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 Rust (1.15.1) (judge verdict: Accepted)

fn read<T: std::str::FromStr>() -> Vec<T>
where
    <T as std::str::FromStr>::Err: std::fmt::Debug,
{
    let mut b = String::new();
    std::io::stdin().read_line(&mut b).unwrap();
    b.split_whitespace()
        .map(|x| x.trim().parse::<T>().unwrap())
        .collect()
}

fn main() {
    let _ = read::<i64>()[0];
    let ai = read::<i64>();

    let mut ans0 = ai[0];
    let mut ans1 = -ai[0];

    for x in 1..ai.len() {
        let a = ai[x];
        let n0 = std::cmp::max(ans0 + a, ans1 - a);
        let n1 = std::cmp::max(ans0 - a, ans1 + a);
        ans0 = n0;
        ans1 = n1;
    }

    println!("{}", ans0);
}