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;

int main() {
	int n;
	cin >> n;

	int a[n], b[n];
	for (int i = 0; i < n; i++) cin >> a[i] >> b[i];

	sort(a, a + n); sort(b, b + n);

	if (n % 2 == 0) {
		int l = a[n / 2] + a[(n - 1) / 2], r = b[n / 2] + b[(n - 1) / 2];
		cout << 2 * (r / 2) - 2 * ((l + 1) / 2) + 1 + (l % 2) + (r % 2);	
	}
	else {
		cout << b[n / 2] - a[(n - 1) / 2] + 1;
	}
}
