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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var n int
	fmt.Scanf("%d", &n)

	a := make([]int, n)
	b := make([]int, n)

	for i := 0; i < n; i++ {
		fmt.Scanf("%d", &a[i])
		b[i] = a[i]
	}

	var c1 int64
	if a[0] <= 0 {
		c1 = int64(-a[0] + 1)
		a[0] = 1
	}
	c1 += solve(a)

	var c2 int64
	if b[0] >= 0 {
		c2 = int64(b[0] + 1)
		b[0] = -1
	}
	c2 += solve(b)

	fmt.Printf("%d\n", min(c1, c2))
}

func min(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

func solve(a []int) int64 {
	n := len(a)

	var count int64
	for i := 1; i < n; i++ {
		a[i] += a[i-1]
		if a[i-1] < 0 && a[i] <= 0 {
			count += int64(-a[i] + 1)
			a[i] = 1
		} else if a[i-1] > 0 && a[i] >= 0 {
			count += int64(a[i] + 1)
			a[i] = -1
		}
	}

	return count
}