Problem:
Score : 1000 points

Problem Statement

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

Initially, only the lamp at (X, 0) 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.

Constraints

1 \leq N \leq 10^5

-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.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print X.

Sample Input 1

4
-2 1
-2 2
0 1
1 0

Sample Output 1

-1

The following picture shows one possible sequence of operations:

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;

multiset<P> poInts;
Int n;
Int res;

int main(){
  cin >> n;
  for(Int i = 0;i < n;i++){
    P a;
    cin >> a.first >> a.second;
    poInts.insert(a);
  }

  while(true){
    auto it = poInts.begin();
    if(poInts.size() == 1){
      res = it->first;break;
    }
    auto jt = it;jt++;
    if(it->first != jt->first){
      res = it->first;break;
    }
    Int x = it->first;
    Int ya = it->second, yb = jt->second;
    Int dist = yb - ya;
    while(dist){
      Int k = dist & -dist;
      poInts.insert(P(x + k, ya));
      
      dist -= k;
      ya += k;
    }
    poInts.erase(poInts.begin());
    poInts.erase(poInts.begin());
  }
  cout << res << endl;
  return 0;
}