There are N integers X_1, X_2, \cdots, X_N, and we know that A_i \leq X_i \leq B_i. Find the number of different values that the median of X_1, X_2, \cdots, X_N can take.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq B_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 B_1
A_2 B_2
:
A_N B_N


Output

Print the answer.

Examples

Input

2
1 2
2 3


Output

3


Input

3
100 100
10 10000
1 1000000000


Output

9991
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main(){
  int n;
  cin >> n;
  vector<int> ai(n), bi(n);
  for(int i=0; i<n; ++i) cin >> ai[i] >> bi[i];
  sort(ai.begin(),ai.end());
  sort(bi.begin(),bi.end());
  if(n%2){
    cout << bi[n/2]-ai[n/2]+1 << endl;
    return 0;
  }
  int a1 = ai[n/2-1], a2 = ai[n/2];
  int b1 = bi[n/2-1], b2 = bi[n/2];
  cout << (b1-a1) + (b2-a2) +1 << endl;
}