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,a,b) for(int i=int(a);i<int(b);++i)
#define SIZE 200005
#define INF 1000000005LL
//#define INF 1e18
#define MOD 1000000007

using namespace std;
typedef long long int ll;
typedef pair <int,int> P;

int n;
vector<ll> a,b;

int main(){
  cin >> n;
  rep(i,0,n){
    ll A,B;
    cin >> A >> B;
    a.push_back(A);
    b.push_back(B);
  }
  sort(a.begin(),a.end());
  sort(b.begin(),b.end());
  ll ans;
  if(n%2==1){
    ans = b[(n+1)/2-1] - a[(n+1)/2-1] + 1;
  }else{
    ans = (b[n/2-1]+b[n/2]) - (a[n/2-1]+a[n/2])+1;
  }

  cout << ans << endl;

  return 0;
}