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)

nums = int(input())
ary = list(map(int,input().split()))

#puls no toki
count = 0
sum = ary[0]
if ary[0] < 0 :
    count += abs(ary[0])+1
    sum = 1
elif ary[0] == 0:
    sum = 1
    count += 1

for i in range (1,nums):
    sum += ary[i]

    if i % 2 == 1:
        if sum > 0 :
            count += abs(sum)+1
            sum = -1
        elif sum == 0:
            sum = -1
            count += 1
    elif i % 2 == 0:
        if sum < 0:
            count += abs(sum)+1
            sum  = 1
        elif sum == 0:
            sum = 1
            count += 1

result_plus = count

#minus no toki
count = 0
sum = ary[0]
if ary[0] > 0:
    count += abs(ary[0]) +1
    sum = -1
elif ary[0] == 0:
    sum = -1
    count += 1

for i in range(1,nums):
    sum += ary[i]
    if i % 2 == 1:
        if sum < 0:
            count += abs(sum)+1
            sum = 1
        elif sum == 0:
            count += 1
            sum = 1
    if i % 2 == 0:
        if sum > 0:
            count += abs(sum)+1
            sum = -1
        elif sum == 0:
            count += 1
            sum = -1

result_minus = count

if result_plus > result_minus:
    print(result_minus)
else:
    print(result_plus)