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(void)
{
	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 min2 = (a[n/2-1] + a[n/2]);
		int max2 = (b[n/2-1] + b[n/2]);
		cout << max2 - min2 +1 << endl;
	} else {
		int min = a[n/2];
		int max = b[n/2];
		cout << max-min+1 << endl;
	}

	return 0;
}
