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: Wrong Answer)

import sys
input = sys.stdin.readline

def main():
    n = int(input())
    a_list = list(map(int, input().split()))
    a_sum = a_list[0]
    if a_list[0] > 0:
        sign = "plus"
    else:
        sign = "minus"
    ans1 = 0
    for i in range(1, n):
        if sign == "plus":
            sign = "minus"
            if a_sum + a_list[i] == 0:
                ans1 += 1
                a_sum = -1
            elif a_sum + a_list[i] > 0:
                ans1 += a_sum + 1 + a_list[i]
                a_sum = -1
            else:
                a_sum += a_list[i]
        elif sign == "minus":
            sign = "plus"
            if a_sum + a_list[i] == 0:
                ans1 += 1
                a_sum = 1
            elif a_sum + a_list[i] < 0:
                ans1 += -1 * a_sum + 1 + -1 * a_list[i]
                a_sum = 1
            else:
                a_sum += a_list[i]

    a_sum = a_list[0]
    if a_list[0] > 0:
        sign = "plus"
    else:
        sign = "minus"
    ans2 = 0
    for i in range(0, n):
        if sign == "plus":
            sign = "minus"
            if a_sum + a_list[i] == 0:
                ans2 += 1
                a_sum = -1
            elif a_sum + a_list[i] > 0:
                ans2 += a_sum + 1 + a_list[i]
                a_sum = -1
            else:
                a_sum += a_list[i]
        elif sign == "minus":
            sign = "plus"
            if a_sum + a_list[i] == 0:
                ans2 += 1
                a_sum = 1
            elif a_sum + a_list[i] < 0:
                ans2 += -1 * a_sum + 1 + -1 * a_list[i]
                a_sum = 1
            else:
                a_sum += a_list[i]

    print(min(ans1, ans2))

if __name__ == '__main__':
    main()