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)

n = int(input())
sa = input().split()

a = [0 for i in range(n)]
sumeven = 0
sumodd = 0
for i,sai in enumerate(sa):
    a[i] = int(sai)

    if i % 2 == 0:
        sumeven += a[i]
    else:
        sumodd += a[i]

ret = 0
sm = 0
for i,ai in enumerate(a):
    if sumeven < sumodd:
        if i == 0:
            ret += max(ai + 1, 0)
            sm += min(-1, ai)
        elif i % 2 == 1:
            ret += max(-sm+1-ai,0)
            sm += max(ai, -sm+1)
        elif i % 2 == 0:
            ret += max(sm+1 + ai, 0)
            sm += min(ai, -(sm+1))
    else:
        if i == 0:
            ret += max(1 - ai, 0)
            sm += max(1, ai)
        elif i % 2 == 0:
            ret += max(-sm+1-ai,0)
            sm += max(ai, -sm+1)
        elif i % 2 == 1:
            ret += max(sm+1 + ai, 0)
            sm += min(ai, -(sm+1))
print(ret)