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;
typedef long long ll;
const int max_n=200005;
int n,a[max_n],b[max_n];
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d%d",a+i,b+i);
    sort(a+1,a+n+1),sort(b+1,b+n+1);
    if(n&1)printf("%d\n",b[(n+1)/2]-a[(n+1)/2]+1);
    else printf("%d\n",b[n/2+1]+b[n/2]-a[n/2]-a[n/2+1]+1);
    return 0;
}