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)

#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <math.h>
#include <complex>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#include <set>
#include <bitset>
#include <assert.h>
#include <numeric>
#include <iomanip>
#define rep(i, a, b) for (int(i) = (a); i < (b); i++)
using namespace std;

using ll = long long;

typedef pair<int, int> P;

const int INF = 100000000;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};

ll pow_mod(ll x, ll y, ll mod)
{
	if (y == 0)
		return 1;

	if (y == 1)
		return x % mod;

	return (pow_mod(x, y - 1, mod) * x) % mod;
}

int N;
int cnt;

int main()
{
	cin.tie(0);
	ios::sync_with_stdio(false);
	//問題文中の添え字が0-indexか1-indexか確認!
	cin>>N;
	vector<ll> A(N);
	rep(i,0,N){
		int a;
		cin>>a;
		if(a<0){
			cnt++;
			a=-a;
		}
		A[i]=a;
	}
	sort(A.begin(),A.end());
	ll ans=0;
	rep(i,0,N)ans+=A[i];
	if(cnt%2)ans-=2*A[0];
	cout<<ans;
	return 0;
}