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())
A = list(map(int, input().split()))
R = [0] * n
R[0] = A[0]
for i in range(1, n):
  R[i] = R[i-1] + A[i]

# search
def solve(r, inc=0):
  ans = 0
  is_plus = (r[0] > 0)
  for i in range(1, n):
    if (is_plus and r[i]+inc >= 0) or (not is_plus and r[i]+inc <= 0):
      ans += abs(r[i]+inc) + 1
      if (r[i]+inc) > 0:
        inc -= abs(r[i]+inc) + 1
      else:
        inc += abs(r[i]+inc) + 1
    is_plus = (r[i]+inc > 0)
  return ans

# normal
ret = solve(R, 0)
#print(R, ret)

# modify 
is_plus = (R[0] > 0)
ans0 = abs(R[0]) + 1
if is_plus:
  for i in range(n):
    R[i] -= abs(R[0]) + 1
else:
  for i in range(n):
    R[i] += abs(R[0]) + 1
ret2 = ans0 + solve(R, 0)
#print(R, ret2)

print(min(ret, ret2))