Problem:
Score : 400 points

Problem Statement

There are N dishes of cuisine placed in front of Takahashi and Aoki.
For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.

When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.

Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat.
Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".

Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \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_N B_N

Output

Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".

Sample Input 1

3
10 10
20 20
30 30

Sample Output 1

20

In this sample, both of them earns 10 points of happiness by eating Dish 1, 20 points by eating Dish 2, and 30 points by eating Dish 3.

In this case, since Takahashi and Aoki have the same "taste", each time they will choose the dish with which they can earn the greatest happiness. Thus, first Takahashi will choose Dish 3, then Aoki will choose Dish 2, and finally Takahashi will choose Dish 1, so the answer is (30 + 10) - 20 = 20.

Sample Input 2

3
20 10
20 20
20 30

Sample Output 2

20

In this sample, Takahashi earns 20 points of happiness by eating any one of the dishes 1, 2 and 3, but Aoki earns 10 points of happiness by eating Dish 1, 20 points by eating Dish 2, and 30 points by eating Dish 3.

In this case, since only Aoki has likes and dislikes, each time they will choose the dish with which Aoki can earn the greatest happiness. Thus, first Takahashi will choose Dish 3, then Aoki will choose Dish 2, and finally Takahashi will choose Dish 1, so the answer is (20 + 20) - 20 = 20.

Sample Input 3

6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000

Sample Output 3

-2999999997

Note that the answer may not fit into a 32-bit integer.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;
using static _20200410.nikkei2019_qual_c.Cin;
using static _20200410.nikkei2019_qual_c.Util;
using Pair = _20200410.nikkei2019_qual_c.VTuple<long, long>;

/// <summary>
/// nikkei2019-qual
/// C - Different Strokes
/// https://atcoder.jp/contests/nikkei2019-qual/tasks/nikkei2019_qual_c
/// </summary>
namespace _20200410.nikkei2019_qual_c
{
    public class Program
    {
        public static void Main(string[] args)
        {
            int N = ri;
            Pair[] ps = new Pair[N];
            for (int i = 0; i < N; i++)
            {
                ps[i] = new Pair(ri, ri);
            }

            Array.Sort(ps, (a, b) =>
                Abs(a.Item1 + a.Item2) > Abs(b.Item1 + b.Item2) ? -1 :
                Abs(a.Item1 + a.Item2) < Abs(b.Item1 + b.Item2) ? 1 :
                0);

            long taka = 0;
            long aoki = 0;
            for (int i = 0; i < N; i++)
            {
                if (i % 2 == 0)
                {
                    taka += ps[i].Item1;
                }
                else
                {
                    aoki += ps[i].Item2;
                }                
            }

            long ans = taka - aoki;
            Console.WriteLine(ans);
        }        
    }

    /// <summary>
    /// ValueTupleのバックポート
    /// (AtCoderのMonoではValueTupleが使えないため）
    /// </summary>
    /// <typeparam name="T1"></typeparam>
    /// <typeparam name="T2"></typeparam>
    public struct VTuple<T1, T2> : System.IComparable<VTuple<T1, T2>>, System.IEquatable<VTuple<T1, T2>>
    {
        public T1 Item1;
        public T2 Item2;

        public T1 First { get { return Item1; } }
        public T2 Second { get { return Item2; } }

        public VTuple(T1 item1, T2 item2)
        {
            Item1 = item1;
            Item2 = item2;
        }

        #region override

        public override bool Equals(object obj)
        {
            return obj is VTuple<T1, T2> && Equals((VTuple<T1, T2>)obj);
        }

        public override int GetHashCode()
        {
            int h1 = Item1 != null ? Item1.GetHashCode() : 0;
            int h2 = Item2 != null ? Item2.GetHashCode() : 0;

            return HashHelpers.CombineHashCodes(h1, h2);
        }

        public override string ToString()
        {
            return "(" + Item1?.ToString() + ", " + Item2?.ToString() + ")";
        }

        #endregion

        #region interface implementation

        public bool Equals(VTuple<T1, T2> other)
        {
            return EqualityComparer<T1>.Default.Equals(Item1, other.Item1)
                && EqualityComparer<T2>.Default.Equals(Item2, other.Item2);
        }

        public int CompareTo(VTuple<T1, T2> other)
        {
            int c = Comparer<T1>.Default.Compare(Item1, other.Item1);
            if (c != 0) return c;

            return Comparer<T2>.Default.Compare(Item2, other.Item2);
        }

        #endregion
    }

    public static class HashHelpers
    {
        public static readonly int RandomSeed = new System.Random().Next(int.MinValue, int.MaxValue);

        public static int Combine(int h1, int h2)
        {
            uint rol5 = ((uint)h1 << 5) | ((uint)h1 >> 27);
            return ((int)rol5 + h1) ^ h2;
        }

        public static int CombineHashCodes(int h1, int h2)
        {
            return Combine(Combine(RandomSeed, h1), h2);
        }

        public static int CombineHashCodes(int h1, int h2, int h3)
        {
            return Combine(CombineHashCodes(h1, h2), h3);
        }

        public static int CombineHashCodes(int h1, int h2, int h3, int h4)
        {
            return Combine(CombineHashCodes(h1, h2, h3), h4);
        }
    }

