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: Wrong Answer)

local n = io.read("*n")
local a = {}
for i = 1, n do a[i] = io.read("*n") end
local ret = 1000000007
for flag = 1, 2 do
  flag = flag * 2 - 3
  local cur = 0
  local cnt = 0
  for i = 1, n do
    cur = cur + a[i]
    if flag < 0 then
      if 0 <= cur then
        cnt = cnt + cur + 1
        cur = -1
      end
    else
      if cur <= 0 then
        cnt = cnt - cur + 1
        cur = 1
      end
    end
    flag = flag * -1
  end
  ret = math.min(ret, cnt)
end
print(ret)