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: Accepted)

n = gets.to_i
a = gets.split.map(&:to_i)

b = a.dup

ans0 = 0

if b[0] <= 0
  ans0 += -b[0] + 1
  b[0] = 1
end

(n-1).times do |i| 
  b[i+1] += b[i]
  seki = b[i+1] * b[i]
  
  if seki < 0
    next
  else
    sgn = b[i] > 0 ? 1 : -1
    ans0 += (b[i+1]).abs + 1
    b[i+1] = -sgn
  end
end

# p b

b = a.dup
ans1 = 0

if b[0] >= 0
  ans1 += b[0] + 1
  b[0] = -1
end

(n-1).times do |i| 
  b[i+1] += b[i]
  seki = b[i+1] * b[i]
  
  if seki < 0
    next
  else
    sgn = b[i] > 0 ? 1 : -1
    ans1 += (b[i+1]).abs + 1
    b[i+1] = -sgn
  end
end

# p b
# p [ans0, ans1]
puts ans0 < ans1 ? ans0 : ans1