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<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#define inf 0x3f3f3f3f
using namespace std;
typedef unsigned long long ull;
int n;
int a[212345], b[212345];
int main() {
	cin >> n;
	int i, min, max;
	for (i = 0; i < n; i++) {
		cin >> a[i] >> b[i];
	}
	sort(a, a + n);
	sort(b, b + n);
	if (n % 2 == 1) {
		cout << b[n / 2] - a[n / 2] + 1 << endl;
	}
	else {
		if(n>=2)
		cout << b[n / 2] - a[n / 2 - 1] + 1 << endl;
	}
	return 0;
}