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: Accepted)

import java.util.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.nextLine());
		List<Long> list = Arrays.stream(sc.nextLine().split(" ",0)).map(Long::valueOf).collect(Collectors.toList());
		int count = 0;
		boolean hasZero = false;
		for (long i : list) {
			if (i == 0) {
				hasZero = true;
				break;
			} else if (i < 0) {
				count++;
			}
		}

		long out;
		if (hasZero || count%2 == 0) {
			//総和
			out = list.stream().mapToLong(Math::abs).sum();
		} else {
			//
			long min = list.stream().mapToLong(Math::abs).min().getAsLong();
			out = list.stream().mapToLong(Math::abs).filter(i -> i != min).sum() - min;
		}

		System.out.println(out);
		sc.close();
	}

}