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;
using ld = long double;

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