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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
int main() {
	int n, a[100010];
	long sgn, cont = 0, ans = 0;

	scanf("%d", &n);
	for (int i = 0; i < n; i++)
	{
		scanf("%d", &a[i]);
	}

	cont += a[0];
	if (cont > 0) sgn = 1;
	else if (cont < 0) sgn = -1;
	else
	{
		ans++;
		int i = 0;
		for (; a[i] == 0; i++)
		{
			sgn = -1 * sgn;
		}
		sgn = (a[i] > 0) ? sgn : -1 * sgn;
	}

	for (int i = 1; i < n; i++)
	{
		cont += a[i];
		if (cont * sgn < 0)
		{
			sgn = -1 * sgn;
		}
		else if (cont * sgn >= 0)
		{
			ans = ans + 1 + cont * sgn;
			sgn = -1 * sgn;
			cont = sgn;
		}
	}

	printf("%ld", ans);

	return 0;
}