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 <cstdio>
#include <algorithm>

using namespace std;

#define MAX_N 200005

int N;
int A[MAX_N], B[MAX_N];

void solve() {
  sort(A, A+N);
  sort(B, B+N);
  printf("%d\n", (N%2 == 1 ? B[N/2]-A[N/2] : (B[N/2]+B[(N-1)/2]-A[N/2]-A[(N-1)/2]))+1);
}

int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    scanf("%d %d", A+i, B+i);
  }
  solve();
}
