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) {

		Scanner sc=new Scanner(System.in);

		int N=sc.nextInt();

		int[] A=new int[N];

		for(int i=0;i<N;i++) A[i]=sc.nextInt();

		long ans=0;

		int cnt=0;

		for(int i=0;i<N;i++) {
			if(A[i]<=0) cnt++;
		}

		if(cnt%2==0) {
			for(int i=0;i<N;i++) ans+=Math.abs(A[i]);
		}else {
			int min=+1000000001;
			int index=0;
			for(int i=0;i<N;i++) {
				if(min>Math.abs(A[i])) {
					min=Math.abs(A[i]);
					index=i;
				}
			}
			for(int i=0;i<N;i++) {
				if(index==i) ans+=-A[i];
				else ans+=Math.abs(A[i]);
			}
		}

		System.out.println(ans);

		sc.close();

	}

}