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.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Math;

namespace CSharpSpiral {
	class Program {
		static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush=
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}
		public void Solve(ConsoleInput cin) {
			var N = cin.ReadInt;
			int[] A = new int[N], B = new int[N];
			for(int i = 0; i<N; i++) {
				var datum = cin.ReadIntArray(2);
				A[i]=datum[0]; B[i]=datum[1];
			}
			A.MergeSort(false);
			B.MergeSort(true);
			var halfN = N/2;
			var res = 0;
			if(N%2!=0) {
				res=B[halfN]-A[halfN]+1;
			} else {
				var higher = B[halfN-1]-A[halfN]+1;
				var lower = B[halfN]-A[halfN-1]+1;
				res=higher+lower-1;
			}
			Console.WriteLine(res);
		}

	}
	static class ExtendClass {
		public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);

		public static void MergeSort<T>(this T[] A, bool desending) where T : IComparable<T> {
			if(desending)
				MergeSort(A, Comparer<T>.Create((x, y) => y.CompareTo(x)));
			else
				MergeSort(A, Comparer<T>.Create((x, y) => x.CompareTo(y)));
		}
		public static void MergeSort<T>(T[] A, IComparer<T> comparer) where T : IComparable<T> {
			MergeSort1(0, A.Length, A, comparer);
		}
		private static void Merge<T>(int left, int mid, int right, T[] A, IComparer<T> comparer)
			where T : IComparable<T> {
			var nl = mid-left;
			var nr = right-mid;
			var L = new T[nl];
			var R = new T[nr];
			for(int i = 0; i<nl; i++)
				L[i]=A[i+left];
			for(int i = 0; i<nr; i++)
				R[i]=A[i+mid];
			int il = 0, ir = 0;
			for(int k = left; k<right; k++) {
				if(comparer.Compare(L[il], R[ir])<=0) {
					A[k]=L[il++];
					if(il==nl) {
						k++;
						for(; ir<nr;)
							A[k++]=R[ir++];
						break;
					}
				} else {
					A[k]=R[ir++];
					if(ir==nr) {
						k++;
						for(; il<nl;)
							A[k++]=L[il++];
						break;
					}
				}
			}
		}
		private static void MergeSort1<T>(int left, int right, T[] A, IComparer<T> comparer)
		where T : IComparable<T> {
			if(left+1<right) {
				var mid = (left+right)/2;
				MergeSort1(left, mid, A, comparer);
				MergeSort1(mid, right, A, comparer);
				Merge(left, mid, right, A, comparer);
			}
		}
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator=separator;
			this._stream=stream;
			inputStream=new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count!=0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i<tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i<N; ++i)
				ret[i]=Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i<N; ++i) ret[i]=ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i<N; ++i) ret[i]=ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i<N; ++i) ret[i]=ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek()==-1; }
		}
	}
}