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 Python (3.8.2) (judge verdict: Wrong Answer)

n = int(input())
a = list(map(int,input().split()))
cnt = 0
if n == 2 and sum(a) >= 0:
    print(abs(sum(a)))
elif n == 2:
    print(max(abs(a[0]),abs(a[1])))
else:
    l3 = abs(a[-3])
    l2 = abs(a[-2])
    l1 = abs(a[-1])
    last = l3 + l2 + l1
    for i in range(n-3):
        if a[i] < 0:
            a[i] *= -1
            a[i+1] *= -1
        cnt += a[i]
    # +,+,+ or +,-,- or -,-,+ or -,+,-
    #print(cnt,a[-3],a[-2],a[-1])
    if (a[-3] >= 0 and a[-2] >= 0 and a[-1] >= 0) or (a[-3] >= 0 and a[-2] <= 0 and a[-1] <= 0) or (a[-3] <= 0 and a[-2] <= 0 and a[-1] >= 0) or (a[-3] <= 0 and a[-2] >= 0 and a[-1] <= 0):
        print(cnt+last)
    elif (a[-3] <= 0 and a[-2] >= 0 and a[-1] >= 0): # -,+,+
        print(cnt + last - 2*min(l1,l2,l3))
    else:
        print(cnt + last - 2*min(l1,l2))