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 <cmath>
#include <cstdlib>
#include <iostream>
#include <vector>
using namespace std;

constexpr long double EPS = 1e-7;

struct point {
	long double x, y;
	point(long double x = 0.0, long double y = 0.0):x(x), y(y) {}
	point(const point &p):x(p.x), y(p.y) {}

	point operator+(const point &p) const {
		return point(x + p.x, y + p.y);
	}

	point operator-(const point &p) const {
		return point(x - p.x, y - p.y);
	}

	point operator*(long double s) const {
		return point(x * s, y * s);
	}
};

long double dot(const point &a, const point &b) {
	return a.x * b.x + a.y * b.y;
}

long double cross(const point &a, const point &b) {
	return a.x * b.y - a.y * b.x;
}

long double norm(const point &p) {
	return p.x * p.x + p.y * p.y;
}

int ccw(const point &a, point b, point c) {
	b = b - a;
	c = c - a;
	const long double t = cross(b, c);
	if(t > EPS) return 1;
	if(t < -EPS) return -1;
	if(dot(b, c) < 0) return 2;
	if(norm(b) < norm(c)) return -2;
	return 0;
}

point rotate(const point &p, long double theta) {
	const long double s = sin(theta), c = cos(theta);
	return point(c * p.x - s * p.y, s * p.x + c * p.y);
}

struct line {
	point a, b;
	line(const point &a_, const point &b_):a(a_), b(b_) {}
};

point crosspoint(const line &a, const line &b) {
	const long double t = cross(a.b - a.a, b.b - b.a);
	if(abs(t) < EPS) return a.a;
	return b.a + (b.b - b.a) * cross(a.b - a.a, a.a - b.a) * (1 / t);
}

typedef vector<point> polygon;

long double area(const polygon &p) {
	const int n = p.size();
	if(n < 3) return 0.0;

	long double res = cross(p[n - 1], p[0]);
	for(int i = 1; i < n; ++i) {
		res += cross(p[i - 1], p[i]);
	}
	return abs(res) * 0.5;
}

polygon convex_cut(const polygon &p, const line &l) {
	const int n = p.size();
	polygon res;
	for(int i = 0; i < n; ++i) {
		const int next = (i + 1) % n;
		const int tmp = ccw(l.a, l.b, p[i]);
		if(tmp != -1) res.emplace_back(p[i]);

		if(tmp * ccw(l.a, l.b, p[next]) < 0) {
			res.emplace_back(crosspoint(l, line(p[i], p[next])));
		}
	}

	return res;
}

bool ok(const point &g, const polygon &p) {
	const long double S_half = area(p) / 2.0;
	for(long double theta = 0; theta < M_PI; theta += 0.01) {
		const long double  S = area(convex_cut(p, line(g, g + rotate(point(10, 0), theta))));
		if(abs((S_half - S) / S_half) > EPS) return false;
	}

	return true;
}

int main() {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	cout.precision(5);
	cout.flags(ios::fixed);

	int n;
	cin >> n;

	point g(0, 0);
	polygon p;
	p.reserve(n);
	for(int i = 0; i < n; ++i) {
		int x, y;
		cin >> x >> y;
		p.emplace_back(x, y);
		g = g + p[i];
	}

	g = g * (1.0 / n);

	if(ok(g, p)) {
		cout << g.x << " " << g.y << endl;
	}
	else {
		cout << "NA" << endl;
	}

	return EXIT_SUCCESS;
}