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>
long long arr[100010];

int main()
{
	int n;
	scanf("%d", &n);
	int flag = 0;
	int nozero = 1;
	int max = 0;
	int min = 0;
	for(int i=1; i<n+1; ++i)
	{
		scanf("%lld", arr + i);	
		if(arr[i] < 0)
		{
			flag = !flag;	
			if(max == 0)
				max = i;
			if(arr[max] < arr[i])
				max = i;		
		}
		else
		{
			if(min == 0)
				min = i;
			if(arr[min] > arr[i])
				min = i;		
		} 

		if(arr[i] == 0)
			nozero = 0;	 		
	}
	if(flag && nozero)
	{
		if(-arr[max] > arr[min])
		{
			arr[max] = -arr[max];
			arr[min] = -arr[min];
		}
	}

	long long res = 0;
	for(int i=1; i<n+1; ++i)
	{
		if(i != min && i != max && arr[i] < 0)
			arr[i] = -arr[i];
		if(nozero == 0 && arr[i] < 0)
			arr[i] = -arr[i];
						
 		res += arr[i];
		
	}
	
	printf("%lld\n", res);
	return 0;
}