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,i;
  cin>>n;
  vector<int> a(n),b(n);
  for(i=0;i<n;i++) cin>>a.at(i)>>b.at(i);
  sort(a.begin(),a.end());
  sort(b.begin(),b.end());
  reverse(b.begin(),b.end());
  if(n%2==1) cout<<b.at((n-1)/2)-a.at((n-1)/2)+1<<endl;
  else if(n%2==0) cout<<b.at(n/2-1)+b.at(n/2)-a.at(n/2-1)-a.at(n/2)+1<<endl;
}