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.Linq;
using System.Collections.Generic;

namespace ConsoleApp1 {
    public class Class {
        static void Main(string[] args) {
            var N = long.Parse(Console.ReadLine());
            var A = new long[N];
            var B = new long[N];
            for(var i = 0; i < N; i++) {
                var AB = RL<long>();
                A[i] = AB[0];
                B[i] = AB[1];
            }
            Array.Sort(A);
            Array.Sort(B);

            if(N % 2 == 0) {
                var a = A[N / 2] + A[(N / 2) - 1];
                var b = B[N / 2] + B[(N / 2) - 1];
                var ans = b - a + 1;
                Console.Write(ans);
            } else {
                var ans = B[(N + 1) / 2　- 1] - A[(N + 1) / 2 - 1] + 1;
                Console.Write(ans);
            }
        }

        static T[] RL<T>() where T : IComparable {
            if (typeof(T) == typeof(int)) {
                return (T[])(object)Console.ReadLine().Trim().Split().Select(int.Parse).ToArray();
            }
            if (typeof(T) == typeof(long)) {
                return (T[])(object)Console.ReadLine().Trim().Split().Select(long.Parse).ToArray();
            }
            if (typeof(T) == typeof(double)) {
                return (T[])(object)Console.ReadLine().Trim().Split().Select(double.Parse).ToArray();
            }
            if (typeof(T) == typeof(decimal)) {
                return (T[])(object)Console.ReadLine().Trim().Split().Select(decimal.Parse).ToArray();
            }
            return (T[])(object)Console.ReadLine().Trim().Split().ToArray();
        }
    }
}