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.Numerics;
using System.Runtime.CompilerServices;
using System.Diagnostics;
using ll=System.Int64;
using static Contest_E.Lib_IO;
using static Contest_E.Lib_Minifunc;



public static class Contest_E
{

	public static void Main() {
		checked{
			long n;
			Lib_IO.rm(out n);
			P<ll,ll>[] ab;
			rl(n,out ab);

			Array.Sort(ab,(x,y)=>x.A.CompareTo(y.A));
			ll ma = n%2==0?ab[n/2-1].A+ab[n/2].A:ab[n/2].A*2;
			Array.Sort(ab,(x,y)=>x.B.CompareTo(y.B));
			ll mb = (n%2==0)?ab[n/2-1].B+ab[n/2].B:ab[n/2].B*2;

			long ans = (n%2==0)?mb-ma+1:mb/2-ma/2+1;


			Lib_IO.wm(ans);
		}
	}



















#region BaseModule


public static class Lib_Minifunc{
	[MethodImpl(256)] public static void swap1<T>(ref T a, ref T b) { T t = a; a = b; b = t; }
	[MethodImpl(256)] public static void swap2<T>(ref T a, ref T b) where T : IComparable { if (a.CompareTo(b)==1) swap1(ref a, ref b); }  // b の方が小さければ交換
	[MethodImpl(256)] public static bool chmin<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)== 1) { a = b; return true; } return false; }  // b の方が小さければ a を更新
	[MethodImpl(256)] public static bool chmax<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)==-1) { a = b; return true; } return false; }  // b の方が大きければ a を更新
	[MethodImpl(256)] public static bool inside(long i, long n) => (0<=i&&i<n);
	[MethodImpl(256)] public static bool inside(long x, long y, long w, long h) => (inside(x,w)&&inside(y,h));
	[MethodImpl(256)] public static T min<T>(params T[] a) where T : IComparable => a.Min();
	[MethodImpl(256)] public static T max<T>(params T[] a) where T : IComparable => a.Max();
	[MethodImpl(256)] public static long mod(long a, long m=MOD1) { var v = a%m; return (v<0?v+m:v); }
	[MethodImpl(256)] public static long ceiling(long a, long b) => (a%b==0?a/b:a/b+1);	// 整数商の切り上げ
	[MethodImpl(256)] public static P<T,U> initp<T,U>(T a,U b) => new P<T,U>(a,b);
	[MethodImpl(256)] public static P<T,U,V> initp<T,U,V>(T a,U b,V c) => new P<T,U,V>(a,b,c);
	[MethodImpl(256)] public static P<T,U,V,W> initp<T,U,V,W>(T a,U b,V c,W d) => new P<T,U,V,W>(a,b,c,d);
	[MethodImpl(256)] public static bool initd<T,U>(Dictionary<T,U> d, T k) { if(d.ContainsKey(k)) { return false; } else { d[k] = default(U); return true; } }
	public static T[] inita<T>(long len1) where T : new() { var m = new T[len1]; for (int i=0;i<m.Length;i++) m[i] = new T(); return m; }
	public static T[][] initm<T>(long len1,long len2,T val) where T : struct { var m = new T[len1][]; for (int i=0;i<m.Length;i++) m[i] = Enumerable.Repeat(val,(int)len2).ToArray(); return m; }
	public static T[][][] initm<T>(long len1,long len2,long len3,T val) where T : struct { var m = new T[len1][][]; for (int i=0;i<m.Length;i++) m[i] = initm(len2,len3,val); return m; }
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;
	public const long INF1 = 1000000000000000;  // 10^15
}

public struct P<T,U>
{
	public T A; public U B;
	public P(T a,U b) { A = a; B = b; }
	public static implicit operator KeyValuePair<T,U>(P<T,U> a) => new KeyValuePair<T,U>(a.A,a.B);
	public static implicit operator P<T,U>(KeyValuePair<T,U> a) => new P<T,U>(a.Key,a.Value);
}
public struct P<T,U,V>
{
	public T A; public U B; public V C;
	public P(T a,U b,V c) { A = a; B = b; C = c; }
}
public struct P<T,U,V,W>
{
	public T A; public U B; public V C; public W D;
	public P(T a,U b,V c,W d) { A = a; B = b; C = c; D = d; }
}

