You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 512.0 MB

# Problem
There are $$$n$$$ armchairs, numbered from $$$1$$$ to $$$n$$$ from left to right. Some armchairs are occupied by people (at most one person per armchair), others are not. The number of occupied armchairs is not greater than $$$\frac{n}{2}$$$.

For some reason, you would like to tell people to move from their armchairs to some other ones. If the $$$i$$$-th armchair is occupied by someone and the $$$j$$$-th armchair is not, you can tell the person sitting in the $$$i$$$-th armchair to move to the $$$j$$$-th armchair. The time it takes a person to move from the $$$i$$$-th armchair to the $$$j$$$-th one is $$$|i - j|$$$ minutes. You may perform this operation any number of times, but these operations must be done sequentially, i. e. you cannot tell a person to move until the person you asked to move in the last operation has finished moving to their destination armchair.

You want to achieve the following situation: every seat that was initially occupied must be free. What is the minimum time you need to do it?

## Input Format
The first line contains one integer $$$n$$$ ($$$2 \le n \le 5000$$$) — the number of armchairs.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 1$$$). $$$a_i = 1$$$ means that the $$$i$$$-th armchair is initially occupied, $$$a_i = 0$$$ means that it is initially free. The number of occupied armchairs is at most $$$\frac{n}{2}$$$.

## Output Format
Print one integer — the minimum number of minutes you have to spend to achieve the following situation: every seat that was initially occupied must be free.

## Examples
```input
7
1 0 0 1 0 0 1
```
```output
3
```
-----
```input
6
1 1 1 0 0 0
```
```output
9
```
-----
```input
5
0 0 0 0 0
```
```output
0
```

## Note
In the first test, you can perform the following sequence:

1. ask a person to move from armchair $$$1$$$ to armchair $$$2$$$, it takes $$$1$$$ minute;
2. ask a person to move from armchair $$$7$$$ to armchair $$$6$$$, it takes $$$1$$$ minute;
3. ask a person to move from armchair $$$4$$$ to armchair $$$5$$$, it takes $$$1$$$ minute.

In the second test, you can perform the following sequence:

1. ask a person to move from armchair $$$1$$$ to armchair $$$4$$$, it takes $$$3$$$ minutes;
2. ask a person to move from armchair $$$2$$$ to armchair $$$6$$$, it takes $$$4$$$ minutes;
3. ask a person to move from armchair $$$4$$$ to armchair $$$5$$$, it takes $$$1$$$ minute;
4. ask a person to move from armchair $$$3$$$ to armchair $$$4$$$, it takes $$$1$$$ minute.

In the third test, no seat is occupied so your goal is achieved instantly.

Now solve the problem and return the code.