diff --git a/MANIFEST.in b/MANIFEST.in
index 06b1a0ed4..fba54ffcd 100644
--- a/MANIFEST.in
+++ b/MANIFEST.in
@@ -1,4 +1,4 @@
include brax/envs/assets/*.xml
-recursive-include brax/experimental/barkour_v0 *.csv *.stl *.xml
+recursive-include brax/experimental/barkour_vb *.csv *.stl *.xml
recursive-include brax/test_data *.xml *.stl *.obj *.urdf
recursive-include brax/visualizer *
diff --git a/brax/base.py b/brax/base.py
index 2242d9a24..35d22f81d 100644
--- a/brax/base.py
+++ b/brax/base.py
@@ -531,15 +531,15 @@ def qd_idx(self, link_type: str) -> jax.Array:
def q_size(self) -> int:
"""Returns the size of the q vector (joint position) for this system."""
- return sum([Q_WIDTHS[t] for t in self.link_types])
+ return self.nq
def qd_size(self) -> int:
"""Returns the size of the qd vector (joint velocity) for this system."""
- return sum([QD_WIDTHS[t] for t in self.link_types])
+ return self.nv
def act_size(self) -> int:
"""Returns the act dimension for the system."""
- return self.actuator.q_id.shape[0]
+ return self.nu
# below are some operation dispatch derivations
diff --git a/brax/envs/ant.py b/brax/envs/ant.py
index aa6b5eee1..2ff166b01 100644
--- a/brax/envs/ant.py
+++ b/brax/envs/ant.py
@@ -233,6 +233,7 @@ def reset(self, rng: jax.Array) -> State:
def step(self, state: State, action: jax.Array) -> State:
"""Run one timestep of the environment's dynamics."""
pipeline_state0 = state.pipeline_state
+ assert pipeline_state0 is not None
pipeline_state = self.pipeline_step(pipeline_state0, action)
velocity = (pipeline_state.x.pos[0] - pipeline_state0.x.pos[0]) / self.dt
diff --git a/brax/envs/fast.py b/brax/envs/fast.py
index 376df3b3a..f7351b71f 100644
--- a/brax/envs/fast.py
+++ b/brax/envs/fast.py
@@ -43,6 +43,7 @@ def reset(self, rng: jax.Array) -> State:
return State(pipeline_state, obs, reward, done)
def step(self, state: State, action: jax.Array) -> State:
+ assert state.pipeline_state is not None
self._step_count += 1
vel = state.pipeline_state.xd.vel + (action > 0) * self._dt
pos = state.pipeline_state.x.pos + vel * self._dt
diff --git a/brax/envs/half_cheetah.py b/brax/envs/half_cheetah.py
index 527c94e14..e99eba608 100644
--- a/brax/envs/half_cheetah.py
+++ b/brax/envs/half_cheetah.py
@@ -178,6 +178,7 @@ def reset(self, rng: jax.Array) -> State:
def step(self, state: State, action: jax.Array) -> State:
"""Runs one timestep of the environment's dynamics."""
pipeline_state0 = state.pipeline_state
+ assert pipeline_state0 is not None
pipeline_state = self.pipeline_step(pipeline_state0, action)
x_velocity = (
diff --git a/brax/envs/hopper.py b/brax/envs/hopper.py
index 373248546..516a63361 100644
--- a/brax/envs/hopper.py
+++ b/brax/envs/hopper.py
@@ -223,6 +223,7 @@ def reset(self, rng: jax.Array) -> State:
def step(self, state: State, action: jax.Array) -> State:
"""Runs one timestep of the environment's dynamics."""
pipeline_state0 = state.pipeline_state
+ assert pipeline_state0 is not None
pipeline_state = self.pipeline_step(pipeline_state0, action)
x_velocity = (
diff --git a/brax/envs/pusher.py b/brax/envs/pusher.py
index 3abe82f09..e1515d013 100644
--- a/brax/envs/pusher.py
+++ b/brax/envs/pusher.py
@@ -193,6 +193,7 @@ def reset(self, rng: jax.Array) -> State:
return State(pipeline_state, obs, reward, done, metrics)
def step(self, state: State, action: jax.Array) -> State:
+ assert state.pipeline_state is not None
x_i = state.pipeline_state.x.vmap().do(
base.Transform.create(pos=self.sys.link.inertia.transform.pos)
)
diff --git a/brax/envs/walker2d.py b/brax/envs/walker2d.py
index d0950e33d..54379e637 100644
--- a/brax/envs/walker2d.py
+++ b/brax/envs/walker2d.py
@@ -203,6 +203,7 @@ def reset(self, rng: jax.Array) -> State:
def step(self, state: State, action: jax.Array) -> State:
"""Runs one timestep of the environment's dynamics."""
pipeline_state0 = state.pipeline_state
+ assert pipeline_state0 is not None
pipeline_state = self.pipeline_step(pipeline_state0, action)
x_velocity = (
diff --git a/brax/experimental/barkour_v0/README.md b/brax/experimental/barkour_v0/README.md
deleted file mode 100644
index a2a11cdcc..000000000
--- a/brax/experimental/barkour_v0/README.md
+++ /dev/null
@@ -1,66 +0,0 @@
-# Google Barkour v0 Joystick Policy
-
-## Overview
-
-NOTE: For an up-to-date version of Brax training for a quadruped robot with best results, please look at the [MJX colab tutorial](https://colab.research.google.com/github/google-deepmind/mujoco/blob/main/mjx/tutorial.ipynb). The environment in this folder uses an older version of the joystick policy training, which exhibited policies with high variance across seeds.
-
-This folder contains a training script for a flat-terrain joystick policy for the [Barkour v0 Quadruped](https://ai.googleblog.com/2023/05/barkour-benchmarking-animal-level.html) which demonstrates sim2real transfer.
-
-`barkour_joystick.py` contains the environment definition, while the [colab](https://colab.research.google.com/github/google/brax/blob/main/brax/experimental/barkour_v0/barkour_v0_joystick.ipynb) shows how to train the policy.
-
-
-
-
-
-## Running the environment
-
-We encourage the usage of the [colab](https://colab.research.google.com/github/google/brax/blob/main/brax/experimental/barkour_v0/barkour_v0_joystick.ipynb) for viewing and training policies. However, the environment can be loaded as follows:
-
-```python
-import jax
-from jax import numpy as jp
-
-from brax import envs
-from brax.experimental.barkour_v0 import barkour_joystick
-
-barkour_env = envs.create('barkour_v0_joystick', backend='generalized')
-```
-
-And to step through the environment:
-
-```python
-jit_env_reset = jax.jit(barkour_env.reset)
-jit_env_step = jax.jit(barkour_env.step)
-
-state = jit_env_reset(jax.random.PRNGKey(0))
-
-rollout = []
-for i in range(500):
- act = jp.sin(i / 500) * jp.ones(barkour_env.sys.act_size())
- state = jit_env_step(state, act)
- rollout.append(state)
-```
-
-## MJCF Instructions
-
-The MuJoCo config in `assets/barkour_v0_brax.xml` was copied from [MuJoCo Menagerie](https://github.com/google-deepmind/mujoco_menagerie/tree/main/google_barkour_v0). The following edits were made to the MJCF specifically for brax:
-
-* `meshdir` was changed from `assets` to `.`.
-* `frictionloss` was removed. `damping` was changed to 0.5239.
-* A custom `init_qpos` was added.
-* A sphere geom `lowerLegFoot` was added to all feet. All other contacts were turned off.
-* The compiler option was changed to ``.
-* Non-visual geoms were removed from the torso, to speed up rendering.
-
-## Publications
-
-If you use this work in an academic context, please cite the following publication:
-
- @misc{caluwaerts2023barkour,
- title={Barkour: Benchmarking Animal-level Agility with Quadruped Robots},
- author={Ken Caluwaerts and Atil Iscen and J. Chase Kew and Wenhao Yu and Tingnan Zhang and Daniel Freeman and Kuang-Huei Lee and Lisa Lee and Stefano Saliceti and Vincent Zhuang and Nathan Batchelor and Steven Bohez and Federico Casarini and Jose Enrique Chen and Omar Cortes and Erwin Coumans and Adil Dostmohamed and Gabriel Dulac-Arnold and Alejandro Escontrela and Erik Frey and Roland Hafner and Deepali Jain and Bauyrjan Jyenis and Yuheng Kuang and Edward Lee and Linda Luu and Ofir Nachum and Ken Oslund and Jason Powell and Diego Reyes and Francesco Romano and Feresteh Sadeghi and Ron Sloat and Baruch Tabanpour and Daniel Zheng and Michael Neunert and Raia Hadsell and Nicolas Heess and Francesco Nori and Jeff Seto and Carolina Parada and Vikas Sindhwani and Vincent Vanhoucke and Jie Tan},
- year={2023},
- eprint={2305.14654},
- archivePrefix={arXiv},
- primaryClass={cs.RO}
- }
\ No newline at end of file
diff --git a/brax/experimental/barkour_v0/assets/abduction.stl b/brax/experimental/barkour_v0/assets/abduction.stl
deleted file mode 100644
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diff --git a/brax/experimental/barkour_v0/assets/barkour_v0_brax.xml b/brax/experimental/barkour_v0/assets/barkour_v0_brax.xml
deleted file mode 100644
index 37ba6ddf9..000000000
--- a/brax/experimental/barkour_v0/assets/barkour_v0_brax.xml
+++ /dev/null
@@ -1,241 +0,0 @@
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diff --git a/brax/experimental/barkour_v0/assets/body.stl b/brax/experimental/barkour_v0/assets/body.stl
deleted file mode 100644
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deleted file mode 100644
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diff --git a/brax/experimental/barkour_v0/barkour_joystick.py b/brax/experimental/barkour_v0/barkour_joystick.py
deleted file mode 100644
index 2da833bc7..000000000
--- a/brax/experimental/barkour_v0/barkour_joystick.py
+++ /dev/null
@@ -1,522 +0,0 @@
-# Copyright 2024 DeepMind Technologies Limited.
