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)

// 問題文読んでないけど負数が奇数の場合は両端どっちかで偶数の場合はなんとなく全部正にできそう
// """0""" の存在を忘れていた...
// 意味不明なことにWA
// アホだった なーにが「両端どっちか」じゃボケが 最小値にすることが可能
package main

import "fmt"

func main() {
	var N int
	fmt.Scan(&N)
	A := make([]int, N)
	S := 0
	minus := 0
	zero := false
	minn := int(1e10)
	for i := 0; i < N; i++ {
		var V int
		fmt.Scan(&V)
		if V == 0 {
			zero = true
		} else {
			minn = min(minn, abs(V))
		}
		A[i] = abs(V)
		S += abs(V)
		if V < 0 {
			minus++
		}
	}
	if zero {
		fmt.Println(S)
	} else if minus%2 == 0 {
		fmt.Println(S)
	} else {
		fmt.Println(S - minn*2)
	}
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func abs(x int) int {
	if x < 0 {
		x *= -1
	}
	return x
}