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>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

#define fi first
#define se second
#define repl(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep(i,n) repl(i,0,n)
#define each(itr,v) for(auto itr:v)
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<x<<endl
#define mmax(x,y) (x>y?x:y)
#define mmin(x,y) (x<y?x:y)
#define maxch(x,y) x=mmax(x,y)
#define minch(x,y) x=mmin(x,y)
#define uni(x) x.erase(unique(all(x)),x.end())
#define exist(x,y) (find(all(x),y)!=x.end())
#define bcnt __builtin_popcount

typedef long double D;
typedef complex<D> P;

#define X real()
#define Y imag()

const D eps=1e-8;
const D inf=1e12;

D cross(P a,P b){ return (conj(a)*b).Y; }
D dot(P a,P b){ return (conj(a)*b).X; }

struct L : public vector<P>{
  L(const P& a,const P &b){
    push_back(a);
    push_back(b);
  }
};

bool intersectLL(L l,L m){
  return abs(cross(l[1]-l[0],m[1]-m[0]))>eps||abs(cross(l[1]-l[0],m[0]-l[0]))<eps;
}

P crosspoint(L l,L m) {
  D A=cross(l[1]-l[0],m[1]-m[0]);
  D B=cross(l[1]-l[0],l[1]-m[0]);
  if (abs(A)<eps&&abs(B)<eps) return m[0]; // same line
  if (abs(A)<eps) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
  return m[0]+B/A*(m[1]-m[0]);
}

int n;
P ps[111];

int main(){
	cin.sync_with_stdio(false);
  cin>>n;
  rep(i,n){
    D x,y;
    cin>>x>>y;
    ps[i]=P(x,y);
  }
  if(n%2==1){
    cout<<"NA"<<endl;
    return 0;
  }
  rep(i,n/2){
    if(abs(norm(ps[i]-ps[i+1])-norm(ps[(i+n/2)%n]-ps[(i+n/2+1)%n]))>eps){
      cout<<"NA"<<endl;
      return 0;
    }
    if(intersectLL(L(ps[i],ps[i+1]),L(ps[(i+n/2)%n],ps[(i+n/2+1)%n]))){
      cout<<"NA"<<endl;
      return 0;
    }
  }
  P res=crosspoint(L(ps[0],ps[n/2]),L(ps[1],ps[n/2+1]));
  printf("%.10Lf %.10Lf\n", res.X,res.Y);
	return 0;
}