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 ll;
typedef pair<int,int> P;
#define rep(i,m,n) for(int i=m;i<n;i++)
ll mod=1e9+7;

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