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)

import copy
n=int(input())
a=list(map(int,input().split()))
b=copy.copy(a)

ct1=0
if a[0]<=0:
  a[0]=1
  ct1+=1-a[0]
for i in range(1,n):
  if i%2==1:
    if sum(a[0:i+1])>=0:
      ct1+=sum(a[0:i+1])+1
      a[i]=-sum(a[0:i])-1
  else:
    if sum(a[0:i+1])<=0:
      ct1+=1-sum(a[0:i+1])
      a[i]=-sum(a[0:i])+1

ct2=0
if b[0]>=0:
  b[0]=-1
  ct2+=b[0]-1
for i in range(1,n):
  if i%2==0:
    if sum(b[0:i+1])>=0:
      ct2+=sum(b[0:i+1])+1
      b[i]=-sum(b[0:i])-1
  else:
    if sum(b[0:i+1])<=0:
      ct2+=1-sum(b[0:i+1])
      b[i]=-sum(b[0:i])+1

print(min(ct1,ct2))