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;

long long n;
vector<long long> l, r;

int main() {
  cin >> n;
  l.resize(n);
  r.resize(n);
  for (int i = 0; i < n; ++i) cin >> l[i] >> r[i];
  sort(l.begin(), l.end());
  sort(r.begin(), r.end());
  if (n % 2)
    cout << r[n / 2] + 1 - l[n / 2] << endl;
  else
    cout << r[n / 2 - 1] + r[n / 2] - l[n / 2] - l[n / 2 - 1] + 1 << endl;

  return 0;
}
