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;

#define rep(i,x,y) for(int i=(x);i<(y);++i)
#define debug(x) #x << "=" << (x)

#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define dump(x) std::cerr << debug(x) << " (L:" << __LINE__ << ")" << std::endl
#else
#define dump(x)
#endif

typedef long long int ll;
typedef pair<int,int> pii;
//template<typename T> using vec=std::vector<T>;

const int inf=1<<30;
const long long int infll=1LL<<58;
const long double eps=1e-6;
const int dx[]={1,0,-1,0},dy[]={0,1,0,-1};

template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec){
    os << "[";
    for (const auto &v : vec) {
    	os << v << ",";
    }
    os << "]";
    return os;
}

typedef complex<long double> point;
typedef pair<point,point> line;
bool equal(const long double x1,const long double x2){ return abs(x1-x2)<eps; }
bool equal(const point& a,const point& b){ return equal(a.real(),b.real()) and equal(a.imag(),b.imag()); }
long double length(const point& a){ return abs(a); }
long double distance(const point& a,const point& b){ return abs(a-b); }
long double dot(const point& a,const point& b){ return a.real()*b.real()+a.imag()*b.imag(); }
long double cross(const point& a,const point& b){ return a.real()*b.imag()-a.imag()*b.real(); }
bool is_orthogonal(const point& a1,const point& a2,const point& b1,const point& b2){ return equal(dot(a1-a2,b1-b2),0.0); }
bool is_orthogonal(const line& l,const line& m){ return is_orthogonal(l.first,l.second,m.first,m.second); }
bool is_parallel(const point& a1,const point& a2,const point& b1,const point& b2){ return equal(cross(a1-a2, b1-b2),0.0); }
bool is_parallel(const line& l,const line& m){ return is_parallel(l.first,l.second,m.first,m.second); }
int ccw(point a,point b,point c) {
    b-=a; c-=a;
    if(cross(b, c) > 0)   return +1;       // counter clockwise
    if(cross(b, c) < 0)   return -1;       // clockwise
    if(dot(b, c) < 0)     return +2;       // c--a--b on line
    if(norm(b) < norm(c)) return -2;       // a--b--c on line
    return 0;
}
bool intersectLL(const line& l, const line& m){
    return abs(cross(l.second-l.first, m.second-m.first)) > eps || // non-parallel
           abs(cross(l.second-l.first, m.first-l.first)) < eps;   // same line
}
bool intersectLS(const line& l, const line& s){
    return cross(l.second-l.first, s.first-l.first)*       // s.first is left of l
           cross(l.second-l.first, s.second-l.first) < eps; // s.second is right of l
}
bool intersectLP(const line& l, const point& p){
    return abs(cross(l.second-p, l.first-p)) < eps;
}
bool intersectSS(const line& s, const line& t){
    return ccw(s.first,s.second,t.first)*ccw(s.first,s.second,t.second) <= 0 &&
           ccw(t.first,t.second,s.first)*ccw(t.first,t.second,s.second) <= 0;
}
bool intersectSP(const line& s, const point& p){
    return abs(s.first-p)+abs(s.second-p)-abs(s.second-s.first) < eps; // triangle inequality
}
point projection(const line& l, const point& p) {
    long double t = dot(p-l.first, l.first-l.second) / norm(l.first-l.second);
    return l.first + t*(l.first-l.second);
}
point reflection(const line& l, const point& p){
    return p+point((projection(l, p) - p).real()*2,(projection(l, p) - p).imag()*2);
}
long double distanceLP(const line &l, const point& p){
    return abs(p - projection(l, p));
}
long double distanceLL(const line &l, const line &m){
    return intersectLL(l, m) ? 0 : distanceLP(l, m.first);
}
long double distanceLS(const line &l, const line &s){
    if (intersectLS(l, s)) return 0;
    return min(distanceLP(l, s.first), distanceLP(l, s.second));
}
long double distanceSP(const line &s, const point& p) {
    const point r = projection(s, p);
    if (intersectSP(s, r)) return abs(r - p);
    return min(abs(s.first - p), abs(s.second - p));
}
long double distanceSS(const line &s, const line &t) {
    if (intersectSS(s, t)) return 0;
    return min(min(distanceSP(s, t.first), distanceSP(s, t.second)),
             min(distanceSP(t, s.second), distanceSP(t, s.second)));
}
// a1,a2???????????´?????¨b1,b2???????????´?????????????¨????
point intersection_l(const point& a1,const point& a2,const point& b1,const point& b2) {
  const point& a=a2-a1,b=b2-b1;
  return a1+a*cross(b, b1-a1)/cross(b, a);
}
point intersection_l(const line& l,const line& m){
    return intersection_l(l.first,l.second,m.first,m.second);
}
// ????§???¢????¬?????????¢???
long double area(const vector<point>& pol){
    long double s=0;
    rep(i,0,pol.size()) s+=cross(pol[i],pol[(i+1)%pol.size()]);
    return s/2;
}

vector<point> convex_cut(const vector<point>& ps, const line& l) {
    vector<point> res;
    for (int i = 0; i < ps.size(); ++i) {
        point a = ps[i], b = ps[(i+1)%ps.size()];
        if (ccw(l.first, l.second, a) != -1) res.push_back(a);
        if (ccw(l.first, l.second, a)*ccw(l.first, l.second, b) < 0) res.push_back(intersection_l(line(a, b), l));
    }
    return res;
}

void solve(){
    int n;
    cin >> n;
    vector<point> ps(n);
    for(point& p:ps){
        long double x,y;
        cin >> x >> y;
        p=point(x,y);
    }

    const long double s=area(ps);
    auto opt=[&](){
        long double left=inf,right=-inf;
        for(const auto& p:ps){
            if(p.real()<left) left=p.real();
            if(p.real()>right) right=p.real();
        }
        line l(point(left,0),point(left,1));
        long double lb=0,ub=distanceLP(l,point(right,0));
        rep(i,0,200){
            long double mid=(lb+ub)/2;
            l=line(point(left+mid,0),point(left+mid,1));
            if(area(convex_cut(ps,l))<=s/2) lb=mid;
            else ub=mid;
        }
        return l;
    };

    line l1=opt();
    for(auto& p:ps) p*=point(0,1);
    line l2=opt();
    l2=line(l2.first*point(0,-1),l2.second*point(0,-1));
    for(auto& p:ps) p*=point(0,-1);
    point ans=intersection_l(l1,l2);
    bool ok=true;
    const long double pi=3.14159265;
    rep(i,0,10000){
        const point tmp=ans+point(1,0)*point(cos(2*pi*i/10000),sin(2*pi*i/10000));
        if(abs(area(convex_cut(ps,line(ans,tmp)))-s/2)>eps){
            ok=false;
            break;
        }
    }
    if(ok) cout << ans.real() << " " << ans.imag() << endl;
    else cout << "NA" << endl;
}

int main(){
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
    cout << fixed << setprecision(8) << endl;
    solve();
    return 0;
}