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 Program{
 class Programin{
   static void Main(string []args){
     int N = int.Parse(Console.ReadLine());
     
     int []A = new int[N+1];
     
     string []buff = Console.ReadLine().Split(' ');
     
     for(int i = 0 ; i < N; i++) A[i+1] = int.Parse(buff[i]);
     
     long []C = new long[N+1];
     
     C[1] = A[1];
     C[2] = C[1] + A[2] > C[0] + (A[1] * -1) + (A[2] * -1) ? C[1] + A[2] : C[0] + (A[1] * -1) + (A[2] * -1) ;
     for(int i = 3 ; i<= N ;i++){
       C[i] = max( C[i-1] + A[i] , C[i-2] + ( A[i-1] * -1) + (A[i] * -1) , C[i-3] + (A[i-2] * -1) + A[i-1] + (A[i] * -1) ) ; 
     }
     
     Console.WriteLine(C[N]) ;
   }
   
   static long max(long a , long b , long c){
     if ( a >= b && a >= c) return a ;
     if( b >=a && a >= c) return b ;
     if ( c >= a && a>= b ) return c ;
     return c ;
   }
 }
}