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 Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
b = [int(x) for x in input().split()]
temp = 0
count1 = 0
count2 = 0

a = b

if a[0] == 0:
	a[0] = 1
	count1 = 1

sum = a[0]
for i in range(1, n):
	if abs(a[i]) <= abs(sum) or a[i] * sum >= 0:
		if sum > 0:
			temp = -1 * abs(sum) - 1
			count1 += abs(temp - a[i])
		else:
			temp = abs(sum) + 1
			count1 += abs(temp - a[i])
		a[i] = temp
	sum += a[i]

count2 = abs(a[0]) + 1

a = b

if a[0] > 0:
	a[0] = -1
else:
	a[0] = 1

sum = a[0]
for i in range(1, n):
	if abs(a[i]) <= abs(sum) or a[i] * sum >= 0:
		count2 += abs(sum - a[i]) + 1
		if sum > 0:
			temp = -1 * abs(sum) - 1
			count2 += abs(temp - a[i])
		else:
			temp = abs(sum) + 1
			count2 += abs(temp - a[i])
		a[i] = temp
	sum += a[i]

print(min(count1, count2))