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;
int main(){int N;cin>>N;vector<long>a(N),b(N);
           for(int i=0;i<N;i++)cin>>a.at(i)>>b.at(i);
   sort(a.begin(),a.end());sort(b.begin(),b.end());
long s,t;
           if(N%2==0){s=a.at(N/2-1)+a.at(N/2);t=b.at(N/2-1)+b.at(N/2);}
else{s=a.at((N-1)/2);t=b.at((N-1)/2);}
cout<<t-s+1<<endl;}