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 Haskell (GHC 7.10.3) (judge verdict: Accepted)


solver::[Int]->Int
solver xs = let h = head xs in minimum (if  h /= 0 then [(check_tot 0 h (tail xs))
                                                       ,(check_tot (abs (h-1)) 1 (tail xs))
                                                       ,(check_tot (abs (h+1)) (-1) (tail xs))]
                                                  else [(check_tot (abs (h-1)) 1 (tail xs))
                                                      ,(check_tot (abs (h+1)) (-1) (tail xs))])

main::IO()
main=do
  _<-getLine
  datc<-getLine
  print (solver (map read (words datc)))
--おそい。Step_sumを作る事無く、シーケンシャルにいく

--今のカウント手数、ここまでの修正されたトータル（これはゼロでない事が保証される）、食べるリスト。
check_tot::Int -> Int -> [Int] -> Int
check_tot st _   [] = st
check_tot st tot xs
      | (tot > 0)&&((tot+(head xs))>=0) = let dec = (tot+(head xs))+1 in check_tot (dec+st) (-1) (tail xs)
      | (tot > 0)&&((tot+(head xs)) <0) = check_tot st (tot+(head xs)) (tail xs)
      | (tot < 0)&&((tot+(head xs)) >0) = check_tot st (tot+(head xs)) (tail xs)
      | (tot < 0)&&((tot+(head xs))<=0) = let inc = 1-(tot+(head xs)) in check_tot (inc+st)   1  (tail xs)