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: Accepted)

#include <stdio.h>

int main(){
    int n, i;

    scanf("%d", &n);

    long a[n], cm=0, cz=0, max=0, min=1000000000, sum=0, ans=0;

    for(i=0; i<n; i++) {
        scanf("%ld", &a[i]);
    }


    for(i=0; i<n; i++) {
        if(a[i]<0) {
            cm += 1;
            sum += -1*a[i];
            if(min >-1*a[i]) {
                min = -1*a[i];
            }
        } else if (a[i]==0) {
            cz += 1;
        } else {
            sum += a[i];
            if(min >a[i]) {
                min = a[i];
            }
        }
    }


    if (cz>0 || (cm%2)==0) {
        ans = sum;
    } else if ((cm%2)==1) {
        ans = sum - min*2;
    }

    printf("%ld \n", ans);
}