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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import static java.util.Comparator.*;

import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.AbstractMap;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	
//	public static Set<String> mem = new HashSet<String>();
//	public static boolean[] mem_1 = new boolean[100];
//	public static boolean[] mem_2 = new boolean[100];
//	public static Set<Integer> mem = new TreeSet<Integer>();
//	public static Map<String, Integer> mem_1= new HashMap<String, Integer>();
//	public static Map<String, Integer> mem_2 = new HashMap<String, Integer>();
	
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        
        Solver solver = new Solver();
        solver.solve(1, in, out);
        
        out.close();
    }
    
    // ======================================================================
    static class Solver {
    	
    	public void solve(int testNumber, MyInput in, PrintWriter out) {
        	long ans = 0;
    		int N = in.nextInt();
    		List<PPP> A = new ArrayList<PPP>();
    		List<PPP> B = new ArrayList<PPP>();
    		boolean[] X = new boolean[N];

    		int a, b;
    		PPP wk = null;
    		for(int i=0; i < N; i++) {
    			a = in.nextInt();
    			b = in.nextInt();
    			wk = new PPP(new Integer(Math.abs(a+b)), new Integer(a), new Integer(b), i);
    			A.add(wk);
    			wk = new PPP(new Integer(Math.abs(b+a)), new Integer(b), new Integer(a), i);
    			B.add(wk);
    		}
    		A.sort(comparing(PPP::getDiff, reverseOrder()).thenComparing(PPP::getVal, reverseOrder()).thenComparing(PPP::getVal_2, reverseOrder()));
    		B.sort(comparing(PPP::getDiff, reverseOrder()).thenComparing(PPP::getVal, reverseOrder()).thenComparing(PPP::getVal_2, reverseOrder()));
    // 		for(int i=0; i < N; i++) {
    // 		    out.println("A : diff = " + A.get(i).getDiff() + "  val = " + A.get(i).getVal() + "  index = " + A.get(i).getKey());
    // 		}
    // 		for(int i=0; i < N; i++) {
    // 		    out.println("B : diff = " + B.get(i).getDiff() + "  val = " + B.get(i).getVal() + "  index = " + B.get(i).getKey());
    // 		}

    		int ia = 0;
    		int ib = 0;
    		int www;
    		for(int i=0; i < N; i++) {
    			if(i % 2 == 0) {
    				while(true) {
     					www = A.get(ia).getKey();
    					if(X[www] == false) {
    						ans += A.get(ia).getVal();
    						X[www] = true;
    						break;
    					}
    					if(ia < N -1)	ia++;
    					else			break;
    				}
    			} else {
    				while(true) {
     					www = B.get(ib).getKey();
    					if(X[www] == false) {
    						ans -= B.get(ib).getVal();
    						X[www] = true;
    						break;
    					}
    					if(ib < N -1)	ib++;
    					else			break;
    				}
    			}
    		}
    		
        	out.println(ans);
        }
    }
    static class PPP {
		Integer diff;
    	Integer val;
    	int key;
    	Integer val_2;
    	
		public PPP(Integer diff, Integer val, Integer val_2, int key) {
			super();
			this.diff = diff;
			this.val = val;
			this.key = key;
			this.val_2 = val_2;
		}
		public Integer getVal() {
			return val;
		}
		public void setVal(Integer val) {
			this.val = val;
		}
		public Integer getDiff() {
			return diff;
		}
		public void setDiff(Integer diff) {
			this.diff = diff;
		}
		public int getKey() {
			return key;
		}
		public void setKey(int key) {
			this.key = key;
		}
		public Integer getVal_2() {
			return val_2;
		}
		public void setVal_2(Integer val_2) {
			this.val_2 = val_2;
		}
    }
    // ======================================================================
    static class Pair<K, V> extends AbstractMap.SimpleEntry<K, V> {
        /** serialVersionUID. */
        private static final long serialVersionUID = 6411527075103472113L;

        public Pair(final K key, final V value) {
            super(key, value);
        }
     }    
    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];
 
        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }
 
        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }
 
        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }
 
        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }
 
        public String nextString() {
        	String ret = new String(nextDChar()).trim();
            return ret;
        }
 
        public char[] nextDChar() {
            int len = 0;
            len = reads(len, isSpace);
            char[] ret = new char[len + 1];
            for (int i=0; i < len; i++)		ret[i] = str[i];
            ret[len] = 0x00;
            return ret;
        }
 
        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }
 
        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }
 
        static class EndOfFileRuntimeException extends RuntimeException {
        }
    }
}