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;
int n,a[200004],b[200004];
int main(){
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i]>>b[i];
	sort(a+1,a+1+n);sort(b+1,b+1+n);
	if(n%2==1)cout<<b[(n+1)/2]-a[(n+1)/2]+1;
	if(n%2==0){
		cout<<(b[n/2+1]+b[n/2])-(a[n/2+1]+a[n/2])+1;
	}
}