-#
-# Licensed under the Apache License, Version 2.0 (the "License");
-# you may not use this file except in compliance with the License.
-# You may obtain a copy of the License at
-#
-# http://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing, software
-# distributed under the License is distributed on an "AS IS" BASIS,
-# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-# See the License for the specific language governing permissions and
-# limitations under the License.
-
-"""Barkour v0 brax environment for flat-terrain joystick policy training."""
-
-from brax import actuator
-from brax import base
-from brax import envs
-from brax import math
-import brax.envs.base as env
-from brax.io import mjcf
-from etils import epath
-import jax
-import jax.numpy as jp
-from ml_collections import config_dict
-
-
-def get_config():
- """Returns reward config."""
-
- def get_default_rewards_config():
- default_config = config_dict.ConfigDict(
- dict(
- # The coefficients for all reward terms used for training. All
- # physical quantities are in SI units, if no otherwise specified,
- # i.e. joint positions are in rad, positions are measured in meters,
- # torques in Nm, and time in seconds, and forces in Newtons.
- scales=config_dict.ConfigDict(
- dict(
- # Tracking rewards are computed using exp(-delta^2/sigma)
- # sigma can be a hyperparameters to tune.
- # Track the base x-y velocity (no z-velocity tracking.)
- tracking_lin_vel=1.5,
- # Track the angular velocity along z-axis, i.e. yaw rate.
- tracking_ang_vel=0.8,
- # Below are regularization terms, we roughly divide the
- # terms to base state regularizations, joint
- # regularizations, and other behavior regularizations.
- # Penalize the base velocity in z direction, L2 penalty.
- lin_vel_z=-2.0,
- # Penalize the base roll and pitch rate. L2 penalty.
- ang_vel_xy=-0.05,
- # Penalize non-zero roll and pitch angles. L2 penalty.
- orientation=-5.0,
- # L2 regularization of joint torques, |tau|^2.
- torques=-0.0002,
- # Penalize the change in the action and encourage smooth
- # actions. L2 regularization |action - last_action|^2
- action_rate=-0.2,
- # Encourage long swing steps. However, it does not
- # encourage high clearances.
- feet_air_time=0.1,
- # Encourage no motion at zero command, L2 regularization
- # |q - q_default|^2.
- stand_still=-0.5,
- # Early termination penalty.
- termination=-1.0,
- # Penalizing foot slipping on the ground.
- foot_slip=-0.1,
- )
- ),
- # Tracking reward = exp(-error^2/sigma).
- tracking_sigma=0.25,
- )
- )
- return default_config
-
- default_config = config_dict.ConfigDict(
- dict(rewards=get_default_rewards_config(),))
-
- return default_config
-
-
-class Barkourv0(env.PipelineEnv):
- """Environment for training the barkour quadruped joystick policy.
-
- This environment demonstrates training the joystick policy as seen in
- https://arxiv.org/abs/2305.14654. A command [x, y, w] is chosen upon reset,
- where x/y are the target linear velocities and w is that target angular
- velocity in the +z direction. The `tracking_lin_vel` and
- `tracking_ang_vel` rewards make sure the robot follows these joystick
- commands. The other rewards regularize the policy such that walking gaits
- are smooth and show better transfer to real.
- """
-
- def __init__(
- self,
- obs_noise: float = 0.05,
- kick_vel=0.05,
- action_scale=0.3,
- backend: str = 'generalized',
- debug=False,
- **kwargs,
- ):
- if backend != 'generalized':
- raise NotImplementedError(
- 'Only generalized backend is supported for barkour.'
- )
-
- n_frames = 10
- path = epath.Path(epath.resource_path('brax')) / (
- 'experimental/barkour_v0/assets/barkour_v0_brax.xml'
- )
- sys = mjcf.load(path)
-
- kwargs['n_frames'] = kwargs.get('n_frames', n_frames)
- kwargs['debug'] = kwargs.get('debug', debug)
- super().__init__(sys=sys, backend=backend, **kwargs)
-
- self._action_scale = action_scale
- self._obs_noise = obs_noise
- self._kick_vel = kick_vel
- self._default_ap_pose = sys.init_q[7:19]
- self.reward_config = get_config()
- self.torso_idx = self.sys.link_names.index('chassis')
- self.lowers = self._default_ap_pose - jp.array([0.2, 0.8, 0.8] * 4)
- self.uppers = self._default_ap_pose + jp.array([0.2, 0.8, 0.8] * 4)
-
- def sample_command(self, rng: jax.Array) -> jax.Array:
- lin_vel_x = [-0.6, 1.5] # min max [m/s]
- lin_vel_y = [-0.8, 0.8] # min max [m/s]
- ang_vel_yaw = [-0.7, 0.7] # min max [rad/s]
-
- _, key1, key2, key3 = jax.random.split(rng, 4)
- lin_vel_x = jax.random.uniform(
- key1, (1,), minval=lin_vel_x[0], maxval=lin_vel_x[1]
- )
- lin_vel_y = jax.random.uniform(
- key2, (1,), minval=lin_vel_y[0], maxval=lin_vel_y[1]
- )
- ang_vel_yaw = jax.random.uniform(
- key3, (1,), minval=ang_vel_yaw[0], maxval=ang_vel_yaw[1]
- )
- new_cmd = jp.array([lin_vel_x[0], lin_vel_y[0], ang_vel_yaw[0]])
-
- return new_cmd
-
- def reset(self, rng: jax.Array) -> env.State:
- rng, key = jax.random.split(rng)
-
- q = self.sys.init_q
- qd = jp.zeros(self.sys.qd_size())
- new_cmd = self.sample_command(key)
- pipeline_state = self.pipeline_init(q, qd)
-
- state_info = {
- 'rng': rng,
- 'last_act': jp.zeros(12),
- 'last_vel': jp.zeros(12),
- 'last_contact_buffer': jp.zeros((20, 4), dtype=bool),
- 'command': new_cmd,
- 'last_contact': jp.zeros(4, dtype=bool),
- 'feet_air_time': jp.zeros(4),
- 'obs_history': jp.zeros(15 * 31),
- 'rew_tuple': {
- 'tracking_lin_vel': 0.0,
- 'tracking_ang_vel': 0.0,
- 'lin_vel_z': 0.0,
- 'ang_vel_xy': 0.0,
- 'orientation': 0.0,
- 'torque': 0.0,
- 'action_rate': 0.0,
- 'stand_still': 0.0,
- 'feet_air_time': 0.0,
- 'foot_slip': 0.0,
- },
- 'step': 0,
- 'kick': jp.array([0.0, 0.0]),
- }
-
- obs = self._get_obs(pipeline_state, state_info)
- reward, done = jp.zeros(2)
- metrics = {'total_dist': 0.0}
- for k in state_info['rew_tuple']:
- metrics[k] = state_info['rew_tuple'][k]
- state = env.State(pipeline_state, obs, reward, done, metrics, state_info) # pytype: disable=wrong-arg-types
- return state
-
- def step(self, state: env.State, action: jax.Array) -> env.State:
- rng, rng_noise, cmd_rng, kick_noise_2 = jax.random.split(
- state.info['rng'], 4
- )
-
- # kick
- push_interval = 100
- kick_theta = jax.random.uniform(kick_noise_2, minval=0.0, maxval=2 * jp.pi)
- state.info['kick'] = jp.where(
- state.info['step'] > push_interval,
- jp.array([jp.cos(kick_theta), jp.sin(kick_theta)]),
- jp.array([0.0, 0.0]),
- )
- state = state.tree_replace(
- {
- 'pipeline_state.qd': state.pipeline_state.qd.at[:2].set(
- state.info['kick'] * self._kick_vel
- + state.pipeline_state.qd[:2] # pytype: disable=attribute-error
- )
- }
- )
-
- # physics step
- cur_action = jp.array(action)
- action = action[:12] * self._action_scale
- motor_targets = jp.clip(
- action + self._default_ap_pose, self.lowers, self.uppers
- )
- pipeline_state = self.pipeline_step(state.pipeline_state, motor_targets)
-
- # observation data
- obs = self._get_obs(pipeline_state, state.info)
- obs_noise = self._obs_noise * jax.random.uniform(
- rng_noise, obs.shape, minval=-1, maxval=1)
- q, qd = pipeline_state.q, pipeline_state.qd
- joint_angles = q[7:]
- joint_vel = qd[6:]
- default_angles = self._default_ap_pose
- torque = actuator.to_tau(self.sys, action, q, qd)
-
- # foot contact data
- foot_contact = 0.017 - self._get_feet_pos_vel(pipeline_state)[0][:, 2]
- contact = foot_contact > -1e-3 # a mm or less off the floor
- contact_filt_mm = jp.logical_or(contact, state.info['last_contact'])
