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: Accepted)

//Optimise
#include <bits/stdc++.h>
using namespace std;

#define Online 1
// #define multitest 1
#define Debug 1
typedef long long ll;
typedef long double ld;
#define f first
#define s second
#define pb push_back
#define mp make_pair
const long long mod = 1000000007;
const long long High = 1e16;
void ControlIO();
void TimerStart();
void TimerStop();
#ifdef Debug
#define db(...) ZZ(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void ZZ(const char *name, Arg1 &&arg1)
{
	std::cerr << name << " = " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void ZZ(const char *names, Arg1 &&arg1, Args &&... args)
{
	const char *comma = strchr(names + 1, ',');
	std::cerr.write(names, comma - names) << " = " << arg1;
	ZZ(comma, args...);
}
#else
#define db(...)
#endif

void solve()
{
    int n;
    cin >> n;
    vector<int> A(n),B(n);
    ll sum = 0,maxi = High,p = 0;;
    for(int i=0;i<n;++i)
    {
        cin >> A[i];
        if(A[i]<0) p++;
        maxi = min(maxi,(ll)abs(A[i]));
        sum += abs(A[i]);
    }
    if(p&1) cout << sum - 2*maxi;
    else cout << sum;
}

int main()
{
	ControlIO();
	int t = 1;
#ifdef multitest
	cin >> t;
#endif
	TimerStart();
	while (t--)
		solve();
	TimerStop();
	return 0;
}

void ControlIO()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
#ifndef Online
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#endif
}

auto TimeStart = chrono::steady_clock::now();
auto TimeEnd = chrono::steady_clock::now();

void TimerStart()
{
#ifndef Online
	TimeStart = chrono::steady_clock::now();
#endif
}

void TimerStop()
{
#ifndef Online
	TimeEnd = chrono::steady_clock::now();
	auto ElapsedTime = TimeEnd - TimeStart;
	cout << "\n\nTime elapsed: " << chrono::duration<double>(ElapsedTime).count() << " seconds.\n";
#endif
}