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 LL long long

int n;
LL A[200005], B[200005];

int main(){
  scanf("%d",&n);
  for ( int i = 0; i < n; i++ ) scanf("%lld %lld",&A[i],&B[i]);
  sort(A,A+n);
  sort(B,B+n);
  if ( n & 1 ){
    printf("%lld\n",B[n/2] - A[n/2] + 1 );
  } else {
    LL a = (A[n/2-1] + A[n/2]);
    LL b = (B[n/2-1] + B[n/2]);
    printf("%lld\n",b-a+1);
  }
  return 0;
}





