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)

# encoding:utf-8
import copy
import random
import bisect #bisect_left　これで二部探索の大小検索が行える
import fractions #最小公倍数などはこっち
import math

mod = 10**9+7

n = int(input())
a = [int(i) for i in input().split()]

sums = [0 for i in range(n)]

tmp = 0
if a[0] > 0:
    status_pos = True
else:
    status_pos = False

ans = 0
for i in range(n):
    tmp += a[i]
    if status_pos and tmp <= 0:
        ans += 1-tmp
        tmp = 1
    elif status_pos == False and tmp >= 0:
        ans += 1+tmp
        tmp = -1
    status_pos = not(status_pos)

ans2 = abs(a[0])+1
if a[0] > 0:
    a[0] = -1
else:
    a[0] = 1

tmp = a[0]
if a[0] > 0:
    status_pos = True
else:
    status_pos = False
for i in range(1,n):
    tmp += a[i]
    if status_pos and tmp <= 0:
        ans2 += 1-tmp
        tmp = 1
    elif status_pos == False and tmp >= 0:
        ans2 += 1+tmp
        tmp = -1
    status_pos = not(status_pos)

print(min(ans,ans2))
"""
1 -2 2 -2
1 -1 1 1
"""