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-----
3
-10 5 -4

-----Sample Output-----
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.

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