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;
int main() {
	int N;
	scanf("%d", &N);
	int A[N], B[N];
	for (int i = 0; i < N; ++i) scanf("%d %d", &A[i], &B[i]);
	sort(A, A + N);
	sort(B, B + N);
	int l = (A[(N - 1) / 2] + A[N / 2]), r = (B[(N - 1) / 2] + B[N / 2]);
	printf("%d", (r - l) / (1 + N % 2) + 1);
	return 0;
}