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: Time Limit Exceeded)

import copy

n = int(input())
a = list(map(int,input().split()))
b = [0]

for i in range(len(a)):
    b.append(b[i] + a[i])

del b[0]

c = copy.copy(b)

first_minus = 0
first_plus = 0

for i in range(len(b)):
    if(i%2 == 0):
        if (b[i] >= 0):
            diff =  abs(b[i]) + 1
            first_minus = first_minus +  diff
            b = list(map(lambda x: x - diff, b))

        if (c[i] <= 0):
            diff =  abs(c[i]) + 1
            first_plus = first_plus +  diff
            c = list(map(lambda x: x + diff, c))
    else:
        if (b[i] <= 0):
            diff =  abs(b[i]) + 1
            first_minus = first_minus +  diff
            b = list(map(lambda x: x + diff, b))

        if (c[i] >= 0):
            diff =  abs(c[i]) + 1
            first_plus = first_plus +  diff
            c = list(map(lambda x: x - diff, c))

print(min(first_minus,first_plus))