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)

N = int(input())
a_lst = [int(x) for x in input().split()]
b_lst = []
for i in a_lst:
    b_lst.append(i)

def my_sign(num):
    return (num > 0) - (num < 0)

cnt_p = 0
cnt_n = 0
sum_lst = []
sum2_lst = []

for i in range(N): #偶数でマイナス、奇数でプラスの和
    sum_lst.append(a_lst[i]) if i == 0 else sum_lst.append(a_lst[i] + sum_lst[i - 1])
    if i%2 == 0 and sum_lst[i] >= 0:
        cnt_p += 1 + sum_lst[i]
        a_lst[i] -= 1 + sum_lst[i]
        sum_lst[i] = -1
    elif i%2 == 1 and sum_lst[i] <= 0:
        cnt_p += 1 + abs(sum_lst[i])
        a_lst[i] += 1 + abs(sum_lst[i])
        sum_lst[i] = 1
for i in range(N): #偶数でプラス、奇数でマイナスの和
    sum2_lst.append(b_lst[i]) if i == 0 else sum2_lst.append(b_lst[i] + sum2_lst[i - 1])
    if i%2 == 0 and sum2_lst[i] <= 0:
        cnt_n += 1 + abs(sum2_lst[i])
        b_lst[i] += 1 + abs(sum2_lst[i])
        sum2_lst[i] = 1
    elif i%2 == 1 and sum2_lst[i] >= 0:
        cnt_n += 1 + sum2_lst[i]
        b_lst[i] -= 1 + sum2_lst[i]
        sum2_lst[i] = -1
print(min(cnt_p, cnt_n))