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 <bits/stdc++.h>
//Remove below header file if c++ version greater than 14
#include <vector>
#include <algorithm>
#include <set>
#include <map>
#include <set>
#include <unordered_set>
#include <unordered_map>
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;

#define pb push_back
#define fastIO ios_base::sync_with_stdio(false); cin.tie(nullptr);
#define endl '\n'
#define deb(x) cout << #x << " "<< x << endl;
#define fo(i, n) for(int i=0; i<n; i++)
#define Fo(i, k, n) for(int i=k; i<n; i++)

struct greaterr
{
    template<class T>
    bool operator()(T const &a, T const &b) const { return a > b; }
};

ll gcd(ll a, ll b) {
	if (b == 0)return a;
	return gcd(b, a%b);
}

ll lcm(ll a, ll b) {
	return a /gcd(a, b) *b;
}
typedef pair<int,int> pii;
const int mod = 1e9+7;

ll xorr(ll n){

    if(n%4==0)
        return n;

    else if(n%4==1)
        return 1;

    else if(n%4==2)
        return n+1;

    else
        return 0;



}

int main() {

   int n;
   cin>>n;

   int arr[n];
   fo(i,n)
    cin>>arr[i];

   fo(i,n-1){
   if(arr[i]<0)
    arr[i]*=-1;
   arr[i+1]*=-1;

   }

 ll res = 0;

 if(arr[n-1]>=0)
    res = accumulate(arr,arr+n,0LL);
 else{
        arr[n-1]*=-1;
    res = accumulate(arr,arr+n,0LL) - 2* (*min_element(arr,arr+n));
 }
 cout<<res;




 return 0;

      }