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)

#!/usr/bin/env python3

import sys

sys.setrecursionlimit(10**7)


def read_h(typ=int):
    return list(map(typ, input().split()))


def read_v(n, m=1, typ=int):
    return [read_h() if m > 1 else typ(input()) for _ in range(n)]


def solve(arr, positive):
    num_op = 0
    cumul = 0
    #  print('current cumul:', cumul)

    for a in arr:
        cumul += a

        if positive and cumul >= 0:
            num_op += 1 + cumul
            cumul = -1
        elif not positive and cumul <= 0:
            num_op += 1 - cumul
            cumul = 1

        positive = not positive

    return num_op


def main():
    read_h()
    arr = read_h()

    op_plus = solve(arr, True)
    #  print('op plus:', op_plus)
    op_minus = solve(arr, False)
    #  print('op minus:', op_minus)

    print(min(op_plus, op_minus))


if __name__ == '__main__':
    main()