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() {
    
    long long int n, i, a[200001], b[200001];
    cin>>n;
    for(i=1;i<=n;i++)
    scanf("%lld %lld", &a[i], &b[i]);
    sort(a+1, a+(n+1));
        
        sort(b+1, b+(n+1));
    if(n%2)
    {
        
        printf("%lld", b[(n+1)/2]-a[(n+1)/2]+1);
    }
    else
    {
        printf("%lld", (b[n/2+1]+b[n/2])-(a[n/2]+a[n/2+1])+1);
    }
}