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 maxn = 2e5+10;
int l[maxn], r[maxn];
int main(){
  	int n;
  	cin>>n;
  	for (int i=1;i<=n;i++) cin>>l[i]>>r[i];
  	sort(l+1,l+1+n);
  	sort(r+1,r+1+n);
 	int a=(n & 1)?l[(n+1)/2]:l[n/2]+l[n/2+1];
  	int b=(n & 1)?r[(n+1)/2]:r[n/2]+r[n/2+1];
  	cout<<b-a+1<<endl;
	return 0;
}