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: Runtime Error)

use std::str::FromStr;
use std::io::*;
 
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main(){
    let n: usize = read();
    let mut a: Vec<i32> = (0..n).map(|_| read()).collect();
    
    for k in 0..n {
    	if a[k] == 0 {
        	if k-1 >= 0 && a[k-1] < 0 {
            	a[k-1] = a[k-1].abs();
            }
            if k+1 < n && a[k+1] < 0 {
            	a[k+1] = a[k+1].abs();
            }
        }
    }
    
    a.sort();
    
    
    let mut minus = 0;
    let mut zero = 0;
    let mut ans = 0;
    
    loop {
    	if a[minus + zero] > 0 {
        	break;
        }
        
        if a[minus + zero] == 0 {
        	zero += 1;
            continue;
        }
                
        minus += 1;
    }
    
    println!("{},{}", minus, zero);
    
    if minus % 2 == 0 || zero > 0 {
    	for k in 0..n {
        	ans += a[k].abs();
        }
    } else {
    	ans += a[0];
        for k in 1..n {
        	ans += a[k].abs();
        }
    }
    
    println!("{}",ans);
}