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 maxn=2e5+5;
LL a[maxn]; LL b[maxn];
int main(void)
{
	int n; scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%lld%lld",&a[i],&b[i]);
	sort(a+1,a+1+n); sort(b+1,b+1+n);
	LL res;
	if(n&1)
	{
		res=(b[(n+1)/2]-a[(n+1)/2])+1;
	}
	else
	{
		res=(b[n/2]-a[n/2])+(b[n/2+1]-a[n/2+1]);
		res=res+1; 
	}
	printf("%lld\n",res);
	return 0;
}