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;

int main() {
  int n;
  cin >> n;
  int a[n], b[n];
  for ( int i = 0; i < n; i++ ) {
    cin >> a[i] >> b[i];
  }
  sort(a, a+n);
  sort(b, b+n);

  int amid;
  int bmid;
  if ( n%2 == 1 ) {
    amid = a[n/2];
    bmid = b[n/2];
  } else {
    amid = a[(n/2)-1]+a[n/2];
    bmid = b[(n/2)-1]+b[n/2];
  }
  cout << (bmid-amid) + 1 << endl;
  return 0;
}
