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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define int long long
using namespace std;

signed main()
{
    int n;
    cin>>n;

    int a[n+1];
    a[0]=0;

    for (int i = 1; i <=n ; ++i) {
        cin>>a[i];
    }

    int dp[n+1][2]={};


    dp[1][0]=a[1];
    dp[1][1]=a[1];


    dp[2][0]=a[1]+a[2];
    dp[2][1]=-a[1]-a[2];

    for(int i=3;i<=n;i++)
    {
        dp[i][0]=max(dp[i-1][0]+a[i],dp[i-1][1]+a[i]);
        dp[i][1]=max(dp[i-1][0]-a[i]-2*a[i-1],dp[i-1][1]+2*a[i-1]-a[i]);
    }

    cout<<max(dp[n][0],dp[n][1]);
}