ll (i)=0;(i)<(n);++(i))
using namespace std;

const double EPS=1e-10;
double add(double l, double r){
    if(abs(l+r)<EPS*(abs(l)+abs(r))) return 0;
    return l+r;
}
//l-r は add(l,-r)
//l==r は add(l,-r)==0
struct Pt{
    double x, y;
    Pt(double xx=0, double yy=0){x=xx; y=yy;}
    Pt& operator=(const Pt &rhs){
        x=rhs.x; y=rhs.y; return *this;
    }
    Pt& operator+=(const Pt &rhs){
        x = add(x,rhs.x); y = add(y,rhs.y); return *this;
    }
    Pt& operator-=(const Pt &rhs){
        x = add(x,-rhs.x); y = add(y,-rhs.y); return *this;
    }
    Pt& operator*=(const double &rhs){
        x *= rhs; y *= rhs; return *this;
    }
    Pt& operator/=(const double &rhs){
        x /= rhs; y /= rhs; return *this;
    }
};
Pt operator+(const Pt &a){return a;}
Pt operator-(const Pt &a){return Pt(-a.x,-a.y);}
Pt operator+(const Pt &lhs, const Pt &rhs){
    Pt ans=lhs; ans += rhs; return ans;
}
Pt operator-(const Pt &lhs, const Pt &rhs){
    Pt ans=lhs; ans -= rhs; return ans;
}
Pt operator*(const Pt &lhs, const double &rhs){
    Pt ans=lhs; ans *= rhs; return ans;
}
Pt operator*(const double &lhs, const Pt &rhs){
    Pt ans=rhs; ans *= lhs; return ans;
}
Pt operator/(const Pt &lhs, const double &rhs){
    Pt ans=lhs; ans /= rhs; return ans;
}
bool operator==(const Pt &lhs, const Pt &rhs){
    return add(lhs.x,-rhs.x)==0 && add(lhs.y,-rhs.y)==0;
}
bool operator!=(const Pt &lhs, const Pt &rhs){return !(lhs==rhs);}
bool operator<(const Pt &lhs, const Pt &rhs){
    return add(lhs.x,-rhs.x)!=0 ? add(lhs.x,-rhs.x)<0 : add(lhs.y,-rhs.y)<0;
}
bool operator>(const Pt &lhs, const Pt &rhs){return rhs<lhs;}
bool operator<=(const Pt &lhs, const Pt &rhs){return !(lhs>rhs);}
bool operator>=(const Pt &lhs, const Pt &rhs){return !(lhs<rhs);}
istream& operator>>(istream &is, Pt &rhs){
    double x, y;
    is >> x >> y;
    rhs=Pt(x,y);
    return is;
}
ostream& operator<<(ostream &os, const Pt &rhs){
    os << rhs.x << " " << rhs.y;
    return os;
}
double norm(const Pt &a){return add(a.x*a.x,a.y*a.y);}
double abs(const Pt &a){return sqrt(norm(a));}
double dot(Pt a, Pt b){return add(a.x*b.x,a.y*b.y);}
double cross(Pt a, Pt b){return add(a.x*b.y,-a.y*b.x);}
int ccw(Pt a, Pt b, Pt c) {
    b -= a; c -= a;
    if(cross(b, c)>0) return +2;  // counter clockwise
    if(cross(b, c)<0) return -2;  // clockwise
    if(dot(b, c)<0) return +1;        // c--a--b on line
    if(norm(c)<norm(b)) return -1;    // b--c--a on line
    return 0;                         // a--b--c on line
}
int main(){
  ll n;
  cin>>n;
  vector<Pt> rec;
  Pt centroid=0;
  rep(i,n){
    Pt tmp;
    cin>>tmp;
    rec.push_back(tmp);
    centroid+=tmp;
  }
  if(n%2==1){
    cout<<"NA"<<endl;
    return 0;
  }
  centroid/=n;
  bool f=true;
  rep(i,n){
    if(ccw(rec[i%n],centroid,rec[(i+n/2)%n])!=0 && f){
      cout<<"NA"<<endl;
      f=false;
    }
  }
  cout<<fixed<<setprecision(10);
  if(f)cout<<centroid<<endl;
}