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
//ref:-  https://codeforces.com/blog/entry/78195
//also see atcoder official editorial
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int main ()
{
 ll n,x,y;
 cin>>n;
 ll a[n],b[n];
 for(ll i=0;i<n;i++)
 cin>>a[i]>>b[i];
 sort(a,a+n);
 sort(b,b+n);
 if(n%2)
 {
     x=a[n/2];
     y=b[n/2];
 }
 else
 {
     x=a[n/2]+a[n/2-1];
     y=b[n/2]+b[n/2-1];
 }
 cout<<(y-x)+1;
 return 0;
}