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)

import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time

sys.setrecursionlimit(10**7)
inf=10**20
mod=10**9+7

def LI(): return list(map(int,input().split()))
def II(): return int(input())
def LS(): return input().split()
def S(): return input()

def main():
  n=II()
  l=LI()

  ad1=0
  f=True
  sm=0
  for x in l:
    if f:
      sm+=x
      if sm<=0:
        ad1+=abs(sm)+1
        sm=1
      f=False
    else:
      sm+=x
      if sm>=0:
        ad1+=abs(sm)+1
        sm=-1
      f=True

  ad2=0
  f=False
  sm=0
  for x in l:
    if not f:
      sm+=x
      if sm>=0:
        ad2+=abs(sm)+1
        sm=-1
      f=True
    else:
      sm+=x
      if sm<=0:
        ad2+=abs(sm)+1
        sm=1
      f=False

  return min(ad1,ad2)

print(main())