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>
#include<algorithm>
using namespace std;
int N_MAX=200000;
int main()
{
  int n,m,i;
  long long res,a[N_MAX],b[N_MAX];
  cin >> n;
  for(i=0;i<n;i++)
    cin >> a[i] >> b[i];
  sort(a,a+n);
  sort(b,b+n);
  m=n/2;
  if(n%2==1){
    res=b[m]-a[m]+1;
  }else{
    res=b[m]+b[m-1]-a[m]-a[m-1]+1;
  }
  cout << res << endl;
  return 0;
}