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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0]);
    const A = arg[1].split(" ").map(n=>parseInt(n));
    
    let totalSum = A[0];
    let answer = 0;
    
    for(let i=1; i<N; i++) {
        // 累積和が＋かつ、A[i]を足しても＋
        while(totalSum >= 0 && totalSum + A[i] >= 0) {
            A[i]--;
            answer++;
        }
        
        // 累積和が-かつ、A[i]を足しても-
        while(totalSum <= 0 && totalSum + A[i] <= 0) {
            A[i]++;
            answer++;
        }
        
        totalSum += A[i];
    }
    
    console.log(answer);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));