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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

#!/usr/bin/env pypy3

import math


def sign(x):
    if x < 0:
        return -1
    elif x > 0:
        return 1
    else:
        return 0


def compute(n, ys):
    xs = ys[:]
    if xs[0] == 0:
        return min(compute(n, [1] + xs[1:]), compute(n, [-1] + xs[1:])) + 1
    ss = [None for _ in range(n)]
    ss[0] = xs[0]
    res = 0
    for i in range(n - 1):
        ss[i + 1] = ss[i] + xs[i + 1]
        dx = 0
        if ss[i + 1] == 0:
            dx = -sign(ss[i])
        elif sign(ss[i]) == sign(ss[i + 1]):
            dx = -sign(ss[i]) * (abs(ss[i + 1]) + 1)
        xs[i + 1] += dx
        ss[i + 1] += dx
        res += abs(dx)
    return res


def main():
    n = int(input())
    ys = [int(y) for y in input().split()]
    print(compute(n, ys))


if __name__ == '__main__':
    main()