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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
namespace inonoa{
    class Aio{
        static void Main(){
            int n = int.Parse(Console.ReadLine());
            int[] a = new int[n];
            string[] a_ = Console.ReadLine().Split(' ');
            for (int i=0;i<n;i++){
                a[i] = int.Parse(a_[i]);
            }
            int min_index = 0;
            int min = 10*9+1;
            for(int i=0;i<n;i++){
                if(a[i]>=0){
                    if(min>a[i]){
                        min = a[i];
                        min_index = i;
                    }
                }else{
                    if(min>-a[i]){
                        min = -a[i];
                        min_index = i;
                    }
                }
            }
 
            
                for(int i=0;i<min_index;i++){
                    if(a[i]<0){
                        a[i] = -a[i];
                        a[i+1] = -a[i+1];
                    }
                }
                for(int i=n-1;i>min_index;i--){
                    if(a[i]<0){
                        a[i] = -a[i];
                        a[i-1] = -a[i-1];
                    }
                }
                long ans = 0;
                for(int i=0;i<n;i++){
                    ans += a[i];
                }
                Console.WriteLine(ans);
 
            /* 
            long ans = 0;
            for(int i=0;i<n;i++){
                if(i==min_index){
                    if(min>0){
                        ans += -min;
                    }else{
                        ans += min;
                    }
                }
                else{
                    if(a[i]>0){
                        ans += a[i];
                    }else{
                        ans -= a[i];
                    }
                }
            }
            */
        }
    }
}