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: Runtime Error)

n = gets.chomp.to_i
a = gets.chomp.split(" ").map(&:to_i)
ans = 0
cumulative_sum = [0]

n.times do |i|
    tmp = cumulative_sum[i] + a[i]
    if tmp == 0 then
        ans += 1
        if 0 < cumulative_sum[i] then
            cumulative_sum << -1
        elsif 0 > cumulative_sum[i] then
            cumulative_sum << 1
        end
    else
        if 0 < tmp && 0 < cumulative_sum[i] then
            ans += tmp + 1
            cumulative_sum << -1
        elsif 0 > tmp && 0 > cumulative_sum[i] then
            ans += 1-tmp
            cumulative_sum << 1
        else
            cumulative_sum << tmp
        end
    end
end

puts ans