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.Scanner;

public class Main {
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){
			
			
			int N = scan.nextInt();
			int[]A = new int [N];
			for(int i = 0;i<N;i++)A[i] = scan.nextInt();
			long goukei = 0;
			
			for(int i = 0;i<N-1;i++) {
				if(i==N-2&&(-A[i]-A[i+1]>A[i]+A[i+1])) {
					A[i]*=-1;
					A[i+1]*=-1;
				}else if((A[i]<=0&&A[i+1]<=0)||(A[i]<0&&A[i+1]>0)) {//0が含むーはこちらで処理00 0- -0　
					A[i]*=-1;
					A[i+1]*=-1;
				}
				
				
				
				
				
				
			}
			
			
			for(int i:A) {
				goukei+=(long)i;
			}
			
			System.out.println(goukei);
			
			
		}
	}
}