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;
typedef long long ll;

const int N = 200010;

int a[N], b[N];

int main() {
	int n;
	scanf("%d", &n);
	for(int i=1; i<=n; i++)
		scanf("%d%d", &a[i], &b[i]);
	sort(a+1, a+n+1);
	sort(b+1, b+n+1);
	if(n&1)
		printf("%d\n", b[(n+1)/2]-a[(n+1)/2]+1);
	else {
		int mn = a[n/2+1]+a[n/2];
		int mx = b[n/2+1]+b[n/2];
		printf("%d\n", mx-mn+1);
	}
	return 0;
}