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;
#define rep(i,n) for(int i = 0; i < (int)n; i++)

int main(){
  int n, l, r;
  cin >> n;
  int a[n], b[n];
  rep(i,n) cin >> a[i] >> b[i];
  sort(a,a+n); sort(b,b+n);
  if(n % 2 == 0) l = a[n/2-1] + a[n/2], r = b[n/2-1] + b[n/2];
  else l = a[n/2], r = b[n/2];
  cout << r- l + 1 << endl;
  return 0;
}
