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>
#include<stdlib.h>
#include<math.h>

int max(int, int);

int dp(int*, int, int);

int main() {
  int N;
  int *A;
  int *a;
  int i;

  scanf("%d", &N);

  A = (int *)malloc(N * sizeof(int));
  a = A;

  for(i = 0; i < N; i++) {
    scanf("%d", a);
    a++;
  }

  printf("%d\n", dp(A, N, 0));

  free(A);

  return 0;
}

int max(int n1, int n2) {
  if(n1 >= n2) return n1;
  else return n2;
}

int dp(int *ary, int i, int j) {
  if(i == 0) {
    if(j == 0) return 0;
    else return -pow(2, 31) + abs(ary[0]);
  }
  else {
    if(j == 0) return max(dp(ary, i-1, 0) + ary[i-1], dp(ary, i-1, 1) - ary[i-1]);
    if(j == 1) return max(dp(ary, i-1, 0) - ary[i-1], dp(ary, i-1, 1) + ary[i-1]);
  }

  return -1;
}