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;
   int a[n+1], b[n+1];
   for(int i =0; i < n; i++)
   {
      cin >> a[i]  >> b[i];
   }
   sort(a, a+n);
   sort(b, b+n);
   int x, y;
   if(n&1)
   {
      x = a[n/2];
      y = b[n/2];
   }
   else
   {
      x = (a[n/2 - 1] + a[n/2]);
      y = (b[n/2 - 1] + b[n/2]);
   }
   cout << y - x + 1;

}
