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)

#define _GLIBCXX_DEBUG
#define rep(i,n) for(int i=0;i<n;i++)
#include <bits/stdc++.h>
#include <numeric>
using namespace std;
typedef long long ll;
const int mod= 1e+9+7;

int main(){
    ll n; cin>>n;
    vector<ll>a(n);
    ll cntmin=0;
    ll sm=0;
    rep(i,n){
        cin>>a[i];
        if(a[i]<=0)cntmin++;
        sm+=abs(a[i]);
    }
    sort(a.begin(),a.end());
    if(cntmin%2==0){
        cout<<sm<<endl;
    }
    else{
        if(cntmin==n){
            cout<<sm-a[n-1]*2<<endl;
            return 0;
        }
        for(int i=0;i<n;i++){
            if(a[i]<0&&a[i+1]>0){
                cout<<max(sm-2*a[i+1],sm+2*a[i])<<endl;
                return 0;
            }
        }
    }
}