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: Wrong Answer)

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

namespace AtCoder.At_Coder_Beginner_Contest_169
{
    class E
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            var listA = new List<int>();
            var listB = new List<int>();
            for (int i = 0; i < N; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                int A = int.Parse(input[0]);
                int B = int.Parse(input[1]);
                listA.Add(A);
                listB.Add(B);
            }

            listA.Sort();
            listB.Sort();

            if (N % 2 != 0)
            {
                int index = (N + 1) / 2;
                Console.WriteLine(listB[index] - listA[index] + 1);
            }
            else
            {
                var set = new HashSet<double>();
                int idx1 = N / 2 - 1;
                int idx2 = N / 2 + 1 - 1;
                Console.WriteLine(listB[idx2] - listA[idx1] + 1 + listB[idx2] - listA[idx1]);
            }

            //Console.ReadKey();
        }
    }
}