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;
using ll=long long;
int main(){
  ll n,meda,medb;
  cin>>n;
  vector<ll>a(n),b(n);
  for(ll i=0;i<n;i++){
    scanf("%lld%lld",&a[i],&b[i]);
  }
  sort(a.begin(),a.end());
  sort(b.begin(),b.end());
  if(n%2==0){
    meda=a[n/2]+a[n/2-1];
    medb=b[n/2]+b[n/2-1];
    cout<<medb-meda+1<<endl;
  }else{
    meda=a[n/2];
    medb=b[n/2];
    cout<<medb-meda+1<<endl;
  }
}