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> As(N), Bs(N);
  for (int i = 0; i < N; ++i) cin >> As[i] >> Bs[i];
  sort(As.begin(), As.end()); sort(Bs.begin(), Bs.end());
  int m = (N - 1) / 2, L = As[m], R = Bs[m];
  if (N % 2 == 0)
    {L += As[m + 1]; R += Bs[m + 1];}
  cout << R - L + 1 << endl;}