Problem:
Score : 1000 points

Problem Statement

Red bold fonts show the difference from C1.

There is an infinitely large triangular grid, as shown below.
Each point with integer coordinates contains a lamp.

Initially, only the lamp at (X, Y) was on, and all other lamps were off.
Then, Snuke performed the following operation zero or more times:

Choose two integers x and y.
Toggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).

After the operations, N lamps (x_1, y_1), \cdots, (x_N, y_N) are on, and all other lamps are off.
Find X and Y.

Constraints

1 \leq N \leq 10^4

-10^{17} \leq x_i, y_i \leq 10^{17}

(x_i, y_i) are pairwise distinct.

The input is consistent with the statement, and you can uniquely determine X and Y.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print X and Y, separated by a space.

Sample Input 1

4
-2 1
-2 2
0 1
1 0

Sample Output 1

-1 0

The following picture shows one possible sequence of operations:

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<iostream>
#include<vector>
using namespace std;
#define int long long
#define V vector
#define vel V<int>
#define rep(i,n) for(int i=0;i<n;i++)
#define mkp make_pair
#define pin pair<int,int>
pin solve(V<pin>& ab, int ex) {
	if (!ex) { return mkp(1,0); }
	V<V<pin>> qab(2);
  int sz=ab.size();
  qab[0].reserve(sz);
  qab[1].reserve(sz);
	for (pin x : ab) {
		qab[x.second & 1].push_back(mkp(x.first / 2,x.second / 2));
		if (x.first & 1) { qab[(x.second + 1) & 1].push_back(mkp(x.first / 2,(x.second + 1) / 2)); }
	}
	V<vel> c(2, vel(2));
	rep(i, 2) {
		for (pin x : qab[i]) {
			int qc = (2 * x.first + x.second) % 3;
          c[i][0]^=(qc+1);c[i][1]^=qc;
		}
	}
	rep(i, 2) {
		if (!((c[1 - i][0])&1)&&!c[1-i][1]) {
			pin ans = solve(qab[i], ex - 1);
			ans.first *= 2; ans.second *= 2; ans.second += i;
			return ans;
		}
	}
	for(pin &v:ab) { v.first++; }
	pin ans = solve(ab, ex); ans.first--;
	return ans;
}
signed main() {
	long long inf = 2e17;
	int n; scanf("%lld", &n);
	V<pin> ab(n);
	rep(i, n) {
		long long a, b; scanf("%lld", &a); scanf("%lld", &b);
		ab[i] = { a + inf,b + inf };
	}
	pin ret = solve(ab, 70);
	cout << ret.first - inf << " " << ret.second - inf << "\n";
}