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)

gets
seq = gets.split.map(&:to_i)

def foo(seq)
  cnt = 0
  sum = seq.shift
  seq.each{|a|
    if sum < 0
      if sum + a > 0
        sum += a
      else
        cnt += 1 - (sum + a)
        sum = 1
      end
    else
      if sum + a < 0
        sum += a
      else
        cnt += 1 + (sum + a)
        sum = -1
      end
    end
    p [a, sum, cnt]

  }
  
  return cnt
end

zero_cnt = 0
while seq.shift == 0
  zero_cnt += 1
end
p (zero_cnt * 2) - 1 + foo(seq)