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