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)

// inputに入力データ全体が入る
function Main(input) {
	// 1行目がinput[0], 2行目がinput[1], …に入る
    input = input.split("\n");
    // 数値の配列を作る
    const numList0 = input[0].split(' ').map(x => parseInt(x, 10));
    const N = numList0[0];
    const AList = input[1].split(' ').map(x => parseInt(x, 10));

    var result = 0;
  
  	if (N === 2) {
		const Ai2 = AList[0];
        const Ainext2 = AList[1];
      
        if (Ai2 > 0 && Ainext2 > 0) {
            console.log(Ai2 + Ainext2);
        } else if (Ai2 < 0 && Ainext2 < 0) {
            console.log((Ai2 + Ainext2) * (-1));
        } else {
            console.log(Math.max(Math.abs(Ai2), Math.abs(Ainext2)));
        }
      
        return;
    }
  
    for (var i = 0; i < N - 1; i++) {
        var Ai = AList[i];
        var Ainext = AList[i + 1];
        // 両方負の時
        if (Ai < 0 && Ainext < 0) {
            // 反転する
            result += Ai * (-1);
            AList[i + 1] = Ainext * (-1);
        } else if (Ai < 0 && Math.abs(Ai) >= Math.abs(Ainext)) {
            // Aiの方が絶対値が大きい時
            // 反転する
            result += Ai * (-1);
            AList[i + 1] = Ainext * (-1);
        } else if (Ai > 0 && Ainext > 0) {
            // そのまま足す
            result += Ai;
        } else {
            result += Ai;
        }
    }
    // 最後はそのまま足す
    result += AList[N - 1];

    console.log(result);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));