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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>

using namespace std;

int main()
{
    int N;
    cin >> N;

    vector<int> As(N);
    for (int i = 0; i < N; ++i)
    {
        cin >> As[i];
    }

    int negativeNum = 0;
    for (const int A : As)
    {
        if (A < 0) ++negativeNum;
    }

    vector<int> absAs;
    for (const int A : As)
    {
        absAs.push_back(abs(A));
    }

    const int sum = accumulate(absAs.begin(), absAs.end(), 0);
    if (negativeNum % 2 == 0)
    {
        cout << sum;
    }
    else
    {
        const int ans = sum
            - *min_element(absAs.begin(), absAs.end()) * 2;
        cout << ans;
    }    

    return 0;
}