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>
#include <cassert>
typedef long long int ll;
using namespace std;

// @@ !! LIM()

int main(int argc, char *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << setprecision(20);

  ll N; cin >> N;
  vector<ll> A(N), B(N);
  for (ll i = 0; i < N; i++) {
    cin >> A.at(i) >> B.at(i);
  }
  sort(A.begin(), A.end());
  sort(B.begin(), B.end());
  if (N % 2 == 1) {
    ll m = N / 2;
    ll s = A.at(m);
    ll l = B.at(m);
    cout << l - s + 1 << endl;
  }else {
    ll m = N / 2;
    ll s = A.at(m - 1) + A.at(m);
    ll l = B.at(m - 1) + B.at(m);
    cout << l - s + 1 << endl;
  }

  return 0;
}