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;

#define FAST() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)

int main()
{
    FAST();
    int i,n,x,y,a[200005],b[200005];
    cin >> n;
    for(i=0;i<n;i++)cin >> a[i] >> b[i];
    sort(a,a+n);
    sort(b,b+n);
    x=a[n/2],y=b[n/2];
    if(n%2 == 0)x+=a[n/2-1],y+=b[n/2-1];
    cout << y-x+1;
    return 0;
}
