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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function main(input) {
	var result = 0;
	var l = input.split("\n")[1].split(" ");
	l = l.map(n => {
		return +n;
	});
	f(l).forEach(n => {
		result += n;
	});
	console.log(result);
}
function f(l) {
	var flg = true;
	for(var i = 0; i < l.length; i ++) {
		if(l[i] < 0) {
			if(i == l.length - 1 && (l[i-1] <= 0 || z(l[i]) >= z(l[i-1]))) {
				flg = false;
				l[i] = l[i] * -1;
				l[i-1] = l[i-1] * -1;
			} else if(l[i+1] <= 0 || z(l[i]) >= z(l[i+1])) {
				flg = false;
				l[i] = l[i] * -1;
				l[i+1] = l[i+1] * -1;
			}
		}
	}
	if(flg) {
		return l;
	} else {
		return f(l);
	}
}
function z(x) {
	return x < 0 ? -1 * x : x;
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));