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(nullptr);

	int n;
	cin>>n;
	vector<int>A(n),B(n);
	for(int i=0;i<n;++i)
		cin>>A[i]>>B[i];

	sort(begin(A),end(A));
	sort(begin(B),end(B));
	int ans=0;
	if(n&1)
	{
		ans=B[n/2]-A[n/2]+1;
	}
	else
	{
		ans=(B[n/2]+B[(n-2)/2])-(A[n/2]+A[(n-2)/2])+1;
	}
	cout<<ans<<'\n';
}
