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: Runtime Error)

n=int(input())
b=list(map(int,input().split()))
a=b
condition=''
cnt=0
wa=0
for i in range(n):
  wa+=a[i]
  if i == 0:
    if a[i]>0:
      condition='minus'
    else:
      condition='plus'
  elif condition == 'plus':
    condition='minus'
    if wa<=0:
      cnt+=abs(wa)+1
      a[i]+=abs(wa)+1
      wa+=abs(wa)+1
  elif condition == 'minus':
    condition='plus'
    if wa>=0:
      cnt+=abs(wa)+1
      a[i]-=abs(wa)+1
      wa-=abs(wa)+1

cnt1=cnt
a=b
condition=''
cnt=0
wa=0
for i in range(n):
  a[i]=a[i]/abs(a[i])*(-1)
  cnt+=abs(a[i])+1
  wa+=a[i]
  if i == 0:
    if a[i]>0:
      condition='minus'
    else:
      condition='plus'
  elif condition == 'plus':
    condition='minus'
    if wa<=0:
      cnt+=abs(wa)+1
      a[i]+=abs(wa)+1
      wa+=abs(wa)+1
  elif condition == 'minus':
    condition='plus'
    if wa>=0:
      cnt+=abs(wa)+1
      a[i]-=abs(wa)+1
      wa-=abs(wa)+1

cnt2=cnt
print(min(cnt1,cnt2))