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: Runtime Error)

n = int(input())
a = list(map(int, input().split()))

cnt=0
for i in range(1,n):
    
    # 条件満たすまでループ
    for _ in range(3):
        print(a)
    
        now_tmp = sum(a[:i])
        next_tmp = sum(a[:i+1])
        print(i, now_tmp, next_tmp)
        
        # 符号が逆転していればOK かつ 現在までの総和が0でない
        #  異なる符号を掛けるとマイナスになる
        if now_tmp * next_tmp <0 and now_tmp !=0:
            break
        else:
            # 現在の合計がマイナスの場合
            if now_tmp < 0:
                a[i] += next_tmp+1
                cnt +=abs(next_tmp+1)

            # 現在の合計がプラスの場合
            elif now_tmp > 0 :
                a[i] += -next_tmp-1
                cnt +=abs(next_tmp+1)
            # 現在の合計が0の場合
            elif now_tmp == 0 :
                # 1個前がプラスの場合、
                if sum(a[:i-1]) > 0:
                    a[i] += -next_tmp+1
                    cnt +=abs(next_tmp+1)
                # 1個前がマイナスの場合
                else:
                    a[i] += next_tmp+1
                    cnt +=abs(next_tmp+1)
                
print(cnt)