From bd73ca5c2b426f6918ad6578e7a700488442a9a3 Mon Sep 17 00:00:00 2001 From: Heiko Zimmermann Date: Tue, 22 Apr 2025 17:28:00 +0200 Subject: [PATCH 1/2] Applied jax recipe to cfd tesseract --- demo/cfd/cfd-tesseract/tesseract_api.py | 233 ++++++++++-------- .../cfd-tesseract/tesseract_requirements.txt | 3 +- 2 files changed, 127 insertions(+), 109 deletions(-) diff --git a/demo/cfd/cfd-tesseract/tesseract_api.py b/demo/cfd/cfd-tesseract/tesseract_api.py index eda9bee..476745a 100644 --- a/demo/cfd/cfd-tesseract/tesseract_api.py +++ b/demo/cfd/cfd-tesseract/tesseract_api.py @@ -1,15 +1,12 @@ -# Copyright 2025 Pasteur Labs. All Rights Reserved. -# SPDX-License-Identifier: Apache-2.0 - -from functools import partial +from typing import Any +import equinox as eqx import jax import jax.numpy as jnp import jax_cfd.base as cfd from pydantic import BaseModel, Field -from tesseract_core.runtime import Array, Differentiable, Float32, ShapeDType - -# TODO: !! Use JAX recipe for this, to avoid re-jitting of VJPs etc. !! +from tesseract_core.runtime import Array, Differentiable, Float32 +from tesseract_core.runtime.tree_transforms import filter_func, flatten_with_paths class InputSchema(BaseModel): @@ -25,10 +22,10 @@ class InputSchema(BaseModel): ] = Field(description="3D Array defining the initial velocity field [...]") density: float = Field(description="Density of the fluid") viscosity: float = Field(description="Viscosity of the fluid") - inner_steps: float = Field( + inner_steps: int = Field( description="Number of solver steps for each timestep", default=25 ) - outer_steps: float = Field(description="Number of timesteps steps", default=10) + outer_steps: int = Field(description="Number of timesteps steps", default=10) max_velocity: float = Field(description="Maximum velocity", default=2.0) cfl_safety_factor: float = Field(description="CFL safety factor", default=0.5) domain_size_x: float = Field(description="Domain size x", default=1.0) @@ -36,31 +33,123 @@ class InputSchema(BaseModel): class OutputSchema(BaseModel): - result: Differentiable[ - Array[ - ( - None, - None, - None, - ), - Float32, - ] - ] = Field(description="3D Array defining the final velocity field [...]") - - -@partial( - jax.jit, - static_argnames=( - "density", - "viscosity", - "inner_steps", - "outer_steps", - "max_velocity", - "cfl_safety_factor", - "domain_size_x", - "domain_size_y", - ), -) + result: Differentiable[Array[(None, None, None), Float32]] = Field( + description="3D Array defining the final velocity field [...]" + ) + + +@eqx.filter_jit +def apply_jit(inputs: dict) -> dict: + vn = cfd_fwd(**inputs) + return dict(result=vn) + + +def apply(inputs: InputSchema) -> OutputSchema: + return apply_jit(inputs.model_dump()) + + +def jacobian( + inputs: InputSchema, + jac_inputs: set[str], + jac_outputs: set[str], +): + return jac_jit(inputs.model_dump(), tuple(jac_inputs), tuple(jac_outputs)) + + +def jacobian_vector_product( + inputs: InputSchema, + jvp_inputs: set[str], + jvp_outputs: set[str], + tangent_vector: dict[str, Any], +): + return jvp_jit( + inputs.model_dump(), + tuple(jvp_inputs), + tuple(jvp_outputs), + tangent_vector, + ) + + +def vector_jacobian_product( + inputs: InputSchema, + vjp_inputs: set[str], + vjp_outputs: set[str], + cotangent_vector: dict[str, Any], +): + return vjp_jit( + inputs.model_dump(), + tuple(vjp_inputs), + tuple(vjp_outputs), + cotangent_vector, + ) + + +def abstract_eval(abstract_inputs): + """Calculate output shape of apply from the shape of its inputs.""" + is_shapedtype_dict = lambda x: type(x) is dict and (x.keys() == {"shape", "dtype"}) + is_shapedtype_struct = lambda x: isinstance(x, jax.ShapeDtypeStruct) + + jaxified_inputs = jax.tree.map( + lambda x: jax.ShapeDtypeStruct(**x) if is_shapedtype_dict(x) else x, + abstract_inputs.model_dump(), + is_leaf=is_shapedtype_dict, + ) + dynamic_inputs, static_inputs = eqx.partition( + jaxified_inputs, filter_spec=is_shapedtype_struct + ) + + def wrapped_apply(dynamic_inputs): + inputs = eqx.combine(static_inputs, dynamic_inputs) + return apply_jit(inputs) + + jax_shapes = jax.eval_shape(wrapped_apply, dynamic_inputs) + return jax.tree.map( + lambda x: ( + {"shape": x.shape, "dtype": str(x.dtype)} if is_shapedtype_struct(x) else x + ), + jax_shapes, + is_leaf=is_shapedtype_struct, + ) + + +@eqx.filter_jit +def jac_jit( + inputs: dict, + jac_inputs: tuple[str], + jac_outputs: tuple[str], +): + filtered_apply = filter_func(apply_jit, inputs, jac_outputs) + return jax.jacrev(filtered_apply)( + flatten_with_paths(inputs, include_paths=jac_inputs) + ) + + +@eqx.filter_jit +def jvp_jit( + inputs: dict, jvp_inputs: tuple[str], jvp_outputs: tuple[str], tangent_vector: dict +): + filtered_apply = filter_func(apply_jit, inputs, jvp_outputs) + return jax.jvp( + filtered_apply, + [flatten_with_paths(inputs, include_paths=jvp_inputs)], + [tangent_vector], + ) + + +@eqx.filter_jit +def vjp_jit( + inputs: dict, + vjp_inputs: tuple[str], + vjp_outputs: tuple[str], + cotangent_vector: dict, +): + filtered_apply = filter_func(apply_jit, inputs, vjp_outputs) + _, vjp_func = jax.vjp( + filtered_apply, flatten_with_paths(inputs, include_paths=vjp_inputs) + ) + return vjp_func(cotangent_vector)[0] + + def cfd_fwd( v0: jnp.ndarray, density: float, @@ -89,7 +178,7 @@ def cfd_fwd( vx0 = cfd.grids.GridArray(vx0, grid=grid, offset=(1.0, 0.5)) vy0 = cfd.grids.GridArray(vy0, grid=grid, offset=(0.5, 1.0)) - # reconstrut GridVariable from input + # reconstruct GridVariable from input vx0 = cfd.grids.GridVariable(vx0, bc) vy0 = cfd.grids.GridVariable(vy0, bc) v0 = (vx0, vy0) @@ -106,80 +195,8 @@ def cfd_fwd( ), steps=inner_steps, ) - rollout_fn = jax.jit(cfd.funcutils.trajectory(step_fn, outer_steps)) + rollout_fn = cfd.funcutils.trajectory(step_fn, outer_steps) _, trajectory = jax.device_get(rollout_fn(v0)) - vxn = trajectory[0].array.data[-1] - vyn = trajectory[1].array.data[-1] - return jnp.stack([vxn, vyn], axis=-1) - - -def apply(inputs: InputSchema) -> OutputSchema: # - vn = cfd_fwd( - v0=inputs.v0, - density=inputs.density, - viscosity=inputs.viscosity, - inner_steps=inputs.inner_steps, - outer_steps=inputs.outer_steps, - max_velocity=inputs.max_velocity, - cfl_safety_factor=inputs.cfl_safety_factor, - domain_size_x=inputs.domain_size_x, - domain_size_y=inputs.domain_size_y, - ) - - return OutputSchema(result=vn) - - -def abstract_eval(abstract_inputs): - """Calculate output shape of apply from the shape of its inputs.""" - return { - "result": ShapeDType(shape=abstract_inputs.v0.shape, dtype="float32"), - } - - -def vector_jacobian_product( - inputs: InputSchema, - vjp_inputs: set[str], - vjp_outputs: set[str], - cotangent_vector, -): - signature = [ - "v0", - "density", - "viscosity", - "inner_steps", - "outer_steps", - "max_velocity", - "cfl_safety_factor", - "domain_size_x", - "domain_size_y", - ] - # We need to do this, rather than just use jvp inputs, as the order in jvp_inputs - # is not necessarily the same as the ordering of the args in the function signature. - static_args = [arg for arg in signature if arg not in