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 Rust (1.15.1) (judge verdict: Accepted)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

fn solve(as_: Vec<i64>) -> i64 {
    let mut sum1 = 0;
    let mut sum2 = 0;
    let mut count1 = 0;
    let mut count2 = 0;

    if as_[0] <= 0 {
        count1 = 1 - as_[0];
        sum1 = 1;
    } else {
        sum1 = as_[0];
    }

    if as_[0] >= 0 {
        count2 = 1 + as_[0];
        sum2 = -1;
    } else {
        sum2 = as_[0];
    }

    for i in 1..as_.len() {
        let cur = as_[i];
        if sum1 > 0 {
            if cur + sum1 < 0 {
                sum1 += cur;
            } else {
                let exp = -1 - sum1;
                count1 += cur - exp;
                sum1 = -1;
            }
        } else if sum1 < 0 {
            if cur + sum1 > 0 {
                sum1 += cur;
            } else {
                let exp = 1 - sum1;
                count1 += exp - cur;
                sum1 = 1;
            }
        }
    }

    for i in 1..as_.len() {
        let cur = as_[i];
        if sum2 > 0 {
            if cur + sum2 < 0 {
                sum2 += cur;
            } else {
                let exp = -1 - sum2;
                count2 += cur - exp;
                sum2 = -1;
            }
        } else if sum2 < 0 {
            if cur + sum2 > 0 {
                sum2 += cur;
            } else {
                let exp = 1 - sum2;
                count2 += exp - cur;
                sum2 = 1;
            }
        }
    }
    std::cmp::min(count1, count2)
}

fn main() {
    input!{
        n: usize,
        as_: [i64; n],
    }
    println!("{}", solve(as_));
}