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<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=2e5+10;
int a[N],b[N];
int main()
{
	int n;
	cin>>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);
	long long ans=0;
	if(n%2)
	{
		ans=b[n/2+1]-a[n/2+1]+1;
	}
	else
	ans=b[n/2]+b[n/2+1]-a[n/2]-a[n/2+1]+1;
	printf("%lld\n",ans);
}