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:
/*
 * 2442.cc: ConvexCut
 */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<functional>
 
using namespace std;

/* constant */

const int MAX_N = 50;
const int ITL = 100;

const double DELTA = 1.0e-4;
const double DINF = 1e18;

/* typedef */

template <typename T>
struct Pt {
  T x, y;

  Pt() {}
  Pt(T _x, T _y) : x(_x), y(_y) {}
  Pt(const Pt& pt) : x(pt.x), y(pt.y) {}

  bool operator==(const Pt pt) const { return x == pt.x && y == pt.y; }
  Pt<T> operator+(const Pt pt) const { return Pt<T>(x + pt.x, y + pt.y); }
  Pt<T> operator-() const { return Pt<T>(-x, -y); }
  Pt<T> operator-(const Pt pt) const { return Pt<T>(x - pt.x, y - pt.y); }
  Pt<T> operator*(T t) const { return Pt<T>(x * t, y * t); }
  Pt<T> operator/(T t) const { return Pt<T>(x / t, y / t); }
  T dot(Pt v) const { return x * v.x + y * v.y; }
  T cross(Pt v) const { return x * v.y - y * v.x; }
  Pt<T> mid(const Pt pt) { return Pt<T>((x + pt.x) / 2, (y + pt.y) / 2); }
  T d2() { return x * x + y * y; }
  double d() { return sqrt(d2()); }

  Pt<T> rot(double th) {
    double c = cos(th), s = sin(th);
    return Pt<T>(c * x - s * y, s * x + c * y);
  }

  Pt<T> rot90() { return Pt<T>(-y, x); }

  bool operator<(const Pt& pt) const {
    return x < pt.x || (x == pt.x && y < pt.y);
  }

  void print(string format) {
    printf(("(" + format + ", " + format + ")\n").c_str(), x, y);
  }
  void print() { print("%.6lf"); }
};

typedef Pt<double> pt;
typedef vector<pt> vpt;

struct CL {
  pt p;
  double t0, t1;
  CL() {}
  CL(const pt& _p, double _t0, double _t1) : p(_p), t0(_t0), t1(_t1) {}
};


/* global variables */

/* subroutines */

bool cross_lines(const pt& ap, const pt av, const pt& bp, const pt bv, CL& cl) {
  double op01 = av.cross(bv);
  //if (op01 == 0.0) return false; /* need to handle parallel?? */

  if (op01 == 0.0) {
    pt v = bp - ap;
    if (v.cross(av) != 0.0) return false;

    pt a1 = ap + av;
    pt b1 = bp + bv;

    return
      ((bp - ap).dot(b1 - ap) <= 0.0 ||
       (bp - a1).dot(b1 - a1) <= 0.0 ||
       (ap - bp).dot(a1 - bp) <= 0.0 ||
       (ap - b1).dot(a1 - b1) <= 0.0);
  }

  pt v = bp - ap;
  double op0 = v.cross(av);
  double op1 = v.cross(bv);

  double t0 = op1 / op01;
  double t1 = op0 / op01;

  cl.p = bv * t1 + bp;
  cl.t0 = t0;
  cl.t1 = t1;

  return true;
  //return (0.0 <= cl.t0 && cl.t0 <= 1.0 && 0.0 <= cl.t1 && cl.t1 <= 1.0);
}

void convex_cut(const vpt& scpol, vpt& dcpol, const pt& p0, const pt& p1) {
  int n = scpol.size();
  pt pv = p1 - p0;
  dcpol.clear();

  for (int i = 0; i < n; i++) {
    const pt& cp0 = scpol[i];
    double cr0 = pv.cross(cp0 - p0);
    if (cr0 >= 0.0) dcpol.push_back(cp0);
    
    const pt& cp1 = scpol[(i + 1) % n];
    double cr1 = pv.cross(cp1 - p0);
    if (cr0 * cr1 < 0.0) {
      CL cl;
      cross_lines(p0, pv, cp0, cp1 - cp0, cl);
      dcpol.push_back(cl.p);
    }
  }
}

double calc_area(const vpt& cpol) {
  int nc = cpol.size();
  if (nc < 3) return 0.0;

  double area = 0.0;
  for (int i = 0; i < nc; i++) {
    const pt &p0 = cpol[i], &p1 = cpol[(i + 1) % nc];
    area += p0.cross(p1);
  }

  return (area / 2);
}

/* main */

int main() {
  int n;
  cin >> n;

  vpt pol;
  double minx = DINF, maxx = -DINF, miny = DINF, maxy = -DINF;

  
  for (int i = 0; i < n; i++) {
    double x, y;
    cin >> x >> y;
    pol.push_back(pt(x, y));
    if (minx > x) minx = x;
    if (maxx < x) maxx = x;
    if (miny > y) miny = y;
    if (maxy < y) maxy = y;
  }

  double pah = calc_area(pol) / 2;
  //printf("pah=%.6lf\n", pah);

  double cx0 = minx, cx1= maxx;
  for (int i = 0; i < ITL; i++) {
    double cx = (cx0 + cx1) / 2;
    pt p0(cx, miny), p1(cx, maxy);
    vpt cpol;

    convex_cut(pol, cpol, p0, p1);
    double ca = calc_area(cpol);
    //printf("  cx=%.6lf => ca=%.6lf\n", cx, ca);
    
    if (ca < pah) cx0 = cx;
    else cx1 = cx;
  }
  //printf("cx0=%.6lf, cx1=%.6lf\n", cx0, cx1);

  double cy0 = miny, cy1= maxy;
  for (int i = 0; i < ITL; i++) {
    double cy = (cy0 + cy1) / 2;
    pt p0(minx, cy), p1(maxx, cy);
    vpt cpol;

    convex_cut(pol, cpol, p0, p1);
    double ca = calc_area(cpol);
    //printf("  cy=%.6lf => ca=%.6lf\n", cy, ca);

    if (ca > pah) cy0 = cy;
    else cy1 = cy;
  }
  //printf("cy0=%.6lf, cy1=%.6lf\n", cy0, cy1);

  bool ok = true;
  pt cp0(cx0, cy0);

  for (int i = 0; i < n; i++) {
    vpt cpol;
    convex_cut(pol, cpol, cp0, pol[i]);
    double ca = calc_area(cpol);

    double d = abs(pah - ca) / pah;
    if (d > DELTA) {
      //printf("d=%.6lf\n", d);
      ok = false;
      break;
    }
  }
  
  if (ok) printf("%.6lf %.6lf\n", cx0, cy0);
  else cout << "NA" << endl;

  return 0;
}