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.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

public class Main{
	
	public static void main(String[] args)
	{
		new Main().run();
	}
	
	public void run()
	{
		Scanner file = new Scanner(System.in);
		int N = file.nextInt();
		long[] ints = new long[N];
		for(int i = 0;i<N;i++)
			ints[i] = file.nextLong();
		long[][] dp = new long[ints.length][2];
		dp[ints.length-1][0] = -ints[ints.length-1];
		dp[ints.length-1][1] = ints[ints.length -1];
		for(int i = ints.length-2;i>=0;i--)
		{
			for(int j = 0;j<2;j++)
			{
				if(j == 0)
				{
					dp[i][j] = Math.max(-ints[i]+dp[i+1][1],ints[i]+dp[i+1][0]);
				}else {
					dp[i][j] = Math.max(ints[i]+dp[i+1][1],-ints[i]+dp[i+1][0]);
				}
			}
		}
		System.out.println(dp[0][1]);
	}
	
	int gcd(int a, int b)
	{
		return BigInteger.valueOf(a).gcd(BigInteger.valueOf(b)).intValue();
	}
	
}