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())
b = list(map(int,input().split()))
for i in range(1,N):b[i] = b[i] + b[i-1]

cost = sub = 0
if b[0] > 0:pass
elif b[0] == 0:cost,sub = 1,1
else:cost,sub = 1 - b[0], 1-b[0]

for i in range(1,N):
    if i % 2 == 0:
        if b[i] + sub <= 0:
            newsub = -1 * (b[i] + sub) + 1
            cost += abs(newsub)
            sub += newsub
    else:
        if b[i] + sub >= 0:
            newsub = -1 * (b[i] + sub + 1)
            cost += abs(newsub)
            sub += newsub

cost2 = sub2 = 0
if b[0] < 0:pass
elif b[0] == 0:cost2,sub2 = 1,-1
else:cost2,sub2 = 1 + b[0], -1 *(1+b[0])

for i in range(1,N):
    if i % 2 == 1:
        if b[i] + sub2 <= 0:
            newsub2 = -1 * (b[i] + sub2) + 1
            cost2 += abs(newsub2)
            sub2 += newsub2
    else:
        if b[i] + sub2 >= 0:
            newsub2 = -1 * (b[i] + sub2 + 1)
            cost2 += abs(newsub2)
            sub2 += newsub2

print(min(cost,cost2))