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: Accepted)

#include<bits/stdc++.h>
#define V vector
#define W V<long>
using namespace std;long E=70,M=2e17,i,a,b;W S(V<W>p){if(!E)return{1,0};V<V<W>>T(2);for(W x:p){T[x[1]&1].push_back({x[0]/2,x[1]/2});if(x[0]&1)T[x[1]&1].push_back({x[0]/2,++x[1]/2});}for(long i;i<2;i++){a=0;for(W x:T[!i])a^=(2*x[0]+x[1])%3+1;if(!a){E--;W A=S(T[i]);A[0]*=2;A[1]*=2;A[1]+=i;return A;}}for(W&v:p)v[0]++;W A=S(p);A[0]--;return A;}int main(){cin>>i;V<W>p(i);while(i--,cin>>a>>b)p[i]={a+M,b+M};W x=S(p);cout<<x[0]-M<<" "<<x[1]-M;}