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;

public class Solution
{
    static long Median2(long[] x)
    {
        x = x.OrderBy(xx => xx).ToArray();
        var n = x.Length;
        if (n % 2 == 0)
        {
            return (x[n / 2 - 1] + x[n / 2]);
        }
        else
        {
            return x[n / 2] * 2;
        }
    }

    public static void Main()
    {
        var N = int.Parse(Console.ReadLine());
        var min = new long[N];
        var max = new long[N];
        for (int i = 0; i < N; i++)
        {
            var vals = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            min[i] = vals[0];
            max[i] = vals[1];
        }
        var left = Median2(min);
        var right = Median2(max);

        var answer = right - left;
        if (N % 2 != 0)
        {
            answer /= 2;
        }
        answer++;

        Console.WriteLine(answer);
    }
}