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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		// 整数の入力
		int n = sc.nextInt();

		int[] B = new int[n];
		int minus = 0;

		for(int i=0;i<n;i++){
			int a = sc.nextInt();
			if(a<=0){
				a = -a;
				minus++;
			}
			B[i] = a;
		}

		if(minus%2==1){
			int min=0;
			switch(n){
				default:
					if(B[min]>B[1])min=1;
					if(B[min]>B[n-2])min=n-2;
					if(B[min]>B[n-1])min=n-1;
					B[min]=-B[min];
					break;
				case 3:
					if(B[min]>B[1])min=1;
					if(B[min]>B[2])min=2;
					B[min]=-B[min];
					break;
				case 2:
					if(B[0]>B[1]){
						B[1] = -B[1];
					} else {
						B[0] = -B[0];
					}
					break;
			}
		}

		long sum = 0;

		for(int i=0;i<n;i++){
			sum += B[i];
		}

		// 出力
		System.out.println(sum);
	}
}