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: Wrong Answer)

package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)

	a := make([]int64, n)
	for i := range a {
		fmt.Scan(&a[i])
	}

	if abs(a[0]) > abs(a[n-1]) {
		for i := 0; i < n-1; i++ {
			if a[i] < 0 {
				a[i], a[i+1] = -a[i], -a[i+1]
			}
		}
	} else {
		for i := n - 1; 0 < i; i-- {
			if a[i] < 0 {
				a[i], a[i-1] = -a[i], -a[i-1]
			}
		}
	}
	var ret int64
	for i := range a {
		ret += a[i]
	}
	fmt.Println(ret)

}

func abs(n int64) int64 {
	if n < 0 {
		return -n
	}
	return n
}