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 arr[n], brr[n];
	for (int i = 0; i < n; ++i)
	{
		cin >> arr[i] >> brr[i];
	}

	sort(arr, arr+n);
	sort(brr, brr+n);

	long long x, y;
	if (n%2==1)
	{
		x = arr[n/2]; y = brr[n/2];
	}
	else
	{
		x = arr[n/2 - 1] + arr[n/2];
		y = brr[n/2 - 1] + brr[n/2];
	}

	cout << y - x + 1;
	return 0;
}