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: Accepted)

import sys
import heapq, math
from itertools import zip_longest, permutations, combinations, combinations_with_replacement
from itertools import accumulate, dropwhile, takewhile, groupby
from functools import lru_cache
from copy import deepcopy

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

p = A[0] if A[0] > 0 else 1
pc = 0 if A[0] > 0 else 1 - A[0]
m = A[0] if A[0] < 0 else -1
mc = 0 if A[0] < 0 else 1 + abs(A[0])

for i in range(1, N):
    p += A[i]
    m += A[i]
    if i % 2 == 0:
        if p <= 0:
            pc += 1 - p
            p = 1
        if m >= 0:
            mc += 1 + m
            m = -1
    else:
        if p >= 0:
            pc += 1 + p
            p = -1
        if m <= 0:
            mc += 1 - m
            m = 1

print(min(pc, mc))