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 <iostream>
using namespace std;

int main() {
  int n; cin >> n;
  int mn[n],mx[n];
  for (int i=0; i<n; i++) cin >> mn[i] >> mx[i];
  sort(mn,mn+n);
  sort(mx,mx+n);
  if (n%2 == 0) {
    int l = mn[n/2]+mn[(n-1)/2],r = mx[n/2]+mx[(n-1)/2];
    cout << 2*(r/2) - 2*((l+1)/2) + 1 + (l%2) + (r%2)<< endl;
  }else {
    cout << mx[n/2] - mn[(n-1)/2] + 1 << endl;
  }
}