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;
double mi[200001],ma[200001];
int main(){
	int n,i;
	cin>>n;
	for(i=1;i<=n;++i)cin>>mi[i]>>ma[i];
	sort(mi+1,mi+n+1);
	sort(ma+1,ma+n+1);
	if(n&1){
		int a=mi[n+1>>1],b=ma[n+1>>1];
		cout<<b-a+1;
	}else{
		double a=(mi[n>>1]+mi[n+2>>1])/2.0,b=(ma[n>>1]+ma[n+2>>1])/2.0;
		int c=(b-a)*2+1;
		cout<<c;
	}
} 