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)

n = int(input())
a = list(map(int, input().split()))
s, ans, i = 0, 0, 0
while a[i] == 0 and i < n:
    ans += 2
    i += 1
ans = max(0, ans - 1)
if i == n:
    print(ans)
    exit()

if ans > 0:
    if abs(a[i]) == 1:
        ans += 1
        s = a[i]
    else:
        s = abs(a[i]) // a[i] * (abs(a[i]) - 1)
else:
    s = a[0]

##print('{} {} {}'.format(a[i], ans, s))
i += 1
for j in range(i, n):
    if abs(a[j]) > abs(s) and (a[j] == abs(a[j])) != (s == abs(s)):
        s += a[j]
    else:
        pre_s = s
        s = -1 * s // abs(s)
        ans += abs(a[j] - s + pre_s)
##    print('{} {} {}'.format(a[j], ans, s))
print(ans)