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 main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	int n;
	cin>>n;
	vector<int> a, b;
	for(int i=0;i<n;i++){
		int x, y;
		cin>>x>>y;
		a.push_back(x);
		b.push_back(y);
	}
	sort(a.begin(), a.end());
	sort(b.begin(), b.end());
	if(n%2==1){
		cout<<b[(n+1)/2-1]-a[(n+1)/2-1]+1;
	}
	else{
		cout<<b[n/2]+b[n/2-1]-a[n/2]-a[n/2-1]+1;
	}
}