<system>
You are an experienced Python developer. You will be provided with an incorrect Python program. The task this program is supposed to perform is described in the following user prompt.
Your task is to rewrite the program so that it performs the task as expected without any errors. You will be rewarded based on the number of test cases your code passes.
</system>

<user>
## Description

The ant is a 3D robot consisting of one torso (free rotational body) with
four legs attached to it with each leg having two body parts. The goal is to
coordinate the four legs to move in the forward (right) direction by applying
torques on the eight hinges connecting the two body parts of each leg and the torso
(nine body parts and eight hinges).

## Action Space
The action space is a `Box(-1, 1, (8,), float32)`. An action represents the torques applied at the hinge joints.

| Num | Action                                                            | Control Min | Control Max | Name (in corresponding XML file) | Joint | Unit         |
| --- | ----------------------------------------------------------------- | ----------- | ----------- | -------------------------------- | ----- | ------------ |
| 0   | Torque applied on the rotor between the torso and back right hip  | -1          | 1           | hip_4 (right_back_leg)           | hinge | torque (N m) |
| 1   | Torque applied on the rotor between the back right two links      | -1          | 1           | angle_4 (right_back_leg)         | hinge | torque (N m) |
| 2   | Torque applied on the rotor between the torso and front left hip  | -1          | 1           | hip_1 (front_left_leg)           | hinge | torque (N m) |
| 3   | Torque applied on the rotor between the front left two links      | -1          | 1           | angle_1 (front_left_leg)         | hinge | torque (N m) |
| 4   | Torque applied on the rotor between the torso and front right hip | -1          | 1           | hip_2 (front_right_leg)          | hinge | torque (N m) |
| 5   | Torque applied on the rotor between the front right two links     | -1          | 1           | angle_2 (front_right_leg)        | hinge | torque (N m) |
| 6   | Torque applied on the rotor between the torso and back left hip   | -1          | 1           | hip_3 (back_leg)                 | hinge | torque (N m) |
| 7   | Torque applied on the rotor between the back left two links       | -1          | 1           | angle_3 (back_leg)               | hinge | torque (N m) |

## Observation Space
Observations consist of positional values of different body parts of the ant,
followed by the velocities of those individual parts (their derivatives) with all
the positions ordered before all the velocities.

By default, observations do not include the x- and y-coordinates of the ant's torso. These may
be included by passing `exclude_current_positions_from_observation=False` during construction.
In that case, the observation space will be a `Box(-Inf, Inf, (29,), float64)` where the first two observations
represent the x- and y- coordinates of the ant's torso.
Regardless of whether `exclude_current_positions_from_observation` was set to true or false, the x- and y-coordinates
of the torso will be returned in `info` with keys `"x_position"` and `"y_position"`, respectively.

However, by default, observation Space is a `Box(-Inf, Inf, (27,), float64)` where the elements correspond to the following:

