UVaUVa 1595 - Symmetry

#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
struct point{
    double x, y;
    bool operator < (const point&a)const{
        if(a.y == y) return a.x > x;
        else return a.y > y;
    }
};
vector<point>a;
vector<point>b;
int main()
{
    int t;
    double mid = 0;
    cin >> t;
    while(t--){
        int n,k = 1;
        point p;
        cin >> n;
        while(n--){
            cin >> p.x >> p.y;
            a.push_back(p);
            b.push_back(p);
        }
        if(n == 1){
            cout << "YES" << endl;
            a.clear();
            b.clear();
            continue;
        }
        sort(a.begin(), a.end());
        for(int i = 1; i < a.size(); i++){
            if(a[0].y != a[i].y){
                mid = (a[0].x + a[i-1].x)/2;
                break;
            }
        }
        for(int i = 0; i < b.size(); i++) b[i].x = 2*mid - b[i].x;
        sort(b.begin(), b.end());
        for(int i = 0; i < a.size(); i++){
            if(a[i].x != b[i].x || a[i].y != b[i].y){
                k = 0;
                break;
            }
        }
        if(k) cout << "YES\n";
        else cout << "NO\n";
        a.clear();
        b.clear();
    }
    return 0;
}