Problem:
Score : 500 points

Problem Statement

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.

Notes

The median of X_1, X_2, \cdots, X_N is defined as follows. Let x_1, x_2, \cdots, x_N be the result of sorting X_1, X_2, \cdots, X_N in ascending order.

If N is odd, the median is x_{(N+1)/2};

if N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.

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.

Sample Input 1

2
1 2
2 3

Sample Output 1

3

If X_1 = 1 and X_2 = 2, the median is \frac{3}{2};

if X_1 = 1 and X_2 = 3, the median is 2;

if X_1 = 2 and X_2 = 2, the median is 2;

if X_1 = 2 and X_2 = 3, the median is \frac{5}{2}.

Thus, the median can take three values: \frac{3}{2}, 2, and \frac{5}{2}.

Sample Input 2

3
100 100
10 10000
1 1000000000

Sample Output 2

9991

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define P pair<int,int>
using ll=int64_t;
using namespace std;
#define ketasuu(n) fixed<<setprecision(n)
#define btoe(p) p.begin(),p.end()
#define etob(p) p.rbegin(),p.rend()




int main(){
    int n; cin>>n;
    vector<int> a(n),b(n);
    rep(i,n) cin>>a[i]>>b[i];
    sort(btoe(a)); sort(btoe(b));
    if(n%2==0){
        int l=a[n/2]+a[n/2-1],r=b[n/2]+b[n/2-1];
        cout<<r-l+1<<endl;
    } 
    else{
        int l=a[(n-1)/2], r=b[(n-1)/2];
        cout<<r-l+1<<endl;
    }
    return 0;
}