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;

#define ll long long
const int MAXN=2e5+1;
ll a[MAXN],b[MAXN];

int main(){
	ll n;
	cin>>n;
	for(ll i=0; i<n; i++) cin>>a[i]>>b[i];
	sort(a,a+n);
	sort(b,b+n);
	if (n%2==1){
		ll x=a[(n+1)/2-1],y=b[(n+1)/2-1];
		cout<<y-x+1<<endl;
	}
	else{
		ll x=a[n/2-1]+a[n/2],y=b[n/2-1]+b[n/2];
		cout<<y-x+1<<endl;
	}
	return 0;
}