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 MOD 1000000007LL
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

int n;
ll a[200005],b[200005];


int main(void){
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		scanf("%lld%lld",&a[i],&b[i]);
	}
	sort(a,a+n);
	sort(b,b+n);
	if(n%2==1){
		printf("%lld\n",(b[n/2]-a[n/2])+1LL);
	}else{
		printf("%lld\n",(b[n/2]+b[n/2-1]-(a[n/2]+a[n/2-1]))+1LL);
	}
	return 0;
}
