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