101253: [AtCoder]ABC125 D - Flipping Signs

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.