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())
a = list(map(int, input().split()))
c = 0
i = 1
k = 1
sum = a[0]

while a[i] == 0:
	i += 1
	if a[i] > 0:
		if i % 2 == 1:
			a[0] = 1
			c = 1
		else:
			a[0] = -1
			c = 1
	else:
		if i % 2 == 1:
			a[0] = -1
			c = 1
		else:
			a[0] = 1
			c = 1
i = 1
if a[0] > 0:
	while i < n:
		if i == 2*k-1:
			sum = sum + a[2*k-1]
			if sum >= 0:
				c = c + sum + 1
				sum = -1
			else:
				pass
			i += 1
		else:
			sum = sum + a[2*k]
			if sum <= 0:
				c = c - sum + 1
				sum = 1
			else:
				pass
			i += 1
			k += 1
	print(c)
elif a[0] < 0:
	while i < n:
		if i == 2*k-1:
			sum = sum + a[2*k-1]
			if sum <= 0:
				c = c - sum + 1
				sum = 1
			else:
				pass
			i += 1
		else:
			sum = sum + a[2*k]
			while sum >= 0:
				c = c + sum + 1
				sum = -1
			else:
				pass
			i += 1
			k += 1
	print(c)