Problem:
Score : 400 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, arranged in a row in this order.

You can perform the following operation on this integer sequence any number of times:

Operation: Choose an integer i satisfying 1 \leq i \leq N-1. Multiply both A_i and A_{i+1} by -1.

Let B_1, B_2, ..., B_N be the integer sequence after your operations.

Find the maximum possible value of B_1 + B_2 + ... + B_N.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

-10^9 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value of B_1 + B_2 + ... + B_N.

Sample Input 1

3
-10 5 -4

Sample Output 1

19

If we perform the operation as follows:

Choose 1 as i, which changes the sequence to 10, -5, -4.

Choose 2 as i, which changes the sequence to 10, 5, 4.

we have B_1 = 10, B_2 = 5, B_3 = 4. The sum here, B_1 + B_2 + B_3 = 10 + 5 + 4 = 19, is the maximum possible result.

Sample Input 2

5
10 -4 -8 -11 3

Sample Output 2

30

Sample Input 3

11
-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000

Sample Output 3

10000000000

The output may not fit into a 32-bit integer type.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.*;
import java.util.Scanner;
import java.util.stream.Collectors;
import java.math.BigInteger;

public class Main {

    // input
    static int n;
    static List<Long> a;

    /**
     * input
     */
    static void input(){
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        a = new ArrayList<Long>();
        for (int i=0;i<n;i++){
            a.add((Long)(sc.nextLong()));
        }
        sc.close();
    }
 
    /**
     * solver
     */
    static void solve(){

        Long ans = new Long(0);

        int countZero = 0;
        int countNegative = 0;

        for (Long l: a) {
            if (l == 0) {
                countZero ++;
            } else if (l < 0) {
                countNegative ++;
            }
        }

        if (countZero > 0 || countNegative % 2 == 0) {
            for (Long l: a) {
                ans += Math.abs(l);
            }
        } else {
            Long tmp = Long.MAX_VALUE;
            for (Long l: a) {
                Long _l = Math.abs(l);
                ans += _l;
                tmp = (tmp < _l) ? tmp : _l;
            }
            ans -= 2 * tmp;
        }

        System.out.println(ans);

    }

    public static void main(String args[]) {

        input();
        solve();
    }
}