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 a = sc.nextInt();
        long[] b = new long[a];
        long[] c = new long[a];
        long sum = 0;
        boolean check = false;
		for(int i=0; i<a; i++){
          b[i] = sc.nextLong();
          c[i] = b[i];
        }
        for(int i=a-1; i>0; i--){
          if(check){
            if(b[i] + b[i-1] < -(b[i] + b[i-1])){
              b[i] = -b[i];
              b[i-1] = -b[i-1];
            }
            else if(c[i] + b[i-1] < -(c[i] + b[i-1])){
              b[i+1] = -c[i+1];
              b[i] = -c[i];
              b[i-1] = -b[i-1];
            }
          }
          if(!check && b[i] + b[i-1] < -(b[i] + b[i-1])){
            b[i] = -b[i];
            b[i-1] = -b[i-1];
            check = false;
          }
          else if(b[i] + b[i-1] == -(b[i] + b[i-1])){
            c[i] = -c[i];
            c[i-1] = -c[i-1];
            check = true;
          }
          else check = false;
        }
        for(int i=0; i<a; i++){
          sum += b[i]; 
        }
		System.out.println(sum);
	}
}