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 <iostream>
#include <cstdio>
#include <vector>
#include <cstring>

typedef long long ll;

using namespace std;

ll GetMaximumSumFlippingSigns(vector<ll>& num) {
    ll cntNegative = 0;
    ll maxNegative = 1;
    ll minPositive = -1;
    ll sum = 0;

    for(int i = 0; i < num.size(); ++i) {
        sum += abs(num[i]);
        if(num[i] > 0) {
            if(minPositive == -1) {
                minPositive = num[i];
            } else {
                if(minPositive > num[i]) {
                    minPositive = num[i];
                }
            }
        } else if(num[i] <= 0) {
            cntNegative += 1;
            if(num[i] == 0) {
                continue;
            }
            if(maxNegative == 1) {
                maxNegative = num[i];
            } else {
                if(maxNegative < num[i]) {
                    num[i] = maxNegative;
                }
            }
        }
    }
    if(cntNegative % 2 == 1){
        sum -= 2 * min(abs(maxNegative), minPositive);
    }
    return sum;
}

int main() {
    int n = 11;
    cin >> n;
    vector<ll> num(n, 0);
    for(int i = 0; i < n; ++i) {
        cin >> num[i];
    }

    ll maxSum = GetMaximumSumFlippingSigns(num);
    cout << maxSum << endl;
    return 0;
}