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 ;

const int MAX = 2e5 + 10 ;

int a[MAX] , b[MAX] ;
int n ;

int main()
{
	ios_base::sync_with_stdio(0) ;
	cin.tie(0) ;
	cin>>n ;
	for(int i = 0 ; i < n ; ++i)
		cin>>a[i]>>b[i] ;
	sort(a , a + n) ;
	sort(b , b + n) ;
	int x , y ;
	if(n % 2 == 0)
		x = a[n/2] + a[n/2-1] , y = b[n/2] + b[n/2-1] ;
	else
		x = a[n/2] , y = b[n/2] ;
	return cout<<y-x+1<<"\n" , 0 ;
}		