    /// <summary>
    /// 競プロライブラリ
    /// https://github.com/ha2ne2/ABC/tree/master/Lib
    /// </summary>
    public struct Mint:System.IComparable<Mint>,System.IEquatable<Mint>{public static readonly long MOD=(long)1e9+7;public long Value;public Mint(long val){Value=val%MOD;if(Value<0)Value+=MOD;}private static Mint Ctor(long val){return new Mint(){Value=val};}public static Mint operator+(Mint a,Mint b){long res=a.Value+b.Value;if(res>MOD)res-=MOD;return Ctor(res);}public static Mint operator-(Mint a,Mint b){long res=a.Value-b.Value;if(res<0)res+=MOD;return Ctor(res);}public static Mint operator*(Mint a,Mint b){long res=a.Value*b.Value;if(res>MOD)res%=MOD;return Ctor(res);}public static Mint operator/(Mint a,Mint b){return a*Inv(b);}public override bool Equals(object obj){return obj is Mint&&Value==((Mint)obj).Value;}public override int GetHashCode(){return Value.GetHashCode();}public override string ToString(){return Value.ToString();}public static implicit operator Mint(long a){return new Mint(a);}public static explicit operator long(Mint a){return a.Value;}public static Mint Pow(Mint a,long n){if(n==0)return new Mint(1);Mint b=Pow(a,n>>1);b*=b;if((n&1)==1)b*=a;return b;}public static Mint Inv(Mint n){long a=n.Value;long b=MOD;long x=1;long u=0;while(b!=0){long k=a/b;long _x=u;u=x-k*u;x=_x;long _a=a;a=b;b=_a-(k*b);}return new Mint(x);}public bool Equals(Mint other){return Value==other.Value;}public int CompareTo(Mint other){return Comparer<long>.Default.Compare(Value,other.Value);}}public class HashMap<K,V>:System.Collections.Generic.Dictionary<K,V>{private V DefaultValue;private static Func<V>CreateInstance=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V defaultValue){DefaultValue=defaultValue;}new public V this[K i]{get{V v;if(TryGetValue(i,out v)){return v;}else{return base[i]=DefaultValue!=null?DefaultValue:CreateInstance();}}set{base[i]=value;}}}public static class Cin{public static int ri{get{return ReadInt();}}public static int[]ria{get{return ReadIntArray();}}public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static string[]rsa{get{return ReadStringArray();}}public static int ReadInt(){return int.Parse(Next());}public static long ReadLong(){return long.Parse(Next());}public static double ReadDouble(){return double.Parse(Next());}public static string ReadString(){return Next();}public static int[]ReadIntArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){Tokens=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static string[]ReadStringArray(){Tokens=null;return Console.ReadLine().Split(' ');}public static void ReadCol(out long[]a,long N){a=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,long N){a=new long[N];b=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();b[i]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long N){a=new long[N];b=new long[N];c=new long[N];for(int i=0;i<N;i++){a[i]=ReadLong();b[i]=ReadLong();c[i]=ReadLong();}}public static int[,]ReadIntTable(int h,int w){Tokens=null;int[,]ret=new int[h,w];for(int i=0;i<h;i++){for(int j=0;j<w;j++){ret[i,j]=ReadInt();}}return ret;}public static long[,]ReadLongTable(long h,long w){Tokens=null;long[,]ret=new long[h,w];for(int i=0;i<h;i++){for(int j=0;j<w;j++){ret[i,j]=ReadLong();}}return ret;}public static char[,]ReadCharTable(int h,int w){Tokens=null;char[,]res=new char[h,w];for(int i=0;i<h;i++){string s=ReadString();for(int j=0;j<w;j++){res[i,j]=s[j];}}return res;}private static string[]Tokens;private static int Pointer;private static string Next(){if(Tokens==null||Tokens.Length<=Pointer){Tokens=Console.ReadLine().Split(' ');Pointer=0;}return Tokens[Pointer++];}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public readonly static int[]DXY4={0,1,0,-1,0};public readonly static int[]DXY8={1,1,0,1,-1,0,-1,-1,1};public static void DontAutoFlush(){if(Console.IsOutputRedirected)return;var sw=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(sw);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]array){Array.Sort<T>(array);return array;}public static T[]SortDecend<T>(T[]array){Array.Sort<T>(array);Array.Reverse(array);return array;}public static void Swap<T>(ref T a,ref T b){T _a=a;a=b;b=_a;}public static long GCD(long a,long b){while(b!=0){long _a=a;a=b;b=_a%b;}return a;}public static long LCM(long a,long b){if(a==0||b==0)return 0;return a*b/GCD(a,b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static void ChMax(ref int a,int b){if(a<b)a=b;}public static void ChMin(ref int a,int b){if(a>b)a=b;}public static void FillArray<T>(T[]array,T value){int max=array.Length;for(int i=0;i<max;i++){array[i]=value;}}public static void FillArray<T>(T[,]array,T value){int max0=array.GetLength(0);int max1=array.GetLength(1);for(int i=0;i<max0;i++){for(int j=0;j<max1;j++){array[i,j]=value;}}}public static void FillArray<T>(T[,,]array,T value){int max0=array.GetLength(0);int max1=array.GetLength(1);int max2=array.GetLength(2);for(int i=0;i<max0;i++){for(int j=0;j<max1;j++){for(int k=0;k<max2;k++){array[i,j,k]=value;}}}}public static long[]Accumulate(long[]array){long[]acc=new long[array.Length+1];for(int i=0;i<array.Length;i++){acc[i+1]=acc[i]+array[i];}return acc;}public static double[]Accumulate(double[]array){double[]acc=new double[array.Length+1];for(int i=0;i<array.Length;i++){acc[i+1]=acc[i]+array[i];}return acc;}}
}