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)

import numpy as np

input()
a = list(map(int, input().split()))

def calc(a):
    value = a[0]
    sign = value >= 0
    result = 0
    for i in a[1:]:
        value += i
        diff = 0
        if sign and value >= 0:
            diff = value + 1
        elif not sign and value < 0:
            diff = value - 1
        result += abs(diff)
        sign = not sign
        value -= diff
        if value == 0:
            diff += sign
            value += diff
            result += diff
    return result

if a[0] == 0:
    a[0] = 1
    r1 = calc(a[:])
    a[0] = -1
    r2 = calc(a[:])
    print(min(r1, r2) + 1)
else:
    r1 = calc(a[:])
    diff = -a[0] - a[0] // abs(a[0])
    a[0] += diff
    r2 = calc(a[:]) + abs(diff)
    print(min(r1, r2))