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() {
  long n,ans;
  cin >> n;
  vector<long> a(n);
  vector<long> b(n);
  for(long i=0;i<n;i++) cin >> a[i] >> b[i];
  sort(a.begin(),a.end());
  sort(b.begin(),b.end());
  if(n%2==0) {
    long m1_min=a[n/2-1],m1_max=b[n/2-1],m2_min=a[n/2],m2_max=b[n/2];
    ans=m1_max+m2_max-m1_min-m2_min+1;
  } else {
    ans=b[n/2]-a[n/2]+1;
  }
  cout << ans << endl;
}