- contact_filt_cm = jp.logical_or(
- foot_contact > -1e-2, state.info['last_contact']
- )
- first_contact = (state.info['feet_air_time'] > 0) * (contact_filt_mm)
- state.info['feet_air_time'] += self.dt
-
- # reward
- qp = pipeline_state
- rew_tuple = {
- 'tracking_lin_vel': (
- self._reward_tracking_lin_vel(state.info['command'], qp)
- * self.reward_config.rewards.scales.tracking_lin_vel
- ),
- 'tracking_ang_vel': (
- self._reward_tracking_ang_vel(state.info['command'], qp)
- * self.reward_config.rewards.scales.tracking_ang_vel
- ),
- 'lin_vel_z': (
- self._reward_lin_vel_z(qp)
- * self.reward_config.rewards.scales.lin_vel_z
- ),
- 'ang_vel_xy': (
- self._reward_ang_vel_xy(qp)
- * self.reward_config.rewards.scales.ang_vel_xy
- ),
- 'orientation': (
- self._reward_orientation(qp)
- * self.reward_config.rewards.scales.orientation
- ),
- 'torque': (
- self._reward_torques(torque)
- * self.reward_config.rewards.scales.torques
- ),
- 'action_rate': (
- self._reward_action_rate(cur_action, state.info['last_act'])
- * self.reward_config.rewards.scales.action_rate
- ),
- 'stand_still': (
- self._reward_stand_still(
- state.info['command'], joint_angles, default_angles
- )
- * self.reward_config.rewards.scales.stand_still
- ),
- 'feet_air_time': (
- self._reward_feet_air_time(
- state.info['feet_air_time'],
- first_contact,
- state.info['command'],
- )
- * self.reward_config.rewards.scales.feet_air_time
- ),
- 'foot_slip': (
- self._reward_foot_slip(qp, contact_filt_cm)
- * self.reward_config.rewards.scales.foot_slip
- ),
- }
- rew = (
- rew_tuple['tracking_lin_vel']
- + rew_tuple['tracking_ang_vel']
- + rew_tuple['orientation']
- + rew_tuple['ang_vel_xy']
- + rew_tuple['lin_vel_z']
- + rew_tuple['torque']
- + rew_tuple['action_rate']
- + rew_tuple['stand_still']
- + rew_tuple['feet_air_time']
- + rew_tuple['foot_slip']
- )
-
- reward = jp.clip(rew * self.dt, 0.0, 10000.0)
-
- # state management
- state.info['last_act'] = cur_action
- state.info['last_vel'] = joint_vel
- state.info['feet_air_time'] *= ~contact_filt_mm
- state.info['last_contact'] = contact
- state.info['last_contact_buffer'] = jp.roll(
- state.info['last_contact_buffer'], 1, axis=0
- )
- state.info['last_contact_buffer'] = (
- state.info['last_contact_buffer'].at[0].set(contact)
- )
- state.info['rew_tuple'] = rew_tuple
- state.info['step'] += 1
- state.info.update(rng=rng)
-
- # resetting logic if joint limits are reached or robot is falling
- done = 0.0
- up = jp.array([0.0, 0.0, 1.0])
- done = jp.where(jp.dot(math.rotate(up, qp.x.rot[0]), up) < 0, 1.0, done)
- done = jp.where(jp.logical_or(
- jp.any(joint_angles < .98 * self.lowers),
- jp.any(joint_angles > .98 * self.uppers)), 1.0, done)
- done = jp.where(qp.x.pos[self.torso_idx, 2] < 0.18, 1.0, done)
-
- # termination reward
- reward += jp.where(
- (done == 1.0) & (state.info['step'] < 500),
- self.reward_config.rewards.scales.termination,
- 0.0,
- )
-
- # when done, reset step counter and sample new command
- state.info['command'] = jp.where(
- (done == 1.0) & (state.info['step'] > 500),
- self.sample_command(cmd_rng), state.info['command'])
- state.info['step'] = jp.where(
- (done == 1.0) | (state.info['step'] > 500), 0, state.info['step']
- )
-
- # log total displacement as a proxy metric
- state.metrics['total_dist'] = math.normalize(qp.x.pos[self.torso_idx])[1]
- for k in state.info['rew_tuple'].keys(): # pytype: disable=attribute-error
- state.metrics[k] = state.info['rew_tuple'][k]
-
- state = state.replace(
- pipeline_state=pipeline_state, obs=obs + obs_noise, reward=reward,
- done=done)
- return state
-
- def _get_obs(self, pipeline_state, state_info) -> jax.Array:
- # Get observations:
- # yaw_rate, projected_gravity, command, motor_angles, last_action
- x, xd = pipeline_state.x, pipeline_state.xd
-
- inv_base_orientation = math.quat_inv(x.rot[0])
- local_rpyrate = math.rotate(xd.ang[0], inv_base_orientation)
- cmd = state_info['command']
-
- obs_list = []
- # yaw rate
- obs_list.append(jp.array([local_rpyrate[2]]) * 0.25)
- # projected gravity
- obs_list.append(
- math.rotate(jp.array([0.0, 0.0, -1.0]), inv_base_orientation))
- # command
- obs_list.append(cmd * jp.array([2.0, 2.0, 0.25]))
- # motor angles
- angles = pipeline_state.q[7:19]
- obs_list.append(angles - self._default_ap_pose)
- # last action
- obs_list.append(state_info['last_act'])
-
- obs = jp.clip(jp.concatenate(obs_list), -100.0, 100.0)
-
- # stack observations through time
- single_obs_size = len(obs)
- state_info['obs_history'] = jp.roll(
- state_info['obs_history'], single_obs_size
- )
- state_info['obs_history'] = jp.array(
- state_info['obs_history']).at[:single_obs_size].set(obs)
- return state_info['obs_history']
-
- # ------------ reward functions----------------
- def _reward_lin_vel_z(self, qp):
- # Penalize z axis base linear velocity
- return jp.square(qp.xd.vel[0, 2])
-
- def _reward_ang_vel_xy(self, qp):
- # Penalize xy axes base angular velocity
- return jp.sum(jp.square(qp.xd.ang[0, :2]))
-
- def _reward_orientation(self, qp):
- # Penalize non flat base orientation
- up = jp.array([0.0, 0.0, 1.0])
- rot_up = math.rotate(up, qp.x.rot[0])
- return jp.sum(jp.square(rot_up[:2]))
-
- def _reward_orientation2(self, qp):
- # Reward flat base orientation
- up = jp.array([0.0, 0.0, 1.0])
- rot_up = math.rotate(up, qp.x.rot[0])
- return jp.sum(rot_up[2])
-
- def _reward_torques(self, torques):
- # Penalize torques
- # return jp.sum(jp.square(torques))
- return jp.sqrt(jp.sum(jp.square(torques))) + jp.sum(jp.abs(torques))
-
- def _reward_action_rate(self, act, last_act):
- # Penalize changes in actions
- return jp.sum(jp.square(act - last_act))
-
- def _reward_tracking_lin_vel(self, commands, qp):
- # Tracking of linear velocity commands (xy axes)
- local_vel = math.rotate(qp.xd.vel[0], math.quat_inv(qp.x.rot[0]))
- lin_vel_error = jp.sum(jp.square(commands[:2] - local_vel[:2]))
- lin_vel_reward = jp.exp(
- -lin_vel_error / self.reward_config.rewards.tracking_sigma
- )
- return lin_vel_reward
-
- def _reward_tracking_ang_vel(self, commands, qp):
- # Tracking of angular velocity commands (yaw)
- base_ang_vel = math.rotate(qp.xd.ang[0], math.quat_inv(qp.x.rot[0]))
- ang_vel_error = jp.square(commands[2] - base_ang_vel[2])
- return jp.exp(-ang_vel_error/self.reward_config.rewards.tracking_sigma)
-
- def _reward_feet_air_time(self, air_time, first_contact, commands):
- # Reward air time.
- rew_air_time = jp.sum((air_time - 0.1) * first_contact)
- rew_air_time *= (
- math.normalize(commands[:2])[1] > 0.05
- ) # no reward for zero command
- return rew_air_time
-
- def _reward_stand_still(
- self,
- commands,
- joint_angles,
- default_angles,
- ):
- # Penalize motion at zero commands
- return jp.sum(jp.abs(joint_angles - default_angles)) * (
- math.normalize(commands[:2])[1] < 0.1
- )
-
- def _get_feet_pos_vel(self, qp):
- foot_indices = jp.array([3, 6, 9, 12])
- offset = jp.array([
- [-0.191284, -0.0191638, 0.013],
- [-0.191284, -0.0191638, -0.013],
- [-0.191284, -0.0191638, 0.013],
- [-0.191284, -0.0191638, -0.013],
- ])
- offset = base.Transform.create(pos=offset)
- pos = qp.x.take(foot_indices).vmap().do(offset).pos
- vel = offset.vmap().do(qp.xd.take(foot_indices)).vel
- return pos, vel
-
- def _reward_foot_slip(self, qp, contact_filt):
- # Get feet velocities
- _, foot_world_vel = self._get_feet_pos_vel(qp)
- # Penalize large feet velocity for feet that are in contact with the ground.
