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 Lua (5.3.2) (judge verdict: Accepted)

local printx = print
local print = function()end
local function sign(a)
  if a>0 then return 1
  elseif a<0 then return -1
  else return 0 end
end
local N = io.read("n")
local A = {}
for i=1,N do A[i] = io.read("n") end
local gans=10^18
for k=-1,1,2 do
  local ans = 0
  local sum = 0
  local s = k
  for i=1,N do
    local newsum = sum + A[i]
    print("i",i,"A[i]",A[i],"sum",sum,"newsum",newsum)
    if sign(newsum) ~= s then
      local add = math.abs(newsum) + 1
      ans = ans + add
      sum = s
      print("abs(add)",add)
    else
      sum = newsum
    end
    s = s * -1
  end
  print("k",k,A[i],sum,ans)
  print()
  gans = math.min(gans, ans)
end
printx(gans)