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) {
  const formatted_input = input.split('\n');

  const N = parseInt(formatted_input[0], 10);
  const As = formatted_input[1].split(' ').map(x => parseInt(x));

  dp = [];

  for(var i=0;i<N;i++){
    var results = [];
    if(i==0){
      results=[As[i], As[i]*-1]
    }else{
      var not_flipped = Math.max(dp[i-1][0] + As[i], dp[i-1][1] - As[i]);
      var flipped = Math.max(dp[i-1][0] - As[i], dp[i-1][1] + As[i]);
      results = [not_flipped, flipped]
    }
    dp.push(results);
  }

  //console.log(dp);
  console.log(dp[N-1][0]);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));