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.*;
import java.math.*;

class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int num = sc.nextInt();
		int[] nums = new int[num];
		int minusNum = 0, zeroNum = 0, min = 1000000000;
		BigInteger ans = BigInteger.ZERO;
		for(int i = 0; i < num; i++) {
			nums[i] = sc.nextInt();
			if(nums[i] == 0) {
				zeroNum++;
			} else if(nums[i] < 0) {
				minusNum++;
				nums[i] = -nums[i];
			}
			min = min > nums[i] ? nums[i] : min;
			ans = ans.add(BigInteger.valueOf(nums[i]));
		}
		if(zeroNum == 0 || minusNum % 2 == 1) {
			ans = ans.subtract(BigInteger.valueOf(min*2));
		}
		System.out.println(ans);
	}
}