- return jp.sum(
- jp.square(foot_world_vel[:, :2]) * contact_filt.reshape((-1, 1))
- )
-
-
-envs.register_environment('barkour_v0_joystick', Barkourv0)
-
-
-def domain_randomize(
- sys,
- rng,
- gain_min=-5,
- gain_max=5,
-):
- """Randomizes the system in training for sim2real transfer."""
-
- @jax.vmap
- def rand(rng):
- """Generates random values."""
- # friction
- _, key = jax.random.split(rng, 2)
- friction = jax.random.uniform(key, (1,), minval=0.8, maxval=1.2)
- friction = sys.geom_friction.at[:, 0].set(friction)
- # actuator
- rng, key1 = jax.random.split(rng, 2)
- gain_range = (gain_min, gain_max)
- gain_noise = jax.random.uniform(
- key1, (1,), minval=gain_range[0], maxval=gain_range[1]
- )
- gain = sys.actuator.gain + gain_noise
- # center of mass
- _, key = jax.random.split(rng)
- com = jax.random.uniform(key, (3,), minval=-0.05, maxval=0.05)
- ltps = sys.link.inertia.transform.pos.at[0, :3].set(
- sys.link.inertia.transform.pos[0, :3] + com
- )
- return friction, gain, ltps
-
- friction, gain, link_inertia_transform_pos = rand(rng)
-
- in_axes = jax.tree_map(lambda x: None, sys)
- in_axes = in_axes.tree_replace({
- 'actuator.gain': 0,
- 'link.inertia.transform.pos': 0,
- 'geom_friction': 0,
- })
-
- sys = sys.tree_replace({
- 'actuator.gain': gain,
- 'link.inertia.transform.pos': link_inertia_transform_pos,
- 'geom_friction': friction,
- })
-
- return sys, in_axes
diff --git a/brax/experimental/barkour_v0/barkour_joystick_test.py b/brax/experimental/barkour_v0/barkour_joystick_test.py
deleted file mode 100644
index 035947707..000000000
--- a/brax/experimental/barkour_v0/barkour_joystick_test.py
+++ /dev/null
@@ -1,32 +0,0 @@
-# Copyright 2024 DeepMind Technologies Limited.
-#
-# Licensed under the Apache License, Version 2.0 (the "License");
-# you may not use this file except in compliance with the License.
-# You may obtain a copy of the License at
-#
-# http://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing, software
-# distributed under the License is distributed on an "AS IS" BASIS,
-# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-# See the License for the specific language governing permissions and
-# limitations under the License.
-
-"""Tests that the barkour joystick env runs."""
-
-from absl.testing import absltest
-from brax.experimental.barkour_v0 import barkour_joystick
-import jax
-import jax.numpy as jp
-
-
-class BarkourJoystickTest(absltest.TestCase):
-
- def test_env_runs(self):
- env = barkour_joystick.Barkourv0()
- state = jax.jit(env.reset)(jax.random.PRNGKey(42))
- _ = jax.jit(env.step)(state, jp.zeros(env.sys.act_size()))
-
-
-if __name__ == "__main__":
- absltest.main()
diff --git a/brax/experimental/barkour_v0/barkour_v0_joystick.ipynb b/brax/experimental/barkour_v0/barkour_v0_joystick.ipynb
deleted file mode 100644
index 41c36b0c7..000000000
--- a/brax/experimental/barkour_v0/barkour_v0_joystick.ipynb
+++ /dev/null
@@ -1,502 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "a3NXzZCjTskz"
- },
- "source": [
- "# Barkour v0 Joystick"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "IcnPQLtRpl8f"
- },
- "source": [
- "\u003ca href=\"https://colab.research.google.com/github/google/brax/blob/main/brax/experimental/barkour_v0/barkour_v0_joystick.ipynb\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" width=\"140\" align=\"center\"/\u003e\u003c/a\u003e This notebook demonstrates training a joystick policy for the Barkour v0 environment with domain randomization."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "ps4L3_FwO9iK"
- },
- "source": [
- "### Copyright notice"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "_UbO9uhtBSX5"
- },
- "source": [
- "\u003e \u003cp\u003e\u003csmall\u003e\u003csmall\u003eCopyright 2023 DeepMind Technologies Limited.\u003c/small\u003e\u003c/p\u003e\n",
- "\u003e \u003cp\u003e\u003csmall\u003e\u003csmall\u003eLicensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at \u003ca href=\"http://www.apache.org/licenses/LICENSE-2.0\"\u003ehttp://www.apache.org/licenses/LICENSE-2.0\u003c/a\u003e.\u003c/small\u003e\u003c/small\u003e\u003c/p\u003e\n",
- "\u003e \u003cp\u003e\u003csmall\u003e\u003csmall\u003eUnless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.\u003c/small\u003e\u003c/small\u003e\u003c/p\u003e"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "TSw4j-GXO-NM"
- },
- "source": [
- "### Imports"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "cellView": "form",
- "id": "2csKCQP5TJhQ"
- },
- "outputs": [],
- "source": [
- "#@markdown ## ⚠️ PLEASE NOTE:\n",
- "#@markdown This colab runs best using a TPU Cloud VM runtime.\n",
- "#@markdown * From the Colab menu, choose \"Connect to a custom GCE VM\".\n",
- "#@markdown\n",
- "#@markdown A GPU runtime can be selected from Runtime \u003e Change Runtime Type, but GPU training performance is not well tuned, and is left for a future release.\n",
- "\n",
- "from datetime import datetime\n",
- "import functools\n",
- "import os\n",
- "from IPython.display import HTML, clear_output\n",
- "\n",
- "try:\n",
- " import brax\n",
- "except ImportError:\n",
- " !pip install git+https://github.com/google/brax.git@main\n",
- " clear_output()\n",
- " import brax\n",
- "\n",
- "import flax\n",
- "from brax import envs\n",
- "from brax.experimental.barkour_v0 import barkour_joystick\n",
- "from brax.io import model\n",
- "from brax.io import json\n",
- "from brax.io import html\n",
- "from brax.training.agents.ppo import train as ppo\n",
- "from brax.training.agents.ppo import networks as ppo_networks\n",
- "import jax\n",
- "import jax.numpy as jp\n",
- "import matplotlib.pyplot as plt\n",
- "\n",
- "plt.rcParams.update({'font.size': 16})"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "id": "A94RP3T9KRlP"
- },
- "outputs": [],
- "source": [
- "jax.devices()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "dFa0HxmY9w58"
- },
- "source": [
- "# Environment\n",
- "\n",
- "First let's create the environment and visualize it.\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "id": "OoViYdX39y_q"
- },
- "outputs": [],
- "source": [
- "barkour_env = envs.create('barkour_v0_joystick',\n",
- " backend='generalized', kick_vel=0.05\n",
- ")\n",
- "state = jax.jit(barkour_env.reset)(rng=jax.random.PRNGKey(seed=0))\n",
- "\n",
- "HTML(html.render(barkour_env.sys, [state.pipeline_state]))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "Y0tIQgi4xzFK"
- },
- "source": [
- "# Train\n",
- "\n",
- "The joystick policy takes in commands of the form `[x, y, w]`, where `[x, y]` are the linear velocity relative to the robot, and `[w]` is an angular velocity about the z-axis. The `Barkourv0` environment contains velocity tracking rewards to make sure the quadruped follows these joystick commands. Other rewards ensure the robot orientation and walking gait are smooth (e.g. the `action_rate` behaves like a low-pass filter on the actuation rate).\n",
- "\n",
