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;
const int N=2e5+7;
int arr[N];
int brr[N];
int main(){
	int n;
	cin>>n;
	for(int i=1;i<=n;i++) {
		cin>>arr[i]>>brr[i];
	}
	sort(arr+1,arr+1+n);
	sort(brr+1,brr+1+n);
	if(n%2==0) 	cout<<brr[n/2]+brr[n/2+1]-arr[n/2]-arr[n/2+1]+1<<endl;
	else  cout<<brr[(n+1)/2]-arr[(n+1)/2]+1<<endl;
	return 0;
}