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

func main() {
	n := getInt()

	as := make([]int, n)
	for i := range as {
		as[i] = getInt()
	}

	ans1 := solve(as, 1)
	ans2 := solve(as, 0)

	fmt.Println(min(ans1, ans2))
}

func solve(as []int, r int) int {
	ans := 0
	sum := 0
	for i, a := range as {
		if i%2 == r {
			if sum+a <= 0 {
				ans += abs(sum+a) + 1
				sum = 1
			} else {
				sum += a
			}
		} else {
			if sum+a >= 0 {
				ans += abs(sum+a) + 1
				sum = -1
			} else {
				sum += a
			}
		}
	}
	return ans
}

func abs(n int) int {
	if n < 0 {
		return -n
	}
	return n
}

func min(ns ...int) int {
	min := ns[0]
	for i := 1; i < len(ns); i++ {
		if min > ns[i] {
			min = ns[i]
		}
	}
	return min
}

// -----------------------------------------

var scanner = wordScanner()

func wordScanner() *bufio.Scanner {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	return sc
}

func getInt() int {
	scanner.Scan()
	i, err := strconv.Atoi(scanner.Text())
	if err != nil {
		panic(err)
	}
	return i
}

func getString() string {
	scanner.Scan()
	s := scanner.Text()
	return s
}