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 <stdio.h>
#include <iostream>
#include <vector>
#include <string>
#include <math.h>
#include <algorithm>
using namespace std;
#define INF 0x7FFFFFFF
const double EPS = 1e-10;


inline bool eq(double a, double b) { return fabs(b - a) < EPS;}

struct p_t{
  double x;
  double y;
  double norm() { return x * x + y * y; }
  double abs() { return sqrt(norm()); }
};
struct l_t{
	p_t a, b;
};

double cross(p_t p,p_t q);
p_t line(p_t p,p_t q);

bool asc(p_t left,p_t right) {
    return left.x == right.x ? left.y < right.y : left.x < right.x;
}
p_t Crosspoint(l_t l,l_t m);

int main(){
  int n;
  cin>>n;
  vector<p_t> a;
  p_t z;
  for(int i=0;i<n;i++){
    cin>>z.x>>z.y;
    a.push_back(z);
  }
  if((n&1)==0){
    z.x=(a[0].x+a[n/2].x)/2;
    z.y=(a[0].y+a[n/2].y)/2;
    int i;
    for(i=2;i<n/2;i++){
      if(eq(z.x,(a[i].x+a[i+n/2].x)/2)==0) break;
      if(eq(z.y,(a[i].y+a[i+n/2].y)/2)==0) break;
    }
    if(i==n/2){
      cout<<fixed<<z.x<<" "<<fixed<<z.y<<endl;
      return 0;
    }
  }
  cout<<"NA"<<endl;
  return 0;
}


p_t line(p_t p,p_t q){
  p_t z;
  z.x=q.x-p.x;
  z.y=q.y-p.y;
  return z;
}


double cross(p_t p,p_t q){
  return p.x*q.y-p.y*q.x;
}

p_t Crosspoint(l_t l,l_t m){
  p_t aa,bb,cc,dd,ee;
  aa.x=l.b.x-l.a.x;
  aa.y=l.b.y-l.a.y;
  bb.x=m.b.x-m.a.x;
  bb.y=m.b.y-m.a.y;
  cc=aa;
  dd.x=l.b.x-m.a.x;
  dd.y=l.b.y-m.a.y;
	double A = cross(aa,bb);
	double B = cross(cc,dd);
	if (abs(A) < EPS && abs(B) < EPS) return m.a;
  ee.x=m.a.x+(m.b.x-m.a.x)*B/A;
  ee.y=m.a.y+(m.b.y-m.a.y)*B/A;
	return ee;
}