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 copy
n = int(input())
a = list(map(int,input().split()))
a_1 = a.copy()

ans = 0
ans_2 = 0
o = 0
for i in range(n):
    if i == 0:
        if a[i] == 0:
            f = "+"
            a[i] = 1
        elif a[0] > 0:
            f = "+"
        elif a[0] < 0:
            f = "-"
    else:
        o += a[i-1]
        if f == "+":
            if a[i] + o > 0:
                c = -1 - o
                ans += abs(c - a[i])
                a[i] = c
                f = "-"
            else:
                if a[i] + o == 0:
                    a[i] -= 1
                    ans += 1
                f = "-"
        elif f == "-":
            if a[i] + o < 0:
                c = 1 - o
                ans += abs(c - a[i])
                a[i] = c
                f = "+"
            else:
                if a[i] + o == 0:
                    a[i] += 1
                    ans += 1
                f = "+"
o = 0
a = a_1
#print(a)
for i in range(n):
    if i == 0:
        if a[i] == 0:
            f = "+"
            a[i] = 1
        elif a[0] > 0:
            f = "-"
            ans_2 += abs(-1 - a[0])
            a[i] = -1
        elif a[0] < 0:
            ans_2 += abs(1 - a[0])
            a[i] = 1
            f = "+"
    else:
        o += a[i-1]
        if f == "+":
            if a[i] + o > 0:
                c = -1 - o
                ans_2 += abs(c - a[i])
                a[i] = c
                f = "-"
            else:
                if a[i] + o == 0:
                    a[i] -= 1
                    ans_2 += 1
                f = "-"
        elif f == "-":
            if a[i] + o < 0:
                c = 1 - o
                ans_2 += abs(c - a[i])
                a[i] = c
                f = "+"
            else:
                if a[i] + o == 0:
                    a[i] += 1
                    ans_2 += 1
                f = "+"
#print(a)
print(min(ans,ans_2))