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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Runtime.CompilerServices;
using static System.Console;
using static System.Math;
using static Macro;
using static Extension;
using static LinqExtension;
using static HelpExtension;
class AC {
    /*------------------------------------------------------------------*/
    int N;
    long[] A, B;

    struct Ryori : IComparable<Ryori> {
        public long Takahashi;
        public long Aoki;
        public Ryori(long t, long a) {
            Takahashi = t;
            Aoki = a;
        }
        public int CompareTo(Ryori a) {
            var ryoriA = Max(a.Takahashi, a.Aoki);
            var ryoriB = Max(this.Takahashi, this.Aoki);
            if (ryoriA > ryoriB) return 1;
            if (ryoriA < ryoriB) return -1;
            return 0;
        }
    }

    void Solve() {
        N = io.Int;
        io.ini(out A, out B, N);

        var pq = new PriorityQueue<Ryori>(false);
        ZIP(A, B).Iter(x => {
            pq.Enqueue(new Ryori(x.Item1, x.Item2));
        });

        var Ts = 0L;
        var As = 0L;
        var isT = true;
        while (pq.Any) {
            var cur = pq.Dequeue();
            if (isT) {
                Ts += cur.Takahashi;
            } else {
                As += cur.Aoki;
            }
            isT = !isT;
        }

        (Ts - As).Prt();

