# ZeroJudge - b604: Center of Symmetry
### 題目連結：https://zerojudge.tw/ShowProblem?problemid=b604
###### tags: `ZeroJudge` `數學` `幾何`

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
#define ERROR 1e-7
#define ROUND(value) ((value) + ERROR > 0 && (value) - ERROR < 0 ? 0 : ((value) < 0 ? int((value) - ERROR) : int((value) + ERROR)))

struct point {
	int x, y;

	point() {}

	point(int X, int Y):x(X), y(Y) {}

	bool operator<(const point &other) const {
		if (this->x != other.x)
			return this->x < other.x;
		return this->y < other.y;
	}

	bool operator>(const point &other) const {
		return other < *this;
	}

	bool operator==(const point &other) const {
		return (this->x == other.x && this->y == other.y);
	}

	bool operator!=(const point &other) const {
		return (this->x != other.x || this->y != other.y);
	}

} points[10001], target;

istream& operator>>(istream& inputstream, point &target) {
	return (inputstream >> target.x >> target.y);
}

int main() {
	cin.sync_with_stdio(false), cin.tie(nullptr);
	double centerX, centerY, bufferX, bufferY;
	bool paired[10001], symmetry;
	int amount, x, y, buffer;
	while (cin >> amount, amount) {
		centerX = centerY = 0.0;
		for (int i = 0; i < amount; ++i) {
			cin >> points[i]; 
			centerX += points[i].x; centerY += points[i].y;
		}
		sort(points, points + amount);
		centerX /= amount; centerY /= amount;
		memset(paired, false, sizeof(paired)); symmetry = true;
		for (int i = 0; i < amount; ++i)
			if (!paired[i]) {
				bufferX = centerX * 2 - points[i].x; bufferY = centerY * 2 - points[i].y;
				target = point(ROUND(bufferX), ROUND(bufferY));
				buffer = int(lower_bound(points, points + amount, target) - points);
				if (buffer == amount || points[buffer] != target) {
					symmetry = false;
					break;
				}
				paired[i] = paired[buffer] = true;
			}
		cout << (symmetry ? "yes" : "no") << '\n';
	}
}