| Num | Observation                                                  | Min    | Max    | Name (in corresponding XML file)       | Joint | Unit                     |
|-----|--------------------------------------------------------------|--------|--------|----------------------------------------|-------|--------------------------|
| 0   | z-coordinate of the torso (centre)                           | -Inf   | Inf    | torso                                  | free  | position (m)             |
| 1   | x-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
| 2   | y-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
| 3   | z-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
| 4   | w-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
| 5   | angle between torso and first link on front left             | -Inf   | Inf    | hip_1 (front_left_leg)                 | hinge | angle (rad)              |
| 6   | angle between the two links on the front left                | -Inf   | Inf    | ankle_1 (front_left_leg)               | hinge | angle (rad)              |
| 7   | angle between torso and first link on front right            | -Inf   | Inf    | hip_2 (front_right_leg)                | hinge | angle (rad)              |
| 8   | angle between the two links on the front right               | -Inf   | Inf    | ankle_2 (front_right_leg)              | hinge | angle (rad)              |
| 9   | angle between torso and first link on back left              | -Inf   | Inf    | hip_3 (back_leg)                       | hinge | angle (rad)              |
| 10  | angle between the two links on the back left                 | -Inf   | Inf    | ankle_3 (back_leg)                     | hinge | angle (rad)              |
| 11  | angle between torso and first link on back right             | -Inf   | Inf    | hip_4 (right_back_leg)                 | hinge | angle (rad)              |
| 12  | angle between the two links on the back right                | -Inf   | Inf    | ankle_4 (right_back_leg)               | hinge | angle (rad)              |
| 13  | x-coordinate velocity of the torso                           | -Inf   | Inf    | torso                                  | free  | velocity (m/s)           |
| 14  | y-coordinate velocity of the torso                           | -Inf   | Inf    | torso                                  | free  | velocity (m/s)           |
| 15  | z-coordinate velocity of the torso                           | -Inf   | Inf    | torso                                  | free  | velocity (m/s)           |
| 16  | x-coordinate angular velocity of the torso                   | -Inf   | Inf    | torso                                  | free  | angular velocity (rad/s) |
| 17  | y-coordinate angular velocity of the torso                   | -Inf   | Inf    | torso                                  | free  | angular velocity (rad/s) |
| 18  | z-coordinate angular velocity of the torso                   | -Inf   | Inf    | torso                                  | free  | angular velocity (rad/s) |
| 19  | angular velocity of angle between torso and front left link  | -Inf   | Inf    | hip_1 (front_left_leg)                 | hinge | angle (rad)              |
| 20  | angular velocity of the angle between front left links       | -Inf   | Inf    | ankle_1 (front_left_leg)               | hinge | angle (rad)              |
| 21  | angular velocity of angle between torso and front right link | -Inf   | Inf    | hip_2 (front_right_leg)                | hinge | angle (rad)              |
| 22  | angular velocity of the angle between front right links      | -Inf   | Inf    | ankle_2 (front_right_leg)              | hinge | angle (rad)              |
| 23  | angular velocity of angle between torso and back left link   | -Inf   | Inf    | hip_3 (back_leg)                       | hinge | angle (rad)              |
| 24  | angular velocity of the angle between back left links        | -Inf   | Inf    | ankle_3 (back_leg)                     | hinge | angle (rad)              |
| 25  | angular velocity of angle between torso and back right link  | -Inf   | Inf    | hip_4 (right_back_leg)                 | hinge | angle (rad)              |
| 26  | angular velocity of the angle between back right links       | -Inf   | Inf    | ankle_4 (right_back_leg)               | hinge | angle (rad)              |
| excluded | x-coordinate of the torso (centre)                      | -Inf   | Inf    | torso                                  | free  | position (m)             |
| excluded | y-coordinate of the torso (centre)                      | -Inf   | Inf    | torso                                  | free  | position (m)             |


If version < `v4` or `use_contact_forces` is `True` then the observation space is extended by 14*6 = 84 elements, which are contact forces
(external forces - force x, y, z and torque x, y, z) applied to the
center of mass of each of the body parts. The 14 body parts are:

| id (for `v2`, `v3`, `v4)` | body parts |
|  ---  |  ------------  |
| 0  | worldbody (note: forces are always full of zeros) |
| 1  | torso |
| 2  | front_left_leg |
| 3  | aux_1 (front left leg) |
| 4  | ankle_1 (front left leg) |
| 5  | front_right_leg |
| 6  | aux_2 (front right leg) |
| 7  | ankle_2 (front right leg) |
| 8  | back_leg (back left leg) |
| 9  | aux_3 (back left leg) |
| 10 | ankle_3 (back left leg) |
| 11 | right_back_leg |
| 12 | aux_4 (back right leg) |
| 13 | ankle_4 (back right leg) |


The (x,y,z) coordinates are translational DOFs while the orientations are rotational
DOFs expressed as quaternions. One can read more about free joints on the [Mujoco Documentation](https://mujoco.readthedocs.io/en/latest/XMLreference.html).


**Note:** Ant-v4 environment no longer has the following contact forces issue.
If using previous Humanoid versions from v4, there have been reported issues that using a Mujoco-Py version > 2.0 results
in the contact forces always being 0. As such we recommend to use a Mujoco-Py version < 2.0
when using the Ant environment if you would like to report results with contact forces (if
contact forces are not used in your experiments, you can use version > 2.0).

