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
N = int(input())
A = list(map(int, input().split()))

res_plus = np.cumsum(A)
res_minus = np.cumsum(A)
ans_plus = 0
ans_minus = 0

tmp_tmp = 0
# 奇数項を正とする
for i in range(N):
    res_plus[i] += tmp_tmp
    if i % 2 == 0:         # 奇数項   
        if res_plus[i] > 0:
            pass
        else:
            tmp = 1 - res_plus[i]
            ans_plus += tmp
            tmp_tmp += tmp
    else:                  # 偶数項
        if res_plus[i] < 0:
            pass
        else:
            tmp = res_plus[i] + 1
            ans_plus += tmp
            tmp_tmp -= tmp


tmp_tmp = 0
# 奇数項を負とする
for i in range(N):
    res_minus[i] += tmp_tmp
    if i % 2 == 0:      # 奇数項
        if res_minus[i] < 0:
            pass
        else:
            tmp = res_minus[i] + 1
            ans_minus += tmp
            tmp_tmp -= tmp
    else:               # 偶数項
        if res_minus[i] > 0:
            pass
        else:
            tmp = 1 - res_minus[i]
            ans_minus += tmp
            tmp_tmp += tmp

##print(ans_minus, ans_plus)
print(min(ans_plus, ans_minus))