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 Python (3.4.3) (judge verdict: Accepted)

N = int(input())
A = list(map(int,input().split()))

#値を修正する場合、1か−1にすればよい
##そのためには、値の絶対値に1を足した数を加えればよい

#正、負のパターンと負、正のパターンの両方について算出し、小さい方を出力する
##没解だと、所与のA[0]の符号を基準としたまま、答えを提出していたが、
##当然、それが最適値であるとは限らない！！！

total = 0
ans = 0
total2 = 0
ans2 = 0

for i in range(N):
    total += A[i]
    #奇数番目を正にする
    if i % 2 == 0:
        #1より小さい == 0以下
        if total < 1:
            ans += 1 - total
            total = 1
    else:
        #0以上
        if total > -1:
            ans += (1 + total)
            total = -1

for i in range(N):
    total2 += A[i]
    #偶数番目を正にする
    if i % 2 == 1:
        if total2 < 1:
            ans2 += 1 - total2
            total2 = 1
    else:
        if total2 > -1:
            ans2 += 1 + total2
            total2 = -1

print(min(ans,ans2))