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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

while ($stdin = fgets(STDIN)) {
    $line[] = trim($stdin);
}
foreach ($line as $key => $value) {
    $data[] = explode(' ', $value);
}

//foreach ($data as &$line) {
//    $line = array_map(function($val) { return (int)$val; }, $line);
//}

$N = $data[0][0];
$A = $data[1];

$min = null;
$sum = 0;
$minusCnt = 0;
for ($i = 0; $i < $N; $i++) {
    $abs = abs($A[$i]);
    if (is_null($min) || $min > $abs) {
        $min = $abs;
    }
    $sum += $abs;
    if ($A[$i] < 0) {
        $minusCnt++;
    }
}

if ($minusCnt % 2 === 1) {
    $sum -= $min * 2;
}
$ans = $sum;

printf('%d', $ans);

?>