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: Accepted)

function Main(input) {
	var inputArr = input.split("\n");
	var n = parseInt(inputArr[0]);
	var a = inputArr[1].split(" ");
    var sum = 0;
    var count = 0;
    var in0 = false;
    var min = 9999999999;
  
    var obj = {};
	for (var i = 0; i < n ; i++) {
      var ai = Math.abs(a[i]);
      if (a[i] < 0) {
        count++;
      }
      if (a[i] === 0) {
        in0 = true;
      }
      if (ai < min) {
        min = ai;
      }
      sum = sum + ai;
    }
    if (count % 2 === 0 || in0 === true) {
        console.log(sum) ;
    } else {
        console.log(sum - min - min) ;
    }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));