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;
using ll = long long;
vector<ll> a,b;

int main()
{
	int n;
	cin >> n;
	a = b = vector<ll>(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)
	{
		cout<<b[n/2]-a[n/2]+1<<endl;
	}
	else
	{
		ll A = a[n/2]+a[n/2-1];
		ll B = b[n/2]+b[n/2-1];
		//cout<<A<<' '<<B<<endl;
		cout<<(B-A)+1<<endl;
	}

}