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;
typedef long long int ll;
vector<ll> a,b;
int main()
{
	int i,n;
	scanf("%d",&n);
	ll x,y;
	for(i=0;i<n;++i)
	{
		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)
	{
		x = a[(n)/2];
		y = b[(n)/2];
		cout << y-x+1;
	}
	if(n%2==0)
	{
		cout << b[n/2-1]+b[n/2]-a[n/2-1]-a[n/2]+1;
	}
}