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: Wrong Answer)

import java.util.*;
public class Main {
    public static void main(String [] args){
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        ArrayList<Long> A = new ArrayList<>();
        for(int i=0;i<N;i++) A.add(sc.nextLong());

        for(int i=0;i<A.size()-1;i++){
            if(i<A.size()-2&&A.get(i)<0) {
                A.set(i, A.get(i) * (-1));
                A.set(i + 1, A.get(i + 1) * (-1));
            }
            else if(i==A.size()-2){
                if(A.get(i)<0&&A.get(i+1)<0){
                    A.set(i, A.get(i) * (-1));
                    A.set(i + 1, A.get(i + 1) * (-1));
                }
                else if(A.get(i)<0&&A.get(i+1)>=0){
                    long num = A.get(i)*(-1);
                    if(num>A.get(i+1)){
                        A.set(i, A.get(i) * (-1));
                        A.set(i + 1, A.get(i + 1) * (-1));
                    }
                }
                else if(A.get(i)>=0&&A.get(i+1)<0){
                    long num = A.get(i+1)*(-1);
                    if(num>A.get(i)){
                        A.set(i, A.get(i) * (-1));
                        A.set(i + 1, A.get(i + 1) * (-1));
                    }
                }
            }
        }
        long opt =0;
        for(long i:A)opt+=i;
        System.out.println(opt);
    }
}