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 long long int LL;
typedef pair<int,int> P;
typedef pair<LL,LL> PL;

int main(){
  LL n;
  cin>>n;
  LL a[200010],b[200010];
  for(LL i=0;i<n;i++){
    cin>>a[i]>>b[i];
  }
  sort(a,a+n);
  sort(b,b+n);
  if(n%2!=0){
    LL m=n/2;
    cout<<b[m]-a[m]+1<<endl;
   
  }
  else{
    LL m=n/2-1;
    cout<<b[m]+b[m+1]-a[m]-a[m+1]+1<<endl;
  }
  return 0;
}
