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: Wrong Answer)

# coding: utf-8
# Here your code



N = int(input())
a = [int(i) for i in input().split()] 

result_1 = 0
before_sum =a[0]
after_sum =a[0]

for i in range(1,N):
    before_sum = after_sum
    after_sum = before_sum + a[i]
    if before_sum * after_sum > 0:
        if after_sum < 0:
            result_1 += 1 - after_sum
            after_sum = 1
        elif after_sum > 0:
            result_1 += 1 + after_sum
            after_sum = -1
    elif before_sum * after_sum == 0:
        result_1 += 1
        if before_sum < 0:
            after_sum = 1
        else:
            after_sum = -1

before_sum =-a[0]
after_sum =-a[0]
result_2 = 1 + abs(before_sum)


for i in range(1,N):
    before_sum = after_sum
    after_sum = before_sum + a[i]
    if before_sum * after_sum > 0:
        if after_sum < 0:
            result_2 += 1 - after_sum
            after_sum = 1
        elif after_sum > 0:
            result_2 += 1 + after_sum
            after_sum = -1
    elif before_sum * after_sum == 0:
        result_2 += 1
        if before_sum < 0:
            after_sum = 1
        else:
            after_sum = -1


print(min(result_1,result_2))