Problem E: Center of symmetry

Given is a set of n points with integer coordinates. Your task is to decide whether the set has a center of symmetry.

A set of points S has the center of symmetry if there exists a point s (not necessarily in S) such that for every point p in S there exists a point q in S such that p-s = s-q.

The first line of input contains a number c giving the number of cases that follow. The first line of data for a single case contains number 1 ≤ n ≤ 10000. The subsequent n lines contain two integer numbers each which are the x and y coordinates of a point. Every point is unique and we have that -10000000 ≤ x, y ≤ 10000000.

For each set of input data print yes if the set of points has a center of symmetry and no otherwise.

Sample input

1
8
1 10
3 6
6 8
6 2
3 -4
1 0
-2 -2
-2 4

Output for sample input

yes


#include <stdio.h>
#include <map>
using namespace std;
long long x[10000], y[10000], avex, avey, n;
void solve() {
    if(avex%n || avey%n) {
        puts("no");
        return;
    }
    avex /= n, avey /= n;
    map<long long, int> r;
    int i;
    for(i = 0; i < n; i++)
        r[x[i]*100000000+y[i]] = 1;
    long long xx, yy;
    for(i = 0; i < n; i++) {
        xx = 2*avex - x[i];
        yy = 2*avey - y[i];
        if(r[x[i]*100000000+y[i]] == 0) {
            puts("no");
            return;
        }
    }
    puts("yes");
}
int main() {
    int t, i;
    scanf("%d", &t);
    while(t--) {
        scanf("%lld", &n);
        avex = 0, avey = 0;
        for(i = 0; i < n; i++) {
            scanf("%lld %lld", &x[i], &y[i]);
            avex += x[i], avey += y[i];
        }
        solve();
    }
    return 0;
}