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: Time Limit Exceeded)

package main

import (
    "fmt"
    "math"
)

var n int
var dp [][]int64

func main() {
  fmt.Scanf("%d", &n)
  var a []int64
  a = make([]int64, n)
  for i := 0; i < n; i++ {
    fmt.Scanf("%d", &a[i])
  }
  dp = make([][]int64, n + 1)
  for i := 0; i < n + 1; i++ {
    dp[i] = make([]int64, n + 1)
    for j := 0; j < n + 1; j++ {
      dp[i][j] = -999999
    }
  }
  dp[0][0] = 0
  for i := 0; i < n; i++ {
    dp[i + 1][0] = int64(math.Max(float64(dp[i][0] + a[i]), float64(dp[i][1] - a[i])))
    dp[i + 1][1] = int64(math.Max(float64(dp[i][0] - a[i]), float64(dp[i][1] + a[i])))
  }
  fmt.Println(dp[n][0])
}