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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
int max(int a,int b){
    return(a<b?b:a);
}

int main(void){
   int N,A[100000],B[50000],C[50000],i,sum1=0,sum2=0;
   
   scanf("%d",&N);
   for(i=0;i<N;i++)
   scanf("%d",&A[i]);
   
   for(i=0;i<N-1;i+=2) /* 0項から2項ずつ */
   sum1+=max(A[i]+A[i+1],-A[i]-A[i+1]);
   if(N%2==1)
   sum1+=max(A[N-1],-A[N-1]);
   
   for(i=1;i<N;i+=2) /* 1項から2項ずつ */
   sum2+=max(A[i]+A[i+1],-A[i]-A[i+1]);
   if(N%2==1)
   sum2+=max(A[0],-A[0]);
   
   printf("%d %d\n",sum1,sum2);
   
   printf("%d",max(sum1,sum2));
   
    return(0);
}