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 (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdbool.h>
long long arr[100010];

int main()
{
	int n;
	scanf("%d", &n);
	bool odd = false;
	bool zero = false;
	int max1 = -1;
	int max2 = -1;
	int min1 = -1;
	int min2 = -1;
	long long res = 0;
	for(int i=0; i<n; ++i)
	{
		scanf("%lld", arr + i);	
		if(arr[i] == 0)
			zero = true;
		if(arr[i] < 0)
		{
			odd = !odd;
			if(max1 < 0)
				max1 = i;
			else
			{
				if(arr[max1] < arr[i])
				{	
					max2 = max1;
					max1 = i;
				}
			}
		}
		if(arr[i] > 0)
		{
			if(min1 < 0)
				min1 = i;
			else
			{
				if(arr[min1] > arr[i])
				{	
					min2= min1;
					min1 = i;
				}
			}
		}
		res += arr[i] < 0 ? -arr[i] : arr[i];	
	}
	if(!zero && odd)
	{
		if(max1 >= 0 && min1 >= 0)
		{
			if( -arr[max1] > arr[min1])
			{
				arr[max1] = -arr[max1];
				res -= arr[min1] + arr[max1];
				arr[min1] = -arr[min1];
				res += arr[min1] + arr[max1] ;
			}
		}
		else if(min1 < 0)
		{
			arr[max1] = -arr[max1];
			res -= arr[max1] + arr[max1];
		}
	}
	
	printf("%lld\n", res);
	return 0;
}