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: Wrong Answer)

#include <bits/stdc++.h>
#define MAX (ll)(2e5 + 7)
#define INF (ll)(4e18)
#define MOD (ll)(998244353)

using namespace std;
using ll = long long;
using cd = complex<double>;

int main () {
	ll n;
	cin >> n;
	pair<ll, ll> p[n];
	ll st[n], en[n];
	for (ll i = 0; i < n; i++) {
		cin >> p[i].first >> p[i].second ;
		st[i] = p[i].first, en[i] = p[i].second;
	}
	sort (st, st + n);
	sort (en, en + n);
	sort (p, p + n);
	if (n & 1) {
		cout << en[n - 1 - n / 2] - st[n / 2] + 1 << "\n";
	}
	else {
		cout << en[n - 1 - (n - 1) / 2] - st[(n - 1) / 2] + 1 << "\n";
	}
}