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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets                                                                                                                                                                                                                                                                        
a = gets.split.map(&:to_i)                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                
def change_count(a, r)                                                                                                                                                                                                                                                          
  sum = 0                                                                                                                                                                                                                                                                       
  change_time = 0                                                                                                                                                                                                                                                               
  a.each do |x|                                                                                                                                                                                                                                                                 
    sum += x                                                                                                                                                                                                                                                                    
    if r * sum < 0 # 符号が違ったとき                                                                                                                                                                                                                                           
      change_time += (r - sum).abs # -1 or +1 までの差分が変更回数                                                                                                                                                                                                      
      sum = r # sum が -1 or 1になる                                                                                                                                                                                                                                      
    end                                                                                                                                                                                                                                                                         
    r *= -1 # 次項の符号をセット                                                                                                                                                                                                                                                
  end                                                                                                                                                                                                                                                                           
  change_time                                                                                                                                                                                                                                                                   
end                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                
p [change_count(a, 1), change_count(a, -1)].min