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>
#define ll long long
using namespace std;
const int maxn=2e5+5;
ll n,a[maxn],b[maxn],c[maxn],cost;
int main()
{
	std::ios::sync_with_stdio(false);
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i]>>b[i];
	}
	sort(a, a + n);
	sort(b, b + n);
	if (n % 2) {
		cout << b[n/2]-a[n/2]+1;
	}
	else {
		cout <<b[n/2-1]+ b[n / 2] - a[n/2]-a[n / 2 - 1] + 1;

	}
}
