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;
using System.IO;

using static System.Console;
using static System.Math;

class MainClass
{
    static void Main()
    {
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        Solve();
        Out.Flush();
    }
    //ここにプログラムを入力
    static void Solve()
    {
        int N = int.Parse(ReadLine());
        var A = new int[N];
        var B = new int[N];
        for (int i = 0; i < N; i++)
        {
            var r = ReadLine().Split();
            A[i] = int.Parse(r[0]);
            B[i] = int.Parse(r[1]);
        }
        Array.Sort(A);
        Array.Sort(B);
        if (N % 2 == 0)
        {
            WriteLine((B[N/2]+B[N/2-1])-(A[N/2]+A[N/2-1])+1);
        }
        else
        {
            WriteLine(B[N/2]-A[N/2]+1);
        }

    }
}