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;
	long long a[n+1], b[n+1];
	a[0] = b[0] = 0;
	for (int i = 1; i <= n; i++)
	{
		cin >> a[i] >> b[i];
	}
	sort(a, a + n + 1);
	sort(b, b + n + 1);

	if(n % 2 == 1) {
		cout << b[(n+1)/2] - a[(n+1)/2] + 1 << endl;
	}
	else {
		long long mida = a[n/2] + a[n/2+1];
		long long midb = b[n/2] + b[n/2+1];
		cout << midb - mida + 1 << endl;
	}

}
