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(){
	int n;
	cin>> n;
	vector<long long int> a(n);
	vector<long long int> b(n);
	for(int i=0;i<n;i++){
		cin >> a.at(i) >> b.at(i);
	}
	sort(a.begin(),a.end());
	sort(b.begin(),b.end());
	if(n%2==1){
		cout << b.at((n-1)/2) - a.at((n-1)/2)+1 << endl;
	}else{
		cout << b.at(n/2) + b.at(n/2-1) - a.at(n/2) - a.at(n/2-1) +1;
	}
}
