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.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class E { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		var A = new long[N];
		var B = new long[N];
		long f = (N % 2 == 0) ? 2 : 1;
		for(long i = 0; i < N; i++)
		{
			A[i] = f * GetLong();
			B[i] = f * GetLong();
		}
		Array.Sort(A);
		Array.Sort(B);

		var ma = median(N, A);
		var mb = median(N, B);

		WriteLine(mb - ma + 1);
	}

	private long median(long N, long[] arr) => (N % 2 == 1) ? arr[N / 2] : (arr[(N - 1) / 2] + arr[N / 2]) / 2;
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}