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: Accepted)

import sys

n = int(sys.stdin.readline().strip())
A = list(map(int, sys.stdin.readline().strip().split()))

S = [0 for _ in range(n)]
acum = 0
for i in range(n):
    acum += A[i]
    S[i] = acum
# print(S)

costs = [0, 0]
for p in (0, 1):
    S_tmp = S[:]
    cost = 0 # BA`:n2s?t
    diff = 0 # +-B$NA`:n$G$NJQF0
    for i in range(n):
        # nB$H0lCW$9$kJ}$rIi$K$9$k
        # print(p, diff + S_tmp[i])
        if i % 2 == p:
            if diff + S_tmp[i] >= 0:
                tmp_cost = diff + S_tmp[i] + 1
                diff -= tmp_cost
                cost += tmp_cost
                # print("cost", cost)
        else:
            # B@5$KJQ49$9$k%3%9%H
            if diff + S_tmp[i] <= 0:
                tmp_cost = 1 - diff - S_tmp[i]
                diff += tmp_cost # +1B$KJQ49$9$k
                cost += tmp_cost
                # print("cost", cost)
    costs[p] = cost

# print(costs)
print(min(costs))