Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N. The i-th term in the sequence is a_i.
In one operation, you can select a term and either increment or decrement it by one.

At least how many operations are necessary to satisfy the following conditions?

For every i (1≤i≤n), the sum of the terms from the 1-st through i-th term is not zero.

For every i (1≤i≤n-1), the sign of the sum of the terms from the 1-st through i-th term, is different from the sign of the sum of the terms from the 1-st through (i+1)-th term.

Constraints

2 ≤ n ≤ 10^5

|a_i| ≤ 10^9

Each a_i is an integer.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print the minimum necessary count of operations.

Sample Input 1

4
1 -3 1 0

Sample Output 1

4

For example, the given sequence can be transformed into 1, -2, 2, -2 by four operations. The sums of the first one, two, three and four terms are 1, -1, 1 and -1, respectively, which satisfy the conditions.

Sample Input 2

5
3 -6 4 -5 7

Sample Output 2

0

The given sequence already satisfies the conditions.

Sample Input 3

6
-1 4 3 2 -5 4

Sample Output 3

8

Solution in Perl (v5.18.2) (judge verdict: Accepted)

<>;
@a=glob<>;
for$a(@a){
	$x+=$a;
	$y+=$a;
	if(--$|){
		if($x<=0){
			$X+=1-$x;
			$x=1;
		}
		if($y>=0){
			$Y+=1+$y;
			$y=-1;
		}
	}else{
		if($x>=0){
			$X+=1+$x;
			$x=-1;
		}
		if($y<=0){
			$Y+=1-$y;
			$y=1;
		}
	}
}
print$X<$Y?$X+0:$Y+0,$/