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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
function Main(input) {
    let cin = new Inputer(input);
    let N = cin.getInt();
    let A = cin.getIntArray(N);
    let dp = new Array(N+1).fill(0).map(() => new Array(2).fill(Number.MIN_SAFE_INTEGER));
    dp[0][0] = 0;
    for (let n = 0; n < N; n++) {
        dp[n+1][0] = Math.max(...[dp[n+1][0], dp[n][0] + A[n], dp[n][1] - A[n]]);
        dp[n+1][1] = Math.max(...[dp[n+1][1], dp[n][0] - A[n], dp[n][1] + A[n]]);
    }
    console.log(dp[N][0]);
}
class Inputer{constructor(t){if(typeof t=='undefined')throw new Error('引数（stdin）を省略できません！');this.cnt=0,this.items=t.split(/\n|\s/)}getInt(){return this.items[this.cnt++]-0}getIntArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getInt();return r}getStr(){return this.items[this.cnt++]}getStrArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getStr();return r}}
if (typeof window == "undefined") Main(require("fs").readFileSync("/dev/stdin", "utf8"));