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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n = int(input())
a = list(map(int,input().split()))
num = a[0]
ans = 0
if a[0]>0:
    for i in range(1,n):
        num += a[i]
        if i%2==1:
            if num>=0:
                ans += num+1
                num = -1
        else:
            if num<=0:
                ans += 1-num
                num = 1
elif a[0]<0:
    for i in range(1,n):
        num += a[i]
        if i%2==1:
            if num <= 0:
                ans += 1-num
                num = 1
        else:
            if num >= 0:
                ans += num+1
                num = -1
else:
    num = 0
    ansp = 1
    ansm = 1
    for i in range(1,n):
        num += a[i]
        if i%2==1:
            if num>=0:
                ansp += num+1
                num = -1
        else:
            if num<=0:
                ansp += 1-num
                num = 1
    for i in range(1,n):
        num += a[i]
        if i%2==1:
            if num <= 0:
                ansm += 1-num
                num = 1
        else:
            if num >= 0:
                ansm += num+1
                num = -1
    ans = min(ansp,ansm)
print(ans)