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>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int main(){
	int n; scanf("%d",&n);
	vector<int> a(n),b(n);
	rep(i,n) scanf("%d%d",&a[i],&b[i]);

	sort(a.begin(),a.end());
	sort(b.begin(),b.end());

	if(n%2==1) printf("%d\n",b[n/2]-a[n/2]+1);
	else       printf("%d\n",b[n/2]+b[n/2-1]-a[n/2]-a[n/2-1]+1);

	return 0;
}
