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 s = new Scanner(System.in)) {
			final int N = s.nextInt();

			long ret = 0;
			long sum = 0;
			boolean zero = false;
			boolean plus = true;
			for (int i = 0; i < N - 1; i++) {
				long a = s.nextLong();
				if (a < 0) {
					plus = !plus;
				} else if (a == 0) {
					ret += sum;
					sum = 0;
					plus = true;
					zero = true;
				}
				sum += Math.abs(a);
			}
			long a = s.nextLong();
			long aa = Math.abs(a);
			if (zero) {
				ret = ret + sum + aa;
			} else if (a < 0 && sum < aa) {
				ret = ret - sum + aa;
			} else if (plus) {
				ret = ret + sum + a;
			} else {
				ret = ret + sum - a;
			}
			System.out.println(ret);
		}
	}
}