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;
typedef int64_t ll;

int main(){
  int n;
  cin >> n;
  int a[n+1],b[n+1];
  for(int i=1;i<=n;i++){
    cin >> a[i] >> b[i];
  }
  sort(a+1,a+n+1);sort(b+1,b+n+1);
  if(n%2==1){cout << b[(n+1)/2] - a[(n+1)/2] + 1 << endl;return 0;}
  else{
    cout << b[n/2+1]+b[n/2]-a[n/2+1]-a[n/2]+1 << endl;return 0;
  }
}