## Rewards
The reward consists of three parts:
- *healthy_reward*: Every timestep that the ant is healthy (see definition in section "Episode Termination"), it gets a reward of fixed value `healthy_reward`
- *forward_reward*: A reward of moving forward which is measured as
*(x-coordinate before action - x-coordinate after action)/dt*. *dt* is the time
between actions and is dependent on the `frame_skip` parameter (default is 5),
where the frametime is 0.01 - making the default *dt = 5 * 0.01 = 0.05*.
This reward would be positive if the ant moves forward (in positive x direction).
- *ctrl_cost*: A negative reward for penalising the ant if it takes actions
that are too large. It is measured as *`ctrl_cost_weight` * sum(action<sup>2</sup>)*
where *`ctr_cost_weight`* is a parameter set for the control and has a default value of 0.5.
- *contact_cost*: A negative reward for penalising the ant if the external contact
force is too large. It is calculated *`contact_cost_weight` * sum(clip(external contact
force to `contact_force_range`)<sup>2</sup>)*.

The total reward returned is ***reward*** *=* *healthy_reward + forward_reward - ctrl_cost*.

But if `use_contact_forces=True` or version < `v4`
The total reward returned is ***reward*** *=* *healthy_reward + forward_reward - ctrl_cost - contact_cost*.

In either case `info` will also contain the individual reward terms.

## Starting State
All observations start in state
(0.0, 0.0,  0.75, 1.0, 0.0  ... 0.0) with a uniform noise in the range
of [-`reset_noise_scale`, `reset_noise_scale`] added to the positional values and standard normal noise
with mean 0 and standard deviation `reset_noise_scale` added to the velocity values for
stochasticity. Note that the initial z coordinate is intentionally selected
to be slightly high, thereby indicating a standing up ant. The initial orientation
is designed to make it face forward as well.

## Episode End
The ant is said to be unhealthy if any of the following happens:

1. Any of the state space values is no longer finite
2. The z-coordinate of the torso is **not** in the closed interval given by `healthy_z_range` (defaults to [0.2, 1.0])

If `terminate_when_unhealthy=True` is passed during construction (which is the default),
the episode ends when any of the following happens:

1. Truncation: The episode duration reaches a 1000 timesteps
2. Termination: The ant is unhealthy

If `terminate_when_unhealthy=False` is passed, the episode is ended only when 1000 timesteps are exceeded.

## Class Definition
The class should be called "Environment". It should have at least:

- an __init__ function to set up the Environment, which defines all the variables described in the above documentation, plus any additional variables needed to maintain the environment state or to implement its functionality.
- a set_state function to set a custom value for the environment and its internal representation (you can assume that when "set_state" is used, the task is not done and internal variables should be set as a consequence). set_state takes a single argument as input: a state observation from the observation space defined above.
- a step function to predict a step in the environment. The input parameters for the step function are:
    - An action, which must be contained in the action space described above.
  
    The outputs required by the step function are:
    - An observation, which must be contained in the observation space described above.
    - The reward for taking the action, as described in the reward definition above.
    - A boolean variable indicating if the episode is done.

## Important Notes
Only produce the environment class, containing the __init__, set_state and step functions and any additional functions you may need to complete this task. Do not write an example of how to use the class or anything else.
Be careful about edge cases.
Make sure to write all the required functions and that they have the exact names as specified in the task description. Missing or incorrectly named functions will not pass the tests and will result in a score of 0.
It is of VITAL importance that you do not leave undefined any function, but implement each of them completely.
Output the FULL corrected program in its entirety and NOTHING ELSE.

First, write an explanation of the error and point out the part of the code responsible for the error and why its logic is erroneous.
Second, suggest how you would fix the error, reasoning about the problem.
Finally fix the program in its entirety following the suggestion. The expected output is in the format:

## Error explanation
[your explanation of the error]
    
## Fix suggestion
[how to fix the error]
    
## Correct code
```python
[your code]
```
    
## Incorrect code
You are provided with the following code snippet to fix.
```python
{CODE}
```
    
{ERROR}

</user>

<assistant>
## Error explanation
</assistant>