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>
#define pb push_back
using namespace std;
const int N=2e5+10;
int a[N];
int b[N];
map <int,int>mp;
string s;
int main()
{
    int n;
    cin>>n;
    for(int i=1;i<=n;i++) cin>>a[i]>>b[i];
    sort(a+1,a+1+n);
    sort(b+1,b+1+n);
    if(n%2){
        cout<<b[(n+1)/2]-a[(n+1)/2]+1<<endl;
    }
    else{
        cout<<b[n/2]+b[n/2+1]-a[n/2]-a[n/2+1]+1<<endl;
    }
}

