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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val l = readLine()!!.split(" ").map { it.toInt() }
    var s_pls = 0
    var s_mns = 0
    var tmp = 0
    var pls_cnt = 0
    var mns_cnt = 0
    for(i in 0 until n){
        s_pls += l[i]
        s_mns += l[i]
        if(i % 2 == 0){
            if(s_pls <= 0){
                pls_cnt += 1 - s_pls
                s_pls = 1
            }
            if(s_mns >= 0){
                mns_cnt += 1 + s_mns
                s_mns = -1
            }
        }
        else{
            if(s_mns <= 0){
                mns_cnt += 1 - s_mns
                s_mns = 1
            }
            if(s_pls >= 0){
                pls_cnt += 1 + s_pls
                s_pls = -1
            }
        }
    }
    println(Math.min(Math.abs(pls_cnt), Math.abs(mns_cnt)))
}