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: Wrong Answer)

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn read_vec_with_capacity<T: std::str::FromStr>(capacity: usize) -> Vec<T> {
    let mut s = String::with_capacity(capacity);
    std::io::stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn get<T: std::str::FromStr + Clone>() -> T {
    let line = read_vec::<T>();
    line[0].clone()
}

fn separate_by_zero(vec: Vec<i32>) -> Vec<Vec<i32>> {
    let mut vecvec = Vec::<Vec<i32>>::new();
    let mut temp_vec = Vec::<i32>::new();

    for x in vec {
        if x == 0 {
            vecvec.push(temp_vec.clone());
            temp_vec.clear();
        } else {
            temp_vec.push(x)
        }
    }

    vecvec
}

fn vecsum(vec: Vec<i32>) -> i32 {
    let mut low_zero_count = 0;
    let mut min = std::i32::MAX;
    let mut sum = 0;

    for x in vec {
        if x < 0 {
            low_zero_count += 1;
        }

        let abs = x.abs();
        if abs < min {
            min = abs;
        }

        sum += x;
    }

    if low_zero_count % 2 != 0 {
        sum -= min * 2;
    }

    return sum;
}

fn main() {
    let N = get::<usize>();
    let mut A = read_vec_with_capacity::<i32>(N);

    let mut sum = 0;
    for vec in separate_by_zero(A) {
        sum += vecsum(vec)
    }

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