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 int
#define ld long double
using namespace std;
int main(void){
	int i,t,n,x,ans;
	cin>>n;
	int a[n],b[n];
	for(i=0;i<n;i++){
		cin>>a[i]>>b[i];
	}
	sort(a,a+n);
	sort(b,b+n);
	if(n&1){
		ans=b[n/2]-a[n/2]+1;
		cout<<ans<<endl;
	}
	else{
		ld ans1=(b[n/2]+b[(n/2)-1])/2.0;
		ld ans2=(a[n/2]+a[(n/2)-1])/2.0;
		ans=(int)((ans1-ans2)/0.5+1);
		cout<<ans<<endl;
	}
}
