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
#pragma GCC optimize("Ofast")
#include<stdio.h>
#include<algorithm>
using namespace std;
int a[200005],b[200005];
int main(){
	int i,n;
	scanf("%d",&n);
	for(i=0;i<n;i++)
		scanf("%d%d",&a[i],&b[i]);
	sort(a,a+n);
	sort(b,b+n);
	if(n&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);
}
