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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func solve(a []int64, ra int) int64 {
	s := int64(0) // S_i = \sum_i a[i]
	ans := int64(0)
	for i, e := range a {
		if i%2 == ra {
			if s+e >= 0 {
				ans += abs(-1 - s - e)
				s = -1
				continue
			}
		} else {
			if s+e <= 0 {
				ans += abs(1 - s - e)
				s = 1
				continue
			}
		}
		s += e
	}
	return ans
}

func abs(x int64) int64 {
	if x < 0 {
		return -x
	}
	return x
}

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

func main() {
	var n int
	fmt.Scan(&n)
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	a := make([]int64, n)
	for i := 0; i < n; i++ {
		sc.Scan()
		x, _ := strconv.Atoi(sc.Text())
		a[i] = int64(x)
	}
	ans := int64(0)
	if a[0] == 0 {
		a[0] = -1
		ans = solve(a, 0)
		a[0] = 1
		ans = min(ans, solve(a, 1))
	} else if a[0] < 0 {
		ans = solve(a, 0)
	} else { // a[0] > 0
		ans = solve(a, 1)
	}
	fmt.Println(ans)
}