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.*;
import java.lang.Math;

public class Main {
  
  
  public Main() {
  }
    
  public static void main(String[] args) {
    
    Scanner scan = new Scanner(System.in);
    
    int size = scan.nextInt();
    int[] num = new int[size];
	
    for(int i = 0; i < size; i++) {
      num[i] = scan.nextInt();
    }
    
    int sum = 0;
    boolean hasZero = false;
    boolean even = false;
    int smallest = Math.abs(num[0]);
    
    for(int i = 0; i < size; i++) {
      if(num[i] == 0) {
        hasZero = true;
      }
      
      if(num[i] < 0) {
        even = !even;
      }
      
      smallest = Math.min(Math.abs(num[i]), smallest);
      sum += Math.abs(num[i]);
    }
    
    if (!even && !hasZero)
      sum -= 2*smallest;
    
    System.out.println(sum);
    
  }
}