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 <stdio.h>
#include <iostream>
#include <string>
#include <vector> 
#include <algorithm>
#include <typeinfo>
#include <cmath>
#include <numeric>
using namespace std;

int getGCD(int a, int b){
    if(b == 0) return a;
    return getGCD(b, a%b);
}
int main()
{
    int N;
    int max_sum;
    std::cin >> N;
    std::vector<int> A(N);
    for (int i = 0; i < N; ++i) std::cin >> A[i];
    
    int minus_cnt = 0;
    int min_r_A = 10^9 + 1;
    int min_index;
    for (int i = 0; i < N; ++i)
    {
        if(A[i] < 0){
            A[i] = -A[i];
            minus_cnt = minus_cnt + 1;
            if(min_r_A > A[i]){
                min_r_A = A[i];
                min_index = i;
            }
        }
    }
    
    if(minus_cnt%2 == 0){
        max_sum = std::accumulate(A.begin(), A.end(), 0);
    }else{
        std::vector<int>::iterator iter = std::min_element(A.begin(), A.end());
        int min_A = *iter;
        int index = std::distance(A.begin(), iter);
        if (min_A < A[min_index])
        {
            A[index] = -A[index];
        }else{
            A[min_index] = -A[min_index];
        }
        max_sum = accumulate(A.begin(), A.end(), 0);
    }
    std::cout << max_sum << "\n";
}