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 (
	"bufio"
	"fmt"
	"os"
)

var sc = bufio.NewScanner(os.Stdin)

func ri() (n int) {
	sc.Scan()
	b := sc.Bytes()
	if b[0] == 45 {
		return -b2i(b[1:])
	} else {
		return b2i(b)
	}
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func b2i(a []byte) (n int) {
	for _, v := range a {
		n = n*10 + int(v-48)
	}
	return
}

func sum(a []int) (x int) {
	for _, i := range a {
		x += i
	}
	return
}

func main() {
	sc.Split(bufio.ScanWords)
	n := ri()

	a := make([]int, n)
	minAbs := int(1e10)
	for i := 0; i < n; i++ {
		a[i] = ri()

		if x := abs(a[i]); x < minAbs {
			minAbs = x
		}
	}

	for i := 0; i <= n-2; i++ {
		if a[i] < 0 {
			a[i] *= -1
			a[i+1] *= -1
		}
	}

	if a[n-1] < 0 {
		fmt.Println(sum(a) + abs(a[n-1])*2 - minAbs*2)
	} else {
		fmt.Println(sum(a))
	}
}