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: Time Limit Exceeded)

l = int(input())
n = [int(i) for i in input().split()] 

ans = []
ans.append(n[0])
count = 0
for i in range(1, l):
  nsum = sum(n[j] for j in range(0, i))
  while(True):
    #print("i:" + str(i))
    #print("n:" + str(n[i]))
    #print(("nsum:" + str(nsum)))
    if (n[i-1] < 0 and n[i] <= 0) or (n[i-1] > 0 and n[i] >= 0) or (nsum * (nsum + n[i]) >= 0):
      if n[i-1] < 0:
        count += 1
        n[i] += 1
      else:
        count += 1
        n[i] -= 1     
    else:
      ans.append(n[i])
      break
      
print(count)