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<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<iomanip>
#include<set>
#include<queue>

using namespace std;

int main()
{
	int n;
	cin >> n;
	vector<int> a(n),b(n);
	for(int i=0;i<n;i++)
		cin >> a[i] >> b[i];
	sort(a.begin(),a.end());
	sort(b.begin(),b.end());

	if(n%2==1)
		cout << b[n/2]-a[n/2]+1 << endl;
	else
		cout << ((b[n/2-1]+b[n/2])-(a[n/2-1]+a[n/2]))+1 << endl;




}