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;

const int N = 200 * 1000 + 20;
int n, a[N], b[N];

int main() {
	ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> a[i] >> b[i];
	sort(a, a + n);
	sort(b, b + n);
	cout << (n % 2 == 1? b[n / 2] - a[n / 2]: (b[n / 2] + b[n / 2 - 1] - a[n / 2] - a[n / 2 - 1])) + 1 << "\n";
}
