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 <stdio.h>
#include <algorithm>
typedef long long ll;

int main(void) {
  ll i, j, n;
  scanf("%lld", &n);
  ll a[n], b[n];
  for(i = 0; i < n; ++i) scanf("%lld%lld", &a[i], &b[i]);
  std::sort(a, a + n), std::sort(b, b + n);
  if(n & 1) printf("%lld", b[n / 2] - a[n / 2] + 1);
  else printf("%lld", b[n / 2 - 1] + b[n / 2] - a[n / 2 - 1] - a[n / 2] + 1);
  return 0;
}