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: Accepted)

N = int(input())
A = [int(x) for x in input().split()]

if A[0] < 0:
	sumP = 1
	sumM = A[0]
	countP = -A[0] + 1
	countM = 0
elif A[0] == 0:
	sumP = 1
	sumM = -1
	countP = 1
	countM = 1
else:
	sumP = A[0]
	sumM = -1
	countP = 0
	countM = A[0] + 1

for i in range(1, N):
	if sumP > 0:
		if A[i] + sumP >= 0:
			countP += A[i] + sumP + 1
			sumP = -1
		else:
			sumP += A[i]
	else:
		if A[i] + sumP <= 0:
			countP += -(A[i] + sumP) + 1
			sumP = 1
		else:
			sumP += A[i]
	
	if sumM > 0:
		if A[i] + sumM >= 0:
			countM += A[i] + sumM + 1
			sumM = -1
		else:
			sumM += A[i]
	else:
		if A[i] + sumM <= 0:
			countM += -(A[i] + sumM) + 1
			sumM = 1
		else:
			sumM += A[i]

print(min(countP, countM))