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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func abs(x int64) int64 {
    if x > 0 {
        return x
    }
    return -x
}

func main() {
    var n int
    fmt.Scan(&n)
    a := make([]int64, n)
    for i := 0; i < n; i++ {
        fmt.Scan(&a[i])
    }
    var ans int64 = 0
    var min_a int64 = 1000000007
    var min_i int
    for i, v := range a {
        v = abs(v)
        if min_a > v {
            min_i = i
            min_a = v
        }
    }
    for i := 0; i < min_i; i++ {
        if a[i] < 0 {
            a[i] *= -1
            a[i + 1] *= -1
        }
    }
    for i := n - 1; i > min_i; i-- {
        if a[i] < 0 {
            a[i] *= -1
            a[i - 1] *= -1
        }
    }
    for _, v := range a {
        ans += v
    }
    fmt.Println(ans)
}