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)

mod reader {
    use std;

    macro_rules! read_line((  ) => {
                           {
                           let mut input = String :: new (  ) ; std :: io ::
                           stdin (  ) . read_line ( & mut input ) . unwrap (
                           ) ; input } } ;);

    pub fn read_to_vec<T: std::str::FromStr>() -> Vec<T> {
        read_line!().split_whitespace().map(|e|
                                                e.parse().ok().unwrap()).collect()
    }

    pub fn read_and_parse<T: std::str::FromStr>() -> T {
        read_line!().trim().parse().ok().unwrap()
    }
}
use reader::*;

fn main() {
    let n: usize = read_and_parse();
    let a: Vec<i64> = read_to_vec();

    let mut last_not_flipped = a[0] + a[1];
    let mut last_flipped = -(a[0] + a[1]);

    for i in 1..n - 1 {
        let (pos, neg) = (last_not_flipped, last_flipped);

        last_not_flipped = std::cmp::max(pos + a[i + 1], neg + a[i + 1]);
        last_flipped =
            std::cmp::max(pos - 2 * a[i] - a[i + 1],
                          neg + 2 * a[i] - a[i + 1]);
    }

    println!("{}" , std :: cmp :: max ( last_not_flipped , last_flipped ));
}