- "We train the policy with domain randomization by using the `domain_randomize` function from [`barkour_joystick.py`](https://github.com/google/brax/blob/main/brax/experimental/barkour_v0/barkour_joystick.py). This randomizes the actuator gains, center of mass of the torso, and friction, which helps with sim2real transfer.\n",
- "\n",
- "The training script below optimizes and plots the joystick reward, but also prints out the total distance that the quadruped travels relative the origin as a proxy metric."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "colab": {
- "height": 983
- },
- "executionInfo": {
- "elapsed": 672385,
- "status": "ok",
- "timestamp": 1692907755486,
- "user": {
- "displayName": "",
- "userId": ""
- },
- "user_tz": 420
- },
- "id": "1e6k8-RF0GBK",
- "outputId": "b6dedd2a-890b-41b7-d706-ca6555fab8fb"
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Total dist: 2.4292915\n"
- ]
- },
- {
- "data": {
- "image/png": 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CMzOrZ6CroerZNr/el1/XJQ0hUmsKMFzS0gMSlZmZvaEwWUgaKmmGpFGt3rmkVUgPVro+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\nZmZW6P8AHJfIQ7Z+KaMAAAAASUVORK5CYII=\n",
- "text/plain": [
- "\u003cFigure size 600x400 with 1 Axes\u003e"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Total dist: 127.773895\n"
- ]
- },
- {
- "data": {
- "image/png": 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kYWZmuXpVspC0laSrJS2S1CLpd5ImFVx3mKQLJc2VtFzSXZIOrHfMvU0X93G0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\nuf4/SCvkP8K3FqcAAAAASUVORK5CYII=\n",
- "text/plain": [
- "\u003cFigure size 600x400 with 1 Axes\u003e"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Total dist: 667.2552\n"
- ]
- },
- {
- "data": {
- "image/png": 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RF0uqnOluGrBtbcMyM7NGUvTKYgzwYCvLVgCDaxOOmZk1oqLJ4lVg51aWvY3U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\nFmZmlsvJwszMcjlZmJlZrv8PPAQUJEmDPFcAAAAASUVORK5CYII=\n",
- "text/plain": [
- "\u003cFigure size 600x400 with 1 Axes\u003e"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "time to jit: 0:00:39.318410\n",
- "time to train: 0:10:32.681755\n"
- ]
- }
- ],
- "source": [
- "make_networks_factory = functools.partial(\n",
- " ppo_networks.make_ppo_networks,\n",
- " policy_hidden_layer_sizes=(128,) * 4)\n",
- "train_fn = functools.partial(\n",
- " ppo.train, num_timesteps=150_000_000, num_evals=3,\n",
- " reward_scaling=1, episode_length=1000, normalize_observations=True,\n",
- " action_repeat=1, unroll_length=20, num_minibatches=32,\n",
- " gae_lambda=0.95,\n",
- " num_updates_per_batch=4, discounting=0.99, learning_rate=3.0e-4,\n",
- " entropy_cost=1e-2, num_envs=8192, batch_size=1024, seed=1,\n",
- " network_factory=make_networks_factory,\n",
- " randomization_fn=barkour_joystick.domain_randomize,\n",
- " num_resets_per_eval=10)\n",
- "\n",
- "max_y = 50\n",
- "min_y = -15\n",
- "\n",
- "xdata = []\n",
- "ydata = []\n",
- "ydataerr = []\n",
- "times = [datetime.now()]\n",
- "\n",
- "def progress(num_steps, metrics):\n",
- " times.append(datetime.now())\n",
- " xdata.append(num_steps)\n",
- " ydata.append(metrics['eval/episode_reward'])\n",
- " ydataerr.append(metrics['eval/episode_reward_std'])\n",
- "\n",
- " print('Total dist: ', metrics['eval/episode_total_dist'])\n",
- "\n",
- " plt.xlim([0, train_fn.keywords['num_timesteps'] * 1.25])\n",
- " plt.ylim([min_y, max_y])\n",
- " plt.xlabel('# environment steps')\n",
- " plt.ylabel('reward per episode')\n",
- " plt.title(f'y={ydata[-1]:.3f}')\n",
- "\n",
- " plt.errorbar(\n",
- " xdata, ydata, yerr=ydataerr)\n",
- " plt.show()\n",
- "\n",
- "# Reset environments since internals may be overwritten by tracers.\n",
- "barkour_env = envs.create('barkour_v0_joystick',\n",
- " backend='generalized', kick_vel=0.05\n",
- ")\n",
- "eval_env = envs.create('barkour_v0_joystick',\n",
- " backend='generalized', kick_vel=0.05)\n",
- "make_inference_fn, params, _= train_fn(environment=barkour_env,\n",
- " progress_fn=progress,\n",
- " eval_env=eval_env)\n",
- "\n",
- "print(f'time to jit: {times[1] - times[0]}')\n",
- "print(f'time to train: {times[-1] - times[1]}')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "id": "u9sdN4Xa5JoH"
- },
- "outputs": [],
- "source": [
- "#@title save model\n",
- "model_path = '/tmp/barkour_joystick'\n",
- "model.save_params(model_path, params)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "id": "8Yge-CGP5JoO"
- },
- "outputs": [],
- "source": [
- "#@title load model\n",
- "params = model.load_params(model_path)\n",
- "\n",
- "inference_fn = make_inference_fn(params)\n",
- "jit_inference_fn = jax.jit(inference_fn)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "id": "O6ugZ7jz5JoO"
- },
- "outputs": [],
- "source": [
- "barkour_env = envs.create('barkour_v0_joystick',\n",
- " backend='generalized', kick_vel=0.05, auto_reset=False,\n",
- ")\n",
- "jit_env_reset = jax.jit(barkour_env.reset)\n",
- "jit_env_step = jax.jit(barkour_env.step)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "tTHa7sNGlIyt"
- },
- "source": [
- "# Eval\n",
- "\n",
- "Try out different joystick commands by changing the values below!"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "colab": {
- "height": 480
- },
- "executionInfo": {
- "elapsed": 44673,
- "status": "ok",
- "timestamp": 1692907801617,
- "user": {
- "displayName": "",
- "userId": ""
- },
- "user_tz": 420
- },
- "id": "M0nz1zXd5JoO",
- "outputId": "3620cb8a-1f29-4c41-a040-65fbb1185f8c"
- },
- "outputs": [
- {
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- " \u003clink rel=\"shortcut icon\" type=\"image/x-icon\" href=\"/favicon.ico\"\u003e\n",
- " \u003c/head\u003e\n",
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- " \u003cstyle\u003e\n",
- " body {\n",
- " margin: 0;\n",
- " padding: 0;\n",
- " }\n",
- "\n",
- " #brax-viewer {\n",
- " height: 480px;\n",
- " margin: 0;\n",
- " padding: 0;\n",
- " }\n",
- " \u003c/style\u003e\n",
- " \u003cscript async src=\"https://unpkg.com/es-module-shims@1.6.3/dist/es-module-shims.js\"\u003e\u003c/script\u003e\n",
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- " \u003cscript type=\"importmap\"\u003e\n",
- " {\n",
- " \"imports\": {\n",
- " \"three\": \"https://unpkg.com/three@0.150.1/build/three.module.js\",\n",
- " \"three/addons/\": \"https://unpkg.com/three@0.150.1/examples/jsm/\",\n",
- " \"lilgui\": \"https://cdn.jsdelivr.net/npm/lil-gui@0.18.0/+esm\",\n",
