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 sys
input = sys.stdin.readline
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
# A = [ int(input()) for _ in range(N) ]
##############################

N = int(input())
A = list(map(int, input().split()))

count = 0
summary = A[0]
for i in range(1, N):
#    print(summary)

    # 次はマイナス
    if summary > 0:
        # 条件を満たしてる？
        if (summary + A[i]) < 0:
            summary += A[i]
        else:
            # プラスになっちゃってるので修正
            summary += A[i]
            count += abs(-1-summary)
            summary = -1

    # 次はプラス
    else:
        if (summary + A[i]) > 0:
            summary += A[i]
        else:
            # マイナスになっちゃってるので修正
            summary += A[i]
            count += abs(1-summary)
            summary = 1

print(count)