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: Time Limit Exceeded)

n = gets.to_i
as = gets.split(' ').map { |e| e.to_i }

x = 0
bs = []
as.each { |e|
  x += e
  bs << x
}

# p bs

ans = 0
for i in (1..(n - 1))
  a, b = bs[i - 1], bs[i]
  if a >= 0 && b >= 0
    d = b + 1
    for j in (i..(n-1))
      bs[j] = bs[j] - d
    end
    # p bs
    ans += d
  elsif a <= 0 && b <= 0
    d = -1 * b + 1
    for j in (i..(n-1))
      bs[j] = bs[j] + d
    end
    # p bs
    ans += d
  end
end

ans += 1 if bs[n-1] == 0
puts ans