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;
  cin >> n;
  vector<int> 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());
  int n2 = n / 2;
  if (n % 2 == 1) {
    cout << b[n2] - a[n2] + 1 << endl;
  } else {
    cout << b[n2] + b[n2 - 1] - a[n2] - a[n2 - 1] + 1 << endl;
  }
  return 0;
}