    }

    /*------------------------------------------------------------------*/
    void Test() {
        //--- TEST ---//
    }
    public static void Main(string[] args) => new AC().Stream();
    const int INF = int.MaxValue / 2;
    IO io = new IO();
    private void Stream() {
        /*
        var exStdIn = new System.IO.StreamReader("stdin.txt");
        SetIn(exStdIn);
        Test();
        */
        Solve();
        io.Flush();
    }
}
class IO {
    #region INPUT
    #region FastRead
    private const int Size = 1 << 12;
    private readonly Stream _stream = OpenStandardInput();
    private readonly byte[] _buffer = new byte[Size];
    private int _ptr = 0, _buffLen = 0;
    private bool HasNextByte() {
        if (_ptr < _buffLen) return true;
        _ptr = 0;
        _buffLen = _stream.Read(_buffer, 0, Size);
        return _buffLen > 0;
    }
    private byte ReadByte() {
        if (HasNextByte()) return _buffer[_ptr++];
        else
            //inputの末尾の改行がないとerror
            throw new EndOfStreamException();
    }
    private bool IsAscii(int c) => '!' <= c && c <= '~';
    private char NextChar() {
        var b = ReadByte();
        while (!IsAscii(b)) b = ReadByte();
        return (char)b;
    }
    private string Next() {
        var sb = new StringBuilder();
        for (var b = NextChar(); IsAscii(b); b = (char)ReadByte()) sb.Append(b);
        return sb.ToString();
    }
    public string String => Next();
    public char Char => NextChar();
    public int Int => int.Parse(Next());
    public long Long => long.Parse(Next());
    public double Double => double.Parse(Next());
    #endregion
    #region LazyRead
    private void scan<T>(ref T x) {
        if (x is int) __refvalue(__makeref(x), int) = int.Parse(Next());
        else if (x is long) __refvalue(__makeref(x), long) = long.Parse(Next());
        else if (x is double) __refvalue(__makeref(x), double) = double.Parse(Next());
        else if (x is char) __refvalue(__makeref(x), char) = NextChar();
        else __refvalue(__makeref(x), string) = Next();
    }
    public void i<T>(out T t) {
        t = default(T);
        scan(ref t);
    }
    public void i<T, TU>(out T t, out TU u) {
        i(out t);
        i(out u);
    }
    public void i<T, TU, TV>(out T t, out TU u, out TV v) {
        i(out t, out u);
        i(out v);
    }
    public void i<T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w) {
        i(out t, out u);
        i(out v, out w);
    }
    public void i<T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x) {
        i(out t, out u, out v);
        i(out w, out x);
    }
    public void i<T, TU, TV, TW, TX, TY>(out T t, out TU u, out TV v, out TW w, out TX x, out TY y) {
        i(out t, out u, out v);
        i(out w, out x, out y);
    }
    public void ini<T>(out T[] a, int n) {
        a = new T[n];
        for (int i = 0; i < n; ++i) i<T>(out a[i]);
    }
    public void ini<T, TU>(out T[] a, out TU[] b, int n) {
        a = new T[n];
        b = new TU[n];
        for (int i = 0; i < n; ++i) i<T, TU>(out a[i], out b[i]);
    }
    public void ini<T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n) {
        a = new T[n];
        b = new TU[n];
        c = new TV[n];
        for (var i = 0; i < n; ++i) i<T, TU, TV>(out a[i], out b[i], out c[i]);
    }
    public void ini<T, TU, TV, TW>(out T[] a, out TU[] b, out TV[] c, out TW[] d, int n) {
        a = new T[n];
        b = new TU[n];
        c = new TV[n];
        d = new TW[n];
        for (var i = 0; i < n; ++i) i<T, TU, TV, TW>(out a[i], out b[i], out c[i], out d[i]);
    }
    public void ini<T>(out T[,] a, int h, int w) {
        a = new T[h, w];
        for (int i = 0; i < h; ++i) for (int j = 0; j < w; ++j) i<T>(out a[i, j]);
    }
    #endregion
    #endregion
    #region OUTPUT
    private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput()) {
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public void Flush() => Out.Flush();
    public void YN(bool f) => yn(f, "YES", "NO");
    public void Yn(bool f) => yn(f, "Yes", "No");
    public void yn(bool f, string y = "yes", string n = "no") => WriteLine(f ? y : n);
    #endregion
    public IO() { SetOut(_sw); }
}
static class Macro {
    public static void FOR(int a, int b, int n, Action<int> f) {
        for (var i = a; i < b; i += n) {
            try {
                f(i);
            } catch (IndexOutOfRangeException e) {
#if DEBUG
                WriteLine($"IndexOutOfRange at [{i}]");
#endif
            }
        }
    }
    public static void FOR(int a, int b, Action<int> f) => FOR(a, b, 1, f);
    public static void REP(int a, Action<int> f) => FOR(0, a, 1, f);
    public static void REP(int a, int n, Action<int> f) => FOR(0, a, n, f);
    public static void FOREQ(int a, int b, Action<int> f) => FOR(a, b + 1, 1, f);
    public static void FOREQ(int a, int b, int n, Action<int> f) => FOR(a, b + 1, n, f);
    public static void REPEQ(int a, Action<int> f) => FOR(0, a + 1, 1, f);
    public static void REPEQ(int a, int n, Action<int> f) => FOR(0, a + 1, n, f);
    public static T MIN<T>(params T[] xs) => xs.Min();
    public static T MAX<T>(params T[] xs) => xs.Max();
    public static IEnumerable<Tuple<T, U>> ZIP<T, U>(IEnumerable<T> x, IEnumerable<U> y)
        => x.Zip(y, (i1, i2) => new Tuple<T,U>(i1, i2));

