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()))

count = 0
sum_i = a[0]

if a[0] < 0:
    sum_i = 1
    pos_count = 1 - a[0]
    for i in range(1, n):
        if sum_i < 0:
            sum_i += a[i]
            if sum_i <= 0:
                pos_count += 1 - sum_i
                sum_i = 1
        elif sum_i > 0:
            sum_i += a[i]
            if sum_i >= 0:
                pos_count += sum_i + 1
                sum_i = -1
    sum_i = a[0]
    neg_count = 0
    for i in range(1, n):
        if sum_i < 0:
            sum_i += a[i]
            if sum_i <= 0:
                neg_count += 1 - sum_i
                sum_i = 1
        elif sum_i > 0:
            sum_i += a[i]
            if sum_i >= 0:
                neg_count += sum_i + 1
                sum_i = -1
    if neg_count < pos_count:
        count = neg_count
    else:
        count = pos_count
elif a[0] > 0:
    sum_i = a[0]
    pos_count = 0
    for i in range(1, n):
        if sum_i < 0:
            sum_i += a[i]
            if sum_i <= 0:
                pos_count += 1 - sum_i
                sum_i = 1
        elif sum_i > 0:
            sum_i += a[i]
            if sum_i >= 0:
                pos_count += sum_i + 1
                sum_i = -1
    sum_i = -1
    neg_count = 1 + a[0]
    for i in range(1, n):
        if sum_i < 0:
            sum_i += a[i]
            if sum_i <= 0:
                neg_count += 1 - sum_i
                sum_i = 1
        elif sum_i > 0:
            sum_i += a[i]
            if sum_i >= 0:
                neg_count += sum_i + 1
                sum_i = -1
    if neg_count < pos_count:
        count = neg_count
    else:
        count = pos_count
else:
    sum_i = 1
    pos_count = 1
    for i in range(1, n):
        if sum_i < 0:
            sum_i += a[i]
            if sum_i <= 0:
                pos_count += 1 - sum_i
                sum_i = 1
        elif sum_i > 0:
            sum_i += a[i]
            if sum_i >= 0:
                pos_count += sum_i + 1
                sum_i = -1
    sum_i = -1
    neg_count = 1
    for i in range(1, n):
        if sum_i < 0:
            sum_i += a[i]
            if sum_i <= 0:
                neg_count += 1 - sum_i
                sum_i = 1
        elif sum_i > 0:
            sum_i += a[i]
            if sum_i >= 0:
                neg_count += sum_i + 1
                sum_i = -1
    if neg_count < pos_count:
        count = neg_count
    else:
        count = pos_count

print(count)