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 (2.7.6) (judge verdict: Accepted)

n = int(raw_input())
A = map(int, raw_input().split())
if A[0] > 0:
    psep = A[0]
    psop = -1
    opop = abs(-1 - A[0])
    opep = 0
elif A[0] < 0:
    psep = 1
    psop = A[0]
    opep = abs(1-A[0])
    opop = 0
else:
    psep = 1
    psop = -1
    opep = 1
    opop = 1
for i in range(1, n):
    if i % 2 == 0:
        if psep + A[i] <= 0:
            opep += abs(1 - (psep + A[i]))
            psep = 1
        else:
            psep = psep + A[i]
        if psop + A[i] >= 0:
            opop += abs(-1 - (psop + A[i]))
            psop = -1
        else:
            psop += A[i]
    else:
        if psep + A[i] >= 0:
            opep += abs(-1 - (psep+A[i]))
            psep = -1
        else:
            psep += A[i]
        if psop + A[i] <= 0:
            opop += abs(1-(psop+A[i]))
            psop = 1
        else:
            psop = psop + A[i]
print min(opop, opep)