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)

//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
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 run() {
    input! {
        n: usize,
        a: [i64; n],
    }
    let mut s = a.clone();
    for i in 1..n {
        s[i] += s[i - 1];
    }
    let a = s;
    let mut ans = std::i64::MAX;
    let mut sum = 0i64;
    let mut add = 0i64;
    if a[0] <= 0 {
        let d = -a[0] + 1;
        add += d;
        sum += d;
    }
    // + - + -
    for i in 1..n {
        if i % 2 == 1 {
            if a[i] + add >= 0 {
                let d = a[i] + add + 1;
                add += -d;
                sum += d;
            }
        } else {
            if a[i] + add <= 0 {
                let d = -(a[i] + add) + 1;
                add += d;
                sum += d;
            }
        }
    }
    ans = std::cmp::min(ans, sum);
    let mut sum = 0i64;
    let mut add = 0i64;
    if a[0] >= 0 {
        let d = a[0] + 1;
        add += -d;
        sum += d;
    }
    // - + -
    for i in 1..n {
        if i % 2 == 0 {
            if a[i] + add >= 0 {
                let d = a[i] + add + 1;
                add += -d;
                sum += d;
            }
        } else {
            if a[i] + add <= 0 {
                let d = -(a[i] + add) + 1;
                add += d;
                sum += d;
            }
        }
    }
    ans = std::cmp::min(ans, sum);
    println!("{}", ans);
}

fn main() {
    run();
}