    public static IEnumerable<Tuple<T, U, V>> ZIP<T, U, V>(
        IEnumerable<T> xs,
        IEnumerable<U> ys,
        IEnumerable<V> zs) {
        using (var eX = xs.GetEnumerator())
        using (var eY = ys.GetEnumerator())
        using (var eZ = zs.GetEnumerator()) {
            while (eX.MoveNext() && eY.MoveNext() && eZ.MoveNext()) {
                yield return new Tuple<T, U, V>(eX.Current, eY.Current, eZ.Current);
            }
        }
    }
}
static class Extension {
    public static void Rep(this int a, Action<int> f) => FOR(0, a, 1, f);
    public static void Rep(this int a, int n, Action<int> f) => FOR(0, a, n, f);
    public static void RepEQ(this int a, Action<int> f) => FOR(0, a + 1, 1, f);
    public static void RepEQ(this int a, int n, Action<int> f) => FOR(0, a + 1, n, f);
    public static void Prt<T>(this T x) => WriteLine(x);
    public static void Prt<T>(this IEnumerable<T> xs) => xs.Iter(x => WriteLine(x));
    public static void Prt_<T>(this IEnumerable<T> xs) {
        xs.Iter(x => Write($"{x} "));
        WriteLine();
    }
    public static bool IsOdd(this int x) => x % 2 != 0;
    public static bool IsOdd(this long x) => x % 2 != 0;
}
static class LinqExtension {
    public struct IndexedValue<T> {
        public int Index;
        public T Value;
        public IndexedValue(int index, T value) {
            this.Index = index;
            this.Value = value;
        }
        public override string ToString() {
            return string.Format("Index: {0}, Value: {1}", Index, Value);
        }
    }
    public struct Pair<T> {
        public T Fst;
        public T Snd;
        public Pair(T fst, T snd) {
            Fst = fst;
            Snd = snd;
        }
        public override string ToString() {
            return string.Format("({0}, {1})", Fst, Snd);
        }
    }
    public static IEnumerable<IndexedValue<T>> Indexed<T>(this IEnumerable<T> source) {
        return source.Select((value, index) => new IndexedValue<T>(index, value));
    }

    public static void Iter<T>(this IEnumerable<T> source, Action<T> action) {
        foreach (var s in source) action(s);
    }

    public static IEnumerable<Pair<T>> PairWise<T>(this IEnumerable<T> source) {
        return source.Zip(source.Skip(1), (fst, snd) => new Pair<T>(fst, snd));
    }

    private static IEnumerable<T> Init<T>(int size, Func<int, T> f) {
        for (var i = 0; i < size; ++i) yield return f(i);
    }

    public static IEnumerable<IEnumerable<T>> Windowed<T>(this IEnumerable<T> source, int size) {
        var tmpArr = new T[size];
        var r = size - 1;
        var i = 0;
        using (var e = source.GetEnumerator()) {
            while (e.MoveNext()) {
                tmpArr[i] = e.Current;
                i = (i + 1) % size;
                if (r == 0) yield return Init<T>(size, j => tmpArr[(i + j) % size]);
                else r--;
            }
        }
    }

    public static IEnumerable<T> Sort<T>(this IEnumerable<T> source) => source.OrderBy(x => x);

    public static IEnumerable<T> Rev<T>(this IEnumerable<T> source) => Sort(source).Reverse();

    public static IEnumerable<T> DistinctBy<T, U>(this IEnumerable<T> source, Func<T, U> groupBy, Func<IGrouping<U, T>, T> selectBy)
        => source.GroupBy(groupBy).Select(selectBy);
    public static IEnumerable<T> DistinctBy<T, U>(this IEnumerable<T> source, Func<T, U> groupBy) => source.DistinctBy(groupBy, x => x.First());

}
static class HelpExtension {
    public class PriorityQueue<T> where T : IComparable<T> {
        private List<T> heap;
        private bool isAsc;
        private int size;
        public T Peek => heap[0];
        public int Count => size;
        public bool Any => size > 0;
        public bool Empty => !Any;

        public PriorityQueue(bool isAsc = true) {
            this.isAsc = isAsc;
            size = 0;
            heap = new List<T>();
        }

        public void Enqueue(T item) {
            heap.Add(item);
            var i = size++;
            while (i > 0) {
                var p = (i - 1) / 2;
                if (Compare(heap[p], item) <= 0) break;
                heap[i] = heap[p];
                i = p;
            }
            heap[i] = item;
        }

        public T Dequeue() {
            var ret = heap[0];
            var x = heap[--size];
            var i = 0;
            while ((i << 1) + 1 < size) {
                var a = (i << 1) + 1;
                var b = (i << 1) + 2;
                if (b < size && Compare(heap[b], heap[a]) < 0) a = b;
                if (Compare(heap[a], x) >= 0) break;
                heap[i] = heap[a];
                i = a;
            }
            heap[i] = x;
            heap.RemoveAt(size);
            return ret;
        }

        private int Compare(T x, T y) => isAsc ? x.CompareTo(y) : y.CompareTo(x);
    }
}