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

#include<bits/stdc++.h>
using namespace std;
#define int long long
signed main(){
    int N;
    cin >> N;
    int A[100010];
    for(int i = 0;i < N;i++){
        cin >> A[i];
    }
    if(A[0] < 0){A[0]*=-1;A[1]*=-1;}
    if(A[N-1] < 0){A[N-1]*=-1;A[N-2]*=-1;}
    for(int i = 0;i < N-1;i++){
        if(A[i] < 0 && A[i+1] < 0){A[i]*=-1;A[i+1]*=-1;}
    }

    for(int i = 1;i < N-1;i++){
        if(A[i] < 0){
            if(abs(A[i+1]) > abs(A[i]) && abs(A[i-1]) > abs(A[i]));
            else if(abs(abs(A[i+1]) - abs(A[i])) >= abs(abs(A[i-1]) - abs(A[i]))){A[i]*=-1;A[i+1]*=-1;}
            else {A[i]*=-1;A[i-1]*=-1;}
        }
    }
    int ans = 0;
    for(int i = 0;i < N;i++){
        ans += A[i];
    }
    cout << ans;
}