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;
long long mi[200005],ma[200005];
int main()
{
    long long n;
    cin>>n;
    for(long long i=0; i<n; i++){
        cin>>mi[i]>>ma[i];
    }
    sort(mi,mi+n);
    sort(ma,ma+n);
    if(n%2==0){
        long long l1=mi[n/2-1],r1=ma[n/2-1],l2=mi[n/2],r2=ma[n/2];
        cout<<l2-l1+r2-r1+(r1-l2)*2+1;
    }else{
        cout<<ma[n/2]-mi[n/2]+1;
    }
    return 0;
}
