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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	private static List<Ab> getStrings(Scanner sc, int num) {
		List<Ab> stringList = new ArrayList<>();
		while(num>0) {
			long a = sc.nextLong();
			long b = sc.nextLong();
			stringList.add(new Ab(a,b));
			num--;
		}
		return stringList;
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		List<Ab> ablist = getStrings(sc, n);
		long suma = 0;
		long sumb = 0;
		List<Long> alist = new ArrayList<>();
		List<Long> blist = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			alist.add(ablist.get(i).a);
			blist.add(ablist.get(i).b);
		}
		alist.sort(Long::compareTo);
		blist.sort(Long::compareTo);
		double mediana = 0;
		double medianb = 0;
		if (n % 2 == 1) {
			mediana = alist.get((n+1)/2-1);
			medianb = blist.get((n+1)/2-1);
			System.out.println((long)(medianb - mediana + 1));
		} else {
			mediana = (alist.get(n/2-1) + alist.get(n/2))/2;
			medianb = (blist.get(n/2-1) + blist.get(n/2))/2;
			System.out.println((long)(medianb - mediana) * 2 + 1);
		}
		return;
	}

	public static class Ab {
		long a;
		long b;

		public Ab(long a, long b) {
			this.a = a;
			this.b = b;
		}
	}

}