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[2377, 2005, 2372], [2378, 2379, 2380], [2379, 2381, 2380], [2380, 2381, 2382], [2383, 2384, 2385], [2384, 2386, 2385], [2387, 2388, 2389], [2388, 2390, 2389], [2389, 2390, 2391], [2392, 2384, 2393], [2387, 2389, 2393], [2389, 2394, 2393], [2393, 2394, 2392], [2395, 2386, 2384], [2395, 2384, 2396], [2392, 2397, 2384], [2397, 2398, 2384], [2384, 2398, 2396], [2398, 2399, 2396], [2396, 2399, 2395], [2012, 2011, 2394], [2318, 2342, 2012], [2342, 2331, 2012], [2335, 2016, 2336], [2016, 2012, 2336], [2336, 2012, 2338], [2012, 2331, 2338], [2238, 2329, 2327], [2239, 2238, 2391], [2238, 2327, 2391], [2391, 2327, 2389], [2327, 2325, 2389], [2389, 2325, 2394], [2325, 2321, 2394], [2394, 2321, 2012], [2321, 2319, 2012], [2012, 2319, 2318], [2312, 2314, 2238], [2314, 2317, 2238], [2238, 2317, 2329], [2335, 2400, 2016], [2400, 2401, 2016], [2402, 2403, 2404], [2403, 2405, 2404], [2406, 2018, 2407], [2018, 2016, 2407], [2407, 2016, 2405], [2016, 2401, 2405], [2405, 2401, 2404], [2401, 2400, 2404], 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[1792, 1800, 1777], [1800, 1799, 1777], [1777, 1799, 1781], [1799, 1798, 1781], [1798, 1801, 1781], [1801, 1779, 1781], [1779, 1789, 1777], [1766, 1768, 1777], [1777, 1768, 1792], [1768, 1770, 1792], [1792, 1770, 1793], [1770, 1771, 1793], [1771, 1774, 1793], [1793, 1774, 1783], [1774, 1760, 1783], [1783, 1760, 1758], [1758, 1762, 1788], [1762, 1763, 1788], [1788, 1763, 1789], [1763, 1766, 1789], [1790, 1802, 1791], [1791, 1802, 1798], [1802, 1803, 1798], [1803, 1804, 1798], [1798, 1804, 1801], [1783, 1785, 1805], [1783, 1805, 1793], [1805, 1806, 1793], [1807, 1795, 1806], [1795, 1793, 1806], [1790, 1795, 1802], [1795, 1807, 1802], [1807, 1806, 1808], [1806, 1809, 1808], [1808, 1809, 1810], [1809, 1802, 1810], [1810, 1802, 1807], [1778, 1782, 1803], [1811, 1809, 1778], [1809, 1767, 1778], [1778, 1767, 1780], [1767, 1776, 1780], [1780, 1776, 1782], [1782, 1776, 1803], [1776, 1804, 1803], [1776, 1767, 1775], [1775, 1767, 1765], [1776, 1765, 1764], [1764, 1761, 1776], [1776, 1761, 1787], [1761, 1757, 1787], [1787, 1812, 1786], [1812, 1805, 1813], [1812, 1814, 1786], [1786, 1814, 1785], [1814, 1813, 1785], [1813, 1805, 1785], [1759, 1773, 1806], [1806, 1773, 1815], [1773, 1772, 1815], [1772, 1769, 1815], [1769, 1809, 1815], [1809, 1806, 1815], [1787, 1757, 1816], [1816, 1757, 1817], [1757, 1805, 1817], [1787, 1816, 1812], [1816, 1818, 1812], [1812, 1818, 1805], [1818, 1817, 1805], [1778, 1803, 1811], [1811, 1803, 1819], [1803, 1802, 1819], [1819, 1802, 1809], [1809, 1769, 1767], [1757, 1759, 1805], [1759, 1806, 1805], [1801, 1804, 1779], [1779, 1804, 1789], [1804, 1776, 1789], [1787, 1788, 1776], [1788, 1789, 1776], [1796, 1818, 1816], [1796, 1816, 1797], [1818, 1796, 1817], [1796, 1758, 1817], [1817, 1758, 1816], [1816, 1758, 1797], [1811, 1799, 1809], [1799, 1800, 1809], [1809, 1800, 1819], [1800, 1791, 1819], [1819, 1791, 1811], [1791, 1799, 1811], [1796, 1813, 1784], [1813, 1814, 1784], [1784, 1814, 1797], [1814, 1812, 1797], [1797, 1812, 1796], [1812, 1813, 1796], [1794, 1807, 1792], [1807, 1808, 1792], [1808, 1810, 1792], [1792, 1810, 1790], [1790, 1810, 1794], [1810, 1807, 1794], [1820, 1821, 1822], [1822, 1821, 1823], [1823, 1824, 1825], [1822, 1823, 1825], [1826, 1827, 1828], [1829, 1826, 1830], [1826, 1828, 1830], [1830, 1828, 1831], [1827, 1832, 1829], [1833, 1832, 1834], [1827, 1833, 1835], [1827, 1835, 1832], [1827, 1826, 1833], [1833, 1829, 1832], [1830, 1831, 1828], [1830, 1828, 1829], [1827, 1829, 1828], [1834, 1835, 1833], [1836, 1835, 1837], [1836, 1838, 1832], [1835, 1836, 1832], [1834, 1837, 1835], [1834, 1838, 1837], [1838, 1834, 1832], [1833, 1826, 1829], [1839, 1838, 1836], [1840, 1839, 1836], [1839, 1841, 1838], [1841, 1842, 1838], [1838, 1842, 1837], [1842, 1843, 1837], [1837, 1843, 1836], [1843, 1840, 1836], [1843, 1824, 1840], [1824, 1823, 1840], [1840, 1823, 1839], [1839, 1821, 1841], [1821, 1842, 1841], [1821, 1839, 1823], [1824, 1843, 1842], [1820, 1824, 1842], [1821, 1820, 1842], [1822, 1825, 1820], [1825, 1824, 1820], [1844, 1845, 1846], [1847, 1848, 1846], [1846, 1848, 1844], [1849, 1846, 1845], [1850, 1849, 1851], [1849, 1845, 1851], [1844, 1852, 1845], [1852, 1851, 1845], [1852, 1844, 1853], [1844, 1848, 1853], [1853, 1848, 1854], [1848, 1847, 1854], [1846, 1855, 1847], [1855, 1854, 1847], [1855, 1846, 1850], [1846, 1849, 1850], [1856, 1857, 1858], [1859, 1860, 1858], [1858, 1860, 1856], [1861, 1858, 1857], [1862, 1861, 1863], [1861, 1857, 1863], [1856, 1864, 1857], [1864, 1863, 1857], [1864, 1856, 1865], [1856, 1860, 1865], [1865, 1860, 1866], [1860, 1859, 1866], [1867, 1868, 1858], [1858, 1868, 1859], [1868, 1866, 1859], [1867, 1858, 1862], [1858, 1861, 1862], [1869, 1870, 1871], [1870, 1872, 1871], [1872, 1873, 1871], [1871, 1873, 1874], [1874, 1873, 1869], [1873, 1870, 1869], [1870, 1875, 1872], [1872, 1876, 1873], [1873, 1876, 1870], [1870, 1877, 1875], [1877, 1878, 1875], [1875, 1878, 1872], [1878, 1879, 1872], [1872, 1879, 1876], [1879, 1880, 1876], [1880, 1881, 1876], [1876, 1881, 1870], [1881, 1877, 1870], [1882, 1883, 1884], [1883, 1885, 1884], [1885, 1886, 1884], [1884, 1886, 1887], [1887, 1886, 1882], [1886, 1883, 1882], [1888, 1889, 1890], [1889, 1891, 1890], [1890, 1891, 1892], [1891, 1893, 1892], [1894, 1895, 1893], [1895, 1892, 1893], [1895, 1894, 1896], [1894, 1897, 1896], [1898, 1899, 1900], [1901, 1900, 1902], [1900, 1899, 1902], [1902, 1903, 1901], [1903, 1904, 1901], [1901, 1904, 1900], [1904, 1905, 1900], [1906, 1853, 1907], [1908, 1896, 1909], [1896, 1910, 1909], [1890, 1911, 1888], [1911, 1912, 1888], [1888, 1912, 1910], [1910, 1912, 1909], [1913, 1890, 1914], [1890, 1892, 1914], [1914, 1892, 1915], [1892, 1895, 1915], [1915, 1895, 1916], [1895, 1896, 1916], [1917, 1918, 1919], [1918, 1908, 1919], [1920, 1869, 1913], [1869, 1871, 1913], [1921, 1922, 1874], [1874, 1922, 1871], [1922, 1911, 1871], [1871, 1911, 1913], [1911, 1890, 1913], [1853, 1854, 1907], [1907, 1854, 1923], [1854, 1855, 1923], [1923, 1855, 1924], [1924, 1855, 1920], [1855, 1850, 1920], [1925, 1921, 1851], [1851, 1921, 1850], [1850, 1921, 1920], [1921, 1874, 1920], [1920, 1874, 1869], [1851, 1852, 1925], [1925, 1852, 1926], [1852, 1853, 1926], [1926, 1853, 1884], [1927, 1928, 1868], [1929, 1926, 1884], [1930, 1931, 1932], [1932, 1933, 1930], [1933, 1934, 1930], [1930, 1934, 1935], [1934, 1936, 1935], [1904, 1936, 1905], [1936, 1937, 1905], [1905, 1937, 1938], [1937, 1939, 1938], [1938, 1939, 1940], [1939, 1941, 1940], [1941, 1942, 1940], [1940, 1942, 1903], [1942, 1943, 1903], [1903, 1943, 1904], [1943, 1932, 1904], [1904, 1932, 1936], [1932, 1931, 1936], [1936, 1931, 1935], [1868, 1928, 1866], [1868, 1867, 1927], [1867, 1862, 1927], [1927, 1862, 1884], [1884, 1862, 1929], [1862, 1863, 1929], [1929, 1863, 1944], [1863, 1864, 1944], [1944, 1864, 1933], [1864, 1865, 1933], [1933, 1865, 1934], [1865, 1866, 1934], [1934, 1866, 1928], [1884, 1853, 1882], [1853, 1906, 1882], [1882, 1906, 1887], [1906, 1927, 1887], [1887, 1927, 1884], [1945, 1916, 1946], [1946, 1916, 1908], [1916, 1896, 1908], [1946, 1908, 1947], [1908, 1918, 1947], [1918, 1948, 1947], [1947, 1948, 1945], [1945, 1948, 1916], [1899, 1940, 1902], [1940, 1903, 1902], [1898, 1938, 1899], [1938, 1940, 1899], [1900, 1905, 1898], [1905, 1938, 1898], [1889, 1888, 1949], [1888, 1910, 1949], [1896, 1897, 1910], [1897, 1949, 1910], [1889, 1949, 