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;

namespace _169E_Count_Median
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            long[] A = new long[n];
            long[] B = new long[n];
            long min, max = 0;
            for (int i=0;i<n;i++)
            {
                int[] ab = Array.ConvertAll(System.Console.ReadLine().Split(' '), int.Parse);
                A[i] = ab[0];
                B[i] = ab[1];
            }
            Array.Sort(A);
            Array.Sort(B);
            if ( n%2==0)//
            {
                min = (A[n/ 2 - 1] + A[n/2]);
                max = (B[n/2-1] + B[n/2]);
                max = max - min+1;
            }
            else
            {
                min = A[n / 2 ];
                max = B[n  / 2];
                max = max - min + 1;
            }
            System.Console.WriteLine(max);

        }
    }
}