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.Collections.Generic;
using System.Linq;

namespace AtcoderSubmit
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ulong.Parse(Console.ReadLine());
            var aList = new int[N];
            var bList = new int[N];
            for(int i = 0; (ulong)i < N; i++) {
                var line = Console.ReadLine().Split(' ');
                aList[i] = int.Parse(line[0]);
                bList[i] = int.Parse(line[1]);
            }
            Array.Sort(aList);
            Array.Sort(bList);

            int ans = 0;
            if(N % 2 == 0) {
                int aMed2 = aList[N / 2 - 1] + aList[N / 2];
                int bMed2 = bList[N / 2 - 1] + bList[N / 2];
                ans = Math.Abs(aMed2 - bMed2) + 1;
            }
            else {
                int aMed = aList[N / 2];
                int bMed = bList[N / 2];
                ans = Math.Abs(aMed - bMed) + 1;
            }
            Console.WriteLine(ans);
        }
    }
}