1894], [1893, 1891, 1894], [1894, 1891, 1889], [1897, 1894, 1949], [1917, 1919, 1950], [1919, 1951, 1950], [1950, 1952, 1917], [1952, 1918, 1917], [1918, 1952, 1953], [1918, 1953, 1948], [1953, 1954, 1948], [1948, 1954, 1916], [1954, 1955, 1916], [1916, 1955, 1915], [1955, 1956, 1915], [1915, 1956, 1914], [1914, 1956, 1913], [1956, 1877, 1913], [1913, 1877, 1920], [1877, 1957, 1920], [1920, 1957, 1924], [1957, 1958, 1924], [1924, 1958, 1923], [1958, 1959, 1923], [1923, 1959, 1907], [1959, 1960, 1907], [1907, 1960, 1906], [1960, 1961, 1906], [1906, 1961, 1927], [1961, 1962, 1927], [1927, 1962, 1928], [1962, 1963, 1928], [1928, 1963, 1934], [1963, 1964, 1934], [1934, 1964, 1936], [1964, 1965, 1936], [1936, 1965, 1937], [1965, 1966, 1937], [1937, 1966, 1939], [1939, 1966, 1941], [1967, 1942, 1941], [1942, 1968, 1943], [1968, 1969, 1943], [1943, 1969, 1932], [1970, 1921, 1971], [1971, 1921, 1972], [1921, 1925, 1972], [1972, 1925, 1973], [1925, 1926, 1973], [1973, 1926, 1974], [1926, 1929, 1974], [1974, 1929, 1975], [1929, 1944, 1975], [1975, 1944, 1976], [1944, 1933, 1976], [1933, 1932, 1976], [1976, 1932, 1969], [1977, 1911, 1970], [1911, 1922, 1970], [1970, 1922, 1921], [1951, 1919, 1978], [1919, 1908, 1978], [1978, 1908, 1979], [1908, 1909, 1979], [1979, 1909, 1977], [1909, 1912, 1977], [1912, 1911, 1977], [1978, 1980, 1951], [1980, 1981, 1951], [1951, 1981, 1950], [1981, 1982, 1950], [1950, 1982, 1952], [1967, 1941, 1966], [1952, 1982, 1953], [1982, 1983, 1953], [1953, 1983, 1954], [1966, 1965, 1967], [1967, 1965, 1984], [1942, 1967, 1968], [1967, 1984, 1968], [1968, 1984, 1969], [1984, 1985, 1969], [1959, 1986, 1960], [1986, 1987, 1960], [1954, 1983, 1955], [1955, 1983, 1980], [1881, 1959, 1958], [1881, 1880, 1971], [1963, 1962, 1987], [1962, 1961, 1987], [1987, 1961, 1960], [1977, 1955, 1979], [1955, 1980, 1979], [1979, 1980, 1978], [1955, 1977, 1878], [1878, 1977, 1879], [1977, 1970, 1879], [1879, 1970, 1880], [1880, 1970, 1971], [1958, 1957, 1881], [1881, 1957, 1877], [1877, 1956, 1878], [1878, 1956, 1955], [1959, 1881, 1986], [1986, 1881, 1988], [1971, 1972, 1881], [1881, 1972, 1988], [1972, 1973, 1988], [1973, 1974, 1988], [1987, 1974, 1975], [1975, 1989, 1987], [1987, 1989, 1963], [1989, 1990, 1963], [1963, 1990, 1964], [1964, 1990, 1965], [1965, 1990, 1984], [1975, 1976, 1989], [1989, 1976, 1985], [1976, 1969, 1985], [1991, 1983, 1992], [1983, 1982, 1992], [1992, 1982, 1993], [1982, 1981, 1993], [1993, 1981, 1994], [1981, 1980, 1994], [1994, 1980, 1995], [1980, 1983, 1995], [1995, 1983, 1991], [1993, 1996, 1991], [1991, 1992, 1993], [1993, 1994, 1997], [1997, 1994, 1996], [1994, 1995, 1996], [1996, 1995, 1991], [1945, 1996, 1947], [1996, 1993, 1947], [1993, 1997, 1947], [1947, 1997, 1946], [1946, 1997, 1945], [1997, 1996, 1945], [1998, 1989, 1999], [1989, 1985, 1999], [1999, 1985, 2000], [1985, 1984, 2000], [2000, 1984, 2001], [1984, 1990, 2001], [2001, 1990, 1998], [1990, 1989, 1998], [1998, 1999, 2000], [2000, 2001, 2002], [2002, 2001, 1998], [1930, 1998, 1931], [1998, 2000, 1931], [2000, 2002, 1931], [1931, 2002, 1935], [1935, 2002, 1930], [2002, 1998, 1930], [2003, 1986, 2004], [1986, 1988, 2004], [2004, 1988, 1885], [1988, 1974, 1885], [1885, 1974, 2005], [1974, 1987, 2005], [2005, 1987, 2006], [1987, 1986, 2006], [2006, 1986, 2003], [1885, 1883, 2003], [2003, 2004, 1885], [1885, 2005, 1886], [1886, 2005, 1883], [2005, 2006, 1883], [1883, 2006, 2003], [2007, 2008, 2009], [2010, 2011, 2007], [2011, 2012, 2007], [2007, 2012, 2008], [2008, 2012, 2013], [2012, 2011, 2013], [2009, 2008, 2014], [2008, 2013, 2014], [2015, 2016, 2017], [2016, 2018, 2017], [2019, 2020, 2021], [2022, 2021, 2023], [2021, 2020, 2023], [2023, 2020, 2024], [2024, 2020, 2025], [2020, 2019, 2025], [2021, 2022, 2026], [2027, 2021, 2026], [2026, 2028, 2027], [2028, 2029, 2027], [2030, 2031, 2032], [2030, 2033, 2034], [2034, 2033, 2031], [2033, 2035, 2031], [2031, 2030, 2036], [2035, 2032, 2031], [2030, 2032, 2037], [2035, 2038, 2032], [2038, 2039, 2032], [2032, 2039, 2037], [2040, 2010, 2007], [2007, 2009, 2014], [2041, 2042, 2043], [2042, 2044, 2043], [2015, 2041, 2043], [2045, 2046, 2047], [2045, 2015, 2046], [2015, 2043, 2046], [2046, 2043, 2047], [2044, 2047, 2043], [2042, 2048, 2044], [2048, 2023, 2047], [2023, 2045, 2047], [2048, 2047, 2044], [2049, 2050, 2051], [2017, 2014, 2041], [2040, 2052, 2010], [2049, 2011, 2050], [2011, 2010, 2050], [2010, 2052, 2050], [2013, 2011, 2023], [2011, 2049, 2023], [2023, 2049, 2022], [2049, 2053, 2022], [2022, 2053, 2026], [2053, 2054, 2026], [2026, 2054, 2028], [2054, 2052, 2028], [2052, 2040, 2028], [2041, 2014, 2042], [2014, 2013, 2042], [2042, 2013, 2048], [2013, 2023, 2048], [2023, 2015, 2045], [2015, 2017, 2041], [2015, 2024, 2016], [2055, 2056, 2057], [2056, 2054, 2057], [2057, 2054, 2053], [2024, 2015, 2023], [2052, 2055, 2050], [2055, 2051, 2050], [2054, 2056, 2052], [2056, 2055, 2052], [2051, 2055, 2057], [2049, 2051, 2053], [2051, 2057, 2053], [2007, 2014, 2040], [2030, 2034, 2036], [2018, 2058, 2017], [2029, 2028, 2040], [2058, 2030, 2017], [2017, 2030, 2014], [2037, 2029, 2030], [2029, 2040, 2030], [2040, 2014, 2030], [2025, 2018, 2024], [2018, 2016, 2024], [2037, 2059, 2029], [2037, 2036, 2019], [2027, 2029, 2021], [2029, 2059, 2021], [2021, 2059, 2019], [2060, 2025, 2019], [2036, 2034, 2019], [2034, 2060, 2019], [2019, 2059, 2061], [2061, 2037, 2019], [2061, 2059, 2037], [2062, 2060, 2058], [2025, 2060, 2062], [2062, 2058, 2025], [2058, 2018, 2025], [2063, 2035, 2033], [2063, 2033, 2060], [2033, 2030, 2060], [2064, 2035, 2063], [2035, 2065, 2038], [2030, 2058, 2065], [2038, 2065, 2066], [2066, 2065, 2058], [2030, 2065, 2060], [2060, 2065, 2064], [2065, 2035, 2064], [2060, 2064, 2058], [2064, 2066, 2058], [2063, 2039, 2064], [2064, 2039, 2066], [2060, 2034, 2031], [2060, 2031, 2063], [2036, 2037, 2039], [2063, 2031, 2039], [2039, 2031, 2036], [2038, 2066, 2039], [2067, 2068, 2069], [2070, 2068, 2067], [2071, 2070, 2072], [2070, 2067, 2072], [2072, 2067, 2073], [2069, 2074, 2075], [2069, 2075, 2067], [2075, 2073, 2067], [2076, 2073, 2077], [2073, 2078, 2079], [2073, 2076, 2078], [2075, 2074, 2069], [2075, 2069, 2073], [2070, 2071, 2072], [2069, 2068, 2077], [2077, 2068, 2079], [2068, 2073, 2079], [2077, 2073, 2069], [2077, 2079, 2076], [2073, 2068, 2072], [2072, 2068, 2070], [2079, 2078, 2076], [2080, 2081, 2082], [2080, 2082, 2083], [2080, 2083, 2081], [2084, 2082, 2081], [2081, 2085, 2084], [2085, 2086, 2084], [2084, 2086, 2085], [2084, 2085, 2082], [2082, 2085, 2083], [2085, 2081, 2083], [2087, 2088, 2089], [2090, 2091, 2092], [2091, 2087, 2092], [2092, 2087, 2089], [2091, 2093, 2087], [2093, 2088, 2087], 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1635, 1967], [1635, 2007, 1967], [1990, 1607, 1606], [2023, 2022, 1632], [2022, 2021, 1632], [1632, 2021, 1648], [2021, 2035, 1648], [1648, 2035, 1628], [2035, 2034, 1628], [1990, 1606, 1991], [1606, 1626, 1991], [1991, 