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 $B_1 + B_2 + ... + B_N$.