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())
A2 = list(map(int,input().split()))

#print(A)

def getSign(a):
	if a < 0:
		return -1
	elif a == 0:
		return 0
	else:
		return 1

counts = []
for j in range(2):
	A = list(A2)
	count = 0
	sumN = A[0]
	beforeSign = getSign(A[0])
	
	if j == 0:
		add = -A[j] - getSign(A[j])
		A[j] += add
		count += abs(add)
	
	for i in range(1,N):
		sumN += A[i]

		#print("be",i,sumN,A[i],count)

		if 0 <= beforeSign * sumN:
			add = -sumN - beforeSign
			A[i] += add
			sumN += add
			count += abs(add)
		
		beforeSign = getSign(sumN)
		#print("af",i,sumN,A[i],count)
	
	counts.append(count)
	
print(min(counts))