1626, 1992], [1626, 1625, 1992], [1992, 1625, 2048], [1625, 1627, 2048], [2048, 1627, 2034], [1627, 1629, 2034], [2034, 1629, 1628], [1990, 2041, 1607], [2041, 2040, 1607], [1607, 2040, 1513], [2040, 2009, 1513], [1513, 2009, 1507], [1507, 2009, 1508], [2009, 2008, 1508], [1508, 2008, 1509], [2008, 2010, 1509], [1509, 2010, 1603], [2010, 2011, 1603], [1603, 2011, 1604], [1980, 1982, 1599], [1982, 1600, 1599], [1599, 1601, 1980], [1601, 1602, 1980], [1980, 1602, 1981], [1602, 1605, 1981], [1981, 1605, 2046], [1605, 1604, 2046], [2046, 1604, 2047], [1604, 2011, 2047], [1993, 1559, 1558], [1982, 1983, 1600], [1983, 2033, 1600], [1600, 2033, 1586], [2033, 2032, 1586], [1586, 2032, 1587], [2032, 2031, 1587], [1993, 1558, 1994], [1558, 1561, 1994], [1994, 1561, 1995], [1561, 1563, 1995], [1995, 1563, 2049], [1563, 1562, 2049], [2049, 1562, 2031], [1562, 1564, 2031], [2031, 1564, 1587], [1993, 2043, 1559], [2043, 2042, 1559], [1559, 2042, 1560], [2042, 2013, 1560], [1560, 2013, 1585], [1585, 2013, 1583], [2013, 2012, 1583], [1583, 2012, 1584], [2012, 2014, 1584], [1584, 2014, 1557], [2014, 2015, 1557], [1557, 2015, 1555], [2020, 2019, 1553], [2019, 1554, 1553], [1553, 1551, 2020], [1551, 1550, 2020], [2020, 1550, 2018], [1550, 1556, 2018], [2018, 1556, 2051], [1556, 1555, 2051], [2051, 1555, 2050], [1555, 2015, 2050], [1996, 1544, 1545], [2019, 2017, 1554], [2017, 2016, 1554], [1554, 2016, 1552], [2016, 2030, 1552], [1552, 2030, 1565], [2030, 2029, 1565], [1996, 1545, 1997], [1545, 1546, 1997], [1997, 1546, 1998], [1546, 1547, 1998], [1998, 1547, 2052], [1547, 1548, 2052], [2052, 1548, 2029], [1548, 1549, 2029], [2029, 1549, 1565], [1996, 2054, 1544], [2054, 2053, 1544], [1544, 2053, 1525], [2053, 2038, 1525], [1525, 2038, 1510], [1510, 2038, 1511], [2038, 2037, 1511], [1511, 2037, 1512], [2037, 2036, 1512], [1512, 2036, 1523], [2036, 2039, 1523], [1523, 2039, 1524], [2039, 2045, 1524], [2045, 2044, 1524], [1524, 2044, 1520], [2044, 1979, 1520], [1520, 1979, 1521], [1979, 1978, 1521], [1978, 1977, 1521], [1521, 1977, 1522], [1977, 2006, 1522], [1522, 2006, 1541], [2006, 2005, 1541], [1541, 2005, 1517], [2005, 2004, 1517], [1517, 2004, 1518], [2004, 1519, 1518], [1516, 2065, 2064], [1516, 2064, 1542], [1516, 1515, 2065], [1515, 1514, 2065], [2065, 1514, 2066], [1514, 1519, 2066], [2066, 1519, 2070], [1519, 2004, 2070], [1542, 2064, 1543], [2064, 2069, 1543], [1543, 2069, 1485], [2069, 2068, 1485], [1485, 2068, 2067], [2105, 1736, 2106], [1736, 1735, 2106], [1735, 1734, 2106], [1734, 1957, 2106], [2106, 1957, 2107], [1957, 2095, 2107], [2107, 2095, 2094], [2094, 2096, 2107], [2096, 2098, 2107], [2107, 2098, 2108], [2098, 2104, 2108], [2108, 2104, 2101], [2109, 1767, 2110], [1767, 1764, 2110], [2110, 1764, 1765], [1739, 1738, 2105], [1738, 1737, 2105], [2105, 1737, 1736], [2101, 2100, 2108], [2100, 1961, 2108], [2108, 1961, 2109], [1961, 1960, 2109], [2109, 1960, 1767], [1765, 1766, 2110], [1766, 1748, 2110], [2110, 1748, 2105], [1748, 1749, 2105], [2105, 1749, 1739], [1487, 1497, 2111], [1479, 1500, 2111], [1500, 1489, 2111], [2111, 1489, 1487], [1497, 1476, 2111], [1476, 1475, 2111], [2111, 1475, 1479], [2112, 2106, 2113], [2106, 2107, 2113], [2113, 2107, 2114], [2114, 2107, 2115], [2107, 2108, 2115], [2115, 2108, 2109], [2105, 2106, 2110], [2106, 2112, 2110], [2110, 2112, 2109], [2112, 2116, 2109], [2109, 2116, 2115], [2117, 2118, 2114], [2118, 2119, 2114], [2114, 2119, 2113], [2119, 2120, 2113], [2113, 2120, 2112], [2120, 2121, 2112], [2112, 2121, 2116], [2121, 2122, 2116], [2116, 2122, 2115], [2122, 2117, 2115], [2115, 2117, 2114], [2117, 2123, 2118], [2123, 2124, 2118], [2118, 2124, 2119], [2124, 2125, 2119], [2119, 2125, 2126], [2117, 2122, 2123], [2122, 2121, 2123], [2123, 2121, 2127], [2121, 2120, 2127], [2128, 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2139, 2141], [2139, 2138, 2141], [2141, 2138, 2142], [2138, 2137, 2142], [2137, 2136, 2143], [2144, 2140, 2141], [2144, 2141, 2143], [2141, 2142, 2143], [2143, 2142, 2137], [2145, 2146, 2147], [2145, 2147, 2148], [2136, 2148, 2149], [2148, 2147, 2149], [2149, 2147, 2150], [2147, 2146, 2150], [2146, 2145, 2151], [2143, 2136, 2149], [2143, 2149, 2151], [2149, 2150, 2151], [2151, 2150, 2146], [2152, 2153, 2154], [2153, 2155, 2154], [2154, 2155, 2156], [2145, 2156, 2157], [2156, 2155, 2157], [2157, 2155, 2158], [2155, 2153, 2158], [2153, 2152, 2159], [2151, 2145, 2157], [2151, 2157, 2159], [2157, 2158, 2159], [2159, 2158, 2153], [2160, 2161, 2162], [2160, 2162, 2163], [2152, 2163, 2164], [2163, 2162, 2164], [2164, 2162, 2165], [2162, 2161, 2165], [2166, 2167, 2168], [2167, 2169, 2168], [2168, 2169, 2170], [2169, 2171, 2170], [2170, 2171, 2160], [2172, 2173, 2174], [2174, 2173, 2175], [2176, 2172, 2177], [2172, 2174, 2177], [2177, 2174, 2178], [2174, 2179, 2178], [2178, 2179, 2180], [2179, 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2333, 2332], [2332, 2333, 2334], [2331, 2335, 2336], [2327, 2329, 2331], [2329, 2337, 2331], [2331, 2337, 2335], [2338, 2339, 2329], [2339, 2340, 2329], [2329, 2340, 2337], [2341, 2338, 2324], [2221, 2342, 2219], [2342, 2343, 2219], [2219, 2343, 2324], [2343, 2344, 2324], [2324, 2344, 2341], [2338, 2329, 2324], [2329, 2345, 2324], [2324, 2345, 2325], [2346, 2347, 2333], [2346, 2333, 2348], [2349, 2350, 2348], [2351, 2352, 2353], [2352, 2354, 2353], [2353, 2354, 2355], [2336, 2356, 2331], [2356, 2357, 2331], [2331, 2357, 2333], [2357, 2358, 2333], [2333, 2358, 2359], [2360, 2361, 2349], [2362, 2363, 2352], [2364, 2365, 2366], [2365, 2349, 2366], [2366, 2349, 2352], [2349, 2361, 2352], [2352, 2361, 2362], [2360, 2349, 2367], [2349, 2348, 2367], [2367, 2348, 2368], [2359, 2369, 2333], [2369, 2370, 2333], [2333, 2370, 2348], [2370, 2371, 2348], [2348, 2371, 2368], [2363, 2372, 2352], [2372, 2373, 2352], [2352, 2373, 2354], [2373, 2374, 2354], [2354, 2374, 2375], [2354, 2376, 2377], [2376, 2378, 2377], [2377, 2378, 2379], [2380, 2381, 2376], [2380, 2376, 2382], [2383, 2384, 2382], [2385, 2386, 2387], [2388, 2389, 2390], [2388, 2390, 2391], [2392, 2393, 2390], [2387, 2394, 2392], [2395, 2396, 2387], [2396, 2397, 2387], [2387, 2397, 2394], [2398, 2395, 2382], [2399, 2400, 2376], [2400, 2401, 2376], [2376, 2401, 2382], [2401, 2402, 2382], [2382, 2402, 2398], [2375, 2403, 2354], [2403, 2404, 2354], [2354, 2404, 2376], [2404, 2405, 2376], [2376, 2405, 2399], [2392, 2390, 2387], [2390, 2406, 2387], [2387, 2406, 2385], [2395, 2387, 2382], [2387, 2407, 2382], [2382, 2407, 2383], [2408, 2409, 2410], [2409, 2411, 2410], [2410, 2411, 2391], [2412, 2413, 2410], [2414, 2415, 2416], [2414, 2416, 2417], [2418, 2419, 2417], [2418, 2417, 2420], [2421, 2422, 2420], [2421, 2420, 2423], [2424, 2425, 2423], [2424, 2423, 2426], [2427, 2428, 2426], [2429, 2430, 2431], [2412, 2410, 2416], [2432, 2433, 2410], [2433, 2434, 2410], [2410, 2434, 2416], [2393, 2435, 2390], [2435, 2436, 2390], [2390, 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