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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;


public class HelloWorld
{

    static long A;
    static long B;
    static long C;
    static long D;
    static long N;
    static SortedDictionary<long, long> dic;
    static public void Main()
    {
        var N = long.Parse(Console.ReadLine());
        var A = new long[N];
        var B = new long[N];
        for (int i = 0; i < N; i++)
        {
            var inp =
            Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            A[i] = inp[0];
            B[i] = inp[1];
        }

        long ans = 0;
        if (N%2 == 1)
        {
            ans = (long)(Median(B) - Median(A) + 1);
        }
        else
        {
            ans = (long)(Median(B) - Median(A)) + 1;
        }

        Console.WriteLine(ans);
    }

    public static long Median(long[] A)
    {
        var N = A.Length;
        Array.Sort(A);
        if(N%2 == 1)
        {
            return A[N / 2];
        }

        return A[N / 2] + A[(N / 2) - 1]; 
    }


}
public static class LINQExtension
{
    public static double Median(this IEnumerable<double>? source)
    {
        if (!(source?.Any() ?? false))
        {
            throw new InvalidOperationException("Cannot compute median for a null or empty set.");
        }

        var sortedList = (from number in source
                          orderby number
                          select number).ToList();

        int itemIndex = sortedList.Count / 2;

        if (sortedList.Count % 2 == 0)
        {
            // Even number of items.
            return (sortedList[itemIndex] + sortedList[itemIndex - 1]) / 2;
        }
        else
        {
            // Odd number of items.
            return sortedList[itemIndex];
        }
    }
}