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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;

public class Main  implements Runnable { //Runnableを実装する

    public static void main(String[] args) {

        new Thread(null, new Main(), "", 16 * 1024 * 1024).start(); //16MBスタックを確保して実行

    }

    public void run() {
		Scanner sc = new Scanner(System.in);
		//Scanner sc = new Scanner("3 -10000000000 5 -4");
		int n = Integer.parseInt(sc.next());
		//int b = Integer.parseInt(sc.next());
		//int t = Integer.parseInt(sc.next());
		//int k = 0;
		//int k = Integer.parseInt(sc.next());
		//String str = sc.next();
		//char c[] = str.toCharArray();
		long a;
		long min= 10000000000l;
		int numofm = 0;
		long ans = 0;
		for (int i = 0; i < n; i++)
		{
			a= Long.parseLong(sc.next());
			if(a<0)
			{
				numofm++;
				if(-a<min)
				{
					min = -a;

				}
				ans = ans-a;
			}
			else
			{
				if(a<min)
				{
					min = a;
				}
				ans = ans+a;
			}
		}
		if(numofm%2==1)
		{
			ans = ans - (2l*min);
		}

		PrintWriter out = new PrintWriter(System.out);
		out.println(ans);
		out.flush();
	}
}