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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n = io.read("*n", "*l")
local str = io.read()
local a = {}
for v in str:gmatch("(%-?%d+)") do
  table.insert(a, tonumber(v))
end
local stepmin = nil
for type = -1, 1, 2 do
  local step = 0
  local sum = 0
  local flag = type
  for i = 1, n do
    sum = sum + a[i]
    if flag == 1 then
      if sum <= 0 then
        step = step + 1 - sum
        sum = 1
      end
    else
      if 0 <= sum then
        step = step + 1 + sum
        sum = -1
      end
    end
    flag = -flag
  end
  if type == -1 then stepmin = step else stepmin = math.min(stepmin, step) end
end
print(stepmin)