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<string>
#include<vector>
#include<algorithm>
#include<cmath>
#include<map>
#include <limits>
#include <numeric>
#include <type_traits>
using namespace std;


int main()
{
	int n;
	cin >> n;
	long long int a[99999];
	for (int i = 0; i < n; i++)
	{
		cin >> a[i];
	}
	for (int i = 0; i < n-1; i++)
	{
		
		if (i == n - 2)
		{
			if (a[i] < 0 || a[i + 1] < 0)
			{
				if (abs(a[i]) < abs(a[i + 1]))
				{

					a[i + 1] = abs(a[i + 1]);
					a[i] = -(abs(a[i]));
				}
				else
				{
					a[i] = abs(a[i]);
					a[i+1] = -(abs(a[i+1]));
					
				}
			}
		}
		else
		{
			if (a[i] < 0)
			{
				if (a[i + 1] < 0)
				{
					a[i] = -(abs(a[i]));
					a[i + 1] = -(abs(a[i+1]));
				}
				else if (a[i + 2] < 0)
				{
					a[i] = -(abs(a[i]));
				
					a[i + 2] = -(abs(a[i + 2]));
				}
				else
				{
					int x = -2;
					if (abs(a[i]) < abs(a[i + 1]))
					{
						x = i;
						
					}
					else
					{
						x = i + 1;
						
					}

					if (abs(a[x]) > abs(a[i + 2]))
					{
						x = i + 2;
						
					}
					for (int g = i; g < i + 3; g++)
					{
						if (g != x)
						{
							a[g] = abs(a[g]);
						}
						else
						{
							a[g] = -(abs(a[g]));
						}
					}
						


				}
			}
		}
		
		
	}
	long long int ans = 0;
	for (int i = 0; i < n; i++)
	{
		ans += a[i];
	}
	cout << ans << endl;
}