public static class Lib_IO
{
	class Prt : System.IO.StreamWriter
	{
		public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
		public Prt(System.IO.Stream s) : base(s,new UTF8Encoding(false,true)) {}
		public Prt(System.IO.Stream s,Encoding e) : base(s,e) {}
	}
	static Prt sw = new Prt(Console.OpenStandardOutput());
	static char[] sp = new char[] {' '};
	[MethodImpl(256)] static bool eq<T,U>() => typeof(T).Equals(typeof(U));
	[MethodImpl(256)] static T ct<T,U>(U a) => (T)Convert.ChangeType(a,typeof(T));
	[MethodImpl(256)] static T cv<T>(string s) =>
		eq<T,int>()	? ct<T,int>(int.Parse(s))
	  : eq<T,long>()   ? ct<T,long>(long.Parse(s))
	  : eq<T,double>() ? ct<T,double>(double.Parse(s,System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T,char>()   ? ct<T,char>(s[0])
					   : ct<T,string>(s);
	public static string[] rm<T>(out T a) {
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(z[0]);
		return z;
	}
	public static string[] rm<T,U>(out T a,out U b) {
		var z = rm<T>(out a); 
		b = cv<U>(z[1]);
		return z;
	}
	public static string[] rm<T,U,V>(out T a,out U b,out V c) {
		var z = rm<T,U>(out a,out b); 
		c = cv<V>(z[2]);
		return z;
	}
	public static string[] rm<T,U,V,W>(out T a,out U b,out V c,out W d) {
		var z = rm<T,U,V>(out a,out b,out c); 
		d = cv<W>(z[3]);
		return z;
	}
	public static string[] rm<T,U,V,W,X>(out T a,out U b,out V c,out W d,out X e) {
		var z = rm<T,U,V,W>(out a,out b,out c,out d); 
		e = cv<X>(z[4]);
		return z;
	}
	public static string[] rm<T,U,V,W,X,Y>(out T a,out U b,out V c,out W d,out X e,out Y f) {
		var z = rm<T,U,V,W,X>(out a,out b,out c,out d,out e); 
		f = cv<Y>(z[5]);
		return z;
	}
	public static string[] ra<T>(out T[] a) {		
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries);
		a = z.Select(cv<T>).ToArray();
		return z;
	}
	public static string[][] rl<T>(long n,out T[] a) {
		a = new T[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = rm(out a[i]);
		return y;
	}
	public static string[][] rl<T,U>(long n,out P<T,U>[] a) {
		a = new P<T,U>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p;
			y[i] = rm(out o,out p);
			a[i] = new P<T,U>(o,p);
		}
		return y;
	}
	public static string[][] rl<T,U,V>(long n,out P<T,U,V>[] a) {
		a = new P<T,U,V>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q;
			y[i] = rm(out o,out p,out q);
			a[i] = new P<T,U,V>(o,p,q);
		}
		return y;
	}
	public static string[][] rl<T,U,V,W>(long n,out P<T,U,V,W>[] a) {
		a = new P<T,U,V,W>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q; W r;
			y[i] = rm(out o,out p,out q,out r);
			a[i] = new P<T,U,V,W>(o,p,q,r);
		}
		return y;
	}
	public static string[][] rx<T>(long n,out T[][] a) {
		a = new T[n][];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = ra(out a[i]);
		return y;
	}

	static void wwp(Action act){
		sw.AutoFlush = false;
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	[MethodImpl(256)] static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void wm(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length-1;i++) Console.Write(wfm(a[i].GetType())+" ",a[i]);
			Console.WriteLine(wfm(a[a.Length-1].GetType()),a[a.Length-1]);
		});
	}
	public static void wa<T>(IList<T> a) { wxa(new IList<T>[]{a}, " "); }
	public static void wl<T>(IList<T> a) {
		wwp(()=>{
			var f = wfm(typeof(T));
			foreach(T x in a) Console.WriteLine(f,x);
		});
	}
	static void wxa<T>(IList<IList<T>> a, string s) {
		wwp(()=>{
			var f = wfm(typeof(T));
			var g = f + s;
			foreach(var b in a) {
				for(int i=0;i<b.Count-1;i++) Console.Write(g,b[i]);
				Console.WriteLine(f,b[b.Count-1]);
			}
		});
	}
	public static void wx<T>(IList<IList<T>> a) { wxa(a, " "); }
	public static void wg<T>(IList<IList<T>> a) { wxa(a, ""); }
}

#endregion



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