vjp_inputs] - nonstatic_args = [arg for arg in signature if arg in vjp_inputs] - - def cfd_fwd_reordered(*args, **kwargs): - return cfd_fwd( - **{**{arg: args[i] for i, arg in enumerate(nonstatic_args)}, **kwargs} - ) - - out = {} - if "result" in vjp_outputs: - # Make the function depend only on nonstatic args, as jax.jvp - # differentiates w.r.t. all free arguments. - func = partial( - cfd_fwd_reordered, **{arg: getattr(inputs, arg) for arg in static_args} - ) - - _, vjp_func = jax.vjp( - func, *tuple(inputs.model_dump(include=vjp_inputs).values()) - ) - - vals = vjp_func(cotangent_vector["result"]) - for arg, val in zip(nonstatic_args, vals, strict=False): - out[arg] = out.get(arg, 0.0) + val - - return out diff --git a/demo/cfd/cfd-tesseract/tesseract_requirements.txt b/demo/cfd/cfd-tesseract/tesseract_requirements.txt index a00f16a..c4607fb 100644 --- a/demo/cfd/cfd-tesseract/tesseract_requirements.txt +++ b/demo/cfd/cfd-tesseract/tesseract_requirements.txt @@ -1,3 +1,4 @@ numpy==1.26.4 jax-cfd==0.2.1 -jax[cpu]==0.4.34 +jax[cpu]==0.6.0 +equinox From b259ea66b826efe5b243518761cece21e1694676 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Wed, 23 Apr 2025 10:29:55 +0200 Subject: [PATCH 2/2] :lipstick:; re-execute demo notebook --- demo/cfd/cfd-tesseract/tesseract_api.py | 127 +++--- demo/cfd/demo.ipynb | 576 ++++++++++++------------ demo/cfd/vorticity.gif | Bin 1274649 -> 1274388 bytes 3 files changed, 361 insertions(+), 342 deletions(-) diff --git a/demo/cfd/cfd-tesseract/tesseract_api.py b/demo/cfd/cfd-tesseract/tesseract_api.py index 476745a..5b3ab39 100644 --- a/demo/cfd/cfd-tesseract/tesseract_api.py +++ b/demo/cfd/cfd-tesseract/tesseract_api.py @@ -1,3 +1,6 @@ +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 + from typing import Any import equinox as eqx @@ -19,7 +22,7 @@ class InputSchema(BaseModel): ), Float32, ] - ] = Field(description="3D Array defining the initial velocity field [...]") + ] = Field(description="3D Array defining the initial velocity field") density: float = Field(description="Density of the fluid") viscosity: float = Field(description="Viscosity of the fluid") inner_steps: int = Field( @@ -34,9 +37,77 @@ class InputSchema(BaseModel): class OutputSchema(BaseModel): result: Differentiable[Array[(None, None, None), Float32]] = Field( - description="3D Array defining the final velocity field [...]" + description="3D Array defining the final velocity field" + ) + + +def cfd_fwd( + v0: jnp.ndarray, + density: float, + viscosity: float, + inner_steps: int, + outer_steps: int, + max_velocity: float, + cfl_safety_factor: float, + domain_size_x: float, + domain_size_y: float, +) -> tuple[jax.Array, jax.Array]: + """Compute the final velocity field using the semi-implicit Navier-Stokes equations. + + Args: + v0: Initial velocity field. + density: Density of the fluid. + viscosity: Viscosity of the fluid. + inner_steps: Number of solver steps for each timestep. + outer_steps: Number of timesteps steps. + max_velocity: Maximum velocity. + cfl_safety_factor: CFL safety factor. + domain_size_x: Domain size in x direction. + domain_size_y: Domain size in y direction. + + Returns: + Final velocity field. + """ + vx0 = v0[..., 0] + vy0 = v0[..., 1] + bc = cfd.boundaries.HomogeneousBoundaryConditions( + ( + (cfd.boundaries.BCType.PERIODIC, cfd.boundaries.BCType.PERIODIC), + (cfd.boundaries.BCType.PERIODIC, cfd.boundaries.BCType.PERIODIC), + ) + ) + + # reconstruct grid from input + grid = cfd.grids.Grid( + vx0.shape, domain=((0.0, domain_size_x), (0.0, domain_size_y)) ) + vx0 = cfd.grids.GridArray(vx0, grid=grid, offset=(1.0, 0.5)) + vy0 = cfd.grids.GridArray(vy0, grid=grid, offset=(0.5, 1.0)) + + # reconstruct GridVariable from input + vx0 = cfd.grids.GridVariable(vx0, bc) + vy0 = cfd.grids.GridVariable(vy0, bc) + v0 = (vx0, vy0) + + # Choose a time step. + dt = cfd.equations.stable_time_step( + max_velocity, cfl_safety_factor, viscosity, grid + ) + + # Define a step function and use it to compute a trajectory. + step_fn = cfd.funcutils.repeated( + cfd.equations.semi_implicit_navier_stokes( + density=density, viscosity=viscosity, dt=dt, grid=grid + ), + steps=inner_steps, + ) + rollout_fn = cfd.funcutils.trajectory(step_fn, outer_steps) + _, trajectory = jax.device_get(rollout_fn(v0)) + vxn = trajectory[0].array.data[-1] + vyn = trajectory[1].array.data[-1] + return jnp.stack([vxn, vyn], axis=-1) + @eqx.filter_jit def apply_jit(inputs: dict) -> dict: @@ -148,55 +219,3 @@ def vjp_jit( filtered_apply, flatten_with_paths(inputs, include_paths=vjp_inputs) ) return vjp_func(cotangent_vector)[0] - - -def cfd_fwd( - v0: jnp.ndarray, - density: float, - viscosity: float, - inner_steps: int, - outer_steps: int, - max_velocity: float, - cfl_safety_factor: float, - domain_size_x: float, - domain_size_y: float, -) -> tuple[jax.Array, jax.Array]: - vx0 = v0[..., 0] - vy0 = v0[..., 1] - bc = cfd.boundaries.HomogeneousBoundaryConditions( - ( - (cfd.boundaries.BCType.PERIODIC, cfd.boundaries.BCType.PERIODIC), - (cfd.boundaries.BCType.PERIODIC, cfd.boundaries.BCType.PERIODIC), - ) - ) - - # reconstruct grid from input - grid = cfd.grids.Grid( - vx0.shape, domain=((0.0, domain_size_x), (0.0, domain_size_y)) - ) - - vx0 = cfd.grids.GridArray(vx0, grid=grid, offset=(1.0, 0.5)) - vy0 = cfd.grids.GridArray(vy0, grid=grid, offset=(0.5, 1.0)) - - # reconstruct GridVariable from input - vx0 = cfd.grids.GridVariable(vx0, bc) - vy0 = cfd.grids.GridVariable(vy0, bc) - v0 = (vx0, vy0) - - # Choose a time step. - dt = cfd.equations.stable_time_step( - max_velocity, cfl_safety_factor, viscosity, grid - ) - - # Define a step function and use it to compute a trajectory. - step_fn = cfd.funcutils.repeated( - cfd.equations.semi_implicit_navier_stokes( - density=density, viscosity=viscosity, dt=dt, grid=grid - ), - steps=inner_steps, - ) - rollout_fn = cfd.funcutils.trajectory(step_fn, outer_steps) - _, trajectory = jax.device_get(rollout_fn(v0)) - vxn = trajectory[0].array.data[-1] - vyn = trajectory[1].array.data[-1] - return jnp.stack([vxn, vyn], axis=-1) diff --git a/demo/cfd/demo.ipynb b/demo/cfd/demo.ipynb index 80dc69d..0f2656b 100644 --- a/demo/cfd/demo.ipynb +++ b/demo/cfd/demo.ipynb @@ -19,8 +19,8 @@ "output_type": "stream", "text": [ "\u001b[2K \u001b[1;2m[\u001b[0m\u001b[34mi\u001b[0m\u001b[1;2m]\u001b[0m Building image \u001b[33m...\u001b[0m\n", - "\u001b[2K\u001b[37m⠇\u001b[0m \u001b[37mProcessing\u001b[0m\n", - "\u001b[1A\u001b[2K \u001b[1;2m[\u001b[0m\u001b[34mi\u001b[0m\u001b[1;2m]\u001b[0m Built image sh\u001b[1;92ma256:b5e2\u001b[0m455fe251, \u001b[1m[\u001b[0m\u001b[32m'jax-cfd:latest'\u001b[0m\u001b[1m]\u001b[0m\n" + "\u001b[2K\u001b[37m⠏\u001b[0m \u001b[37mProcessing\u001b[0m\n", + "\u001b[1A\u001b[2K \u001b[1;2m[\u001b[0m\u001b[34mi\u001b[0m\u001b[1;2m]\u001b[0m Built image sh\u001b[1;92ma256:fd2a\u001b[0m8eca0747, \u001b[1m[\u001b[0m\u001b[32m'jax-cfd:latest'\u001b[0m\u001b[1m]\u001b[0m\n" ] }, { @@ -390,7 +390,7 @@ "Loss: 0.500 Iteration: 34\n", "Loss: 0.496 Iteration: 35\n", "Loss: 0.491 Iteration: 36\n", - "Loss: 0.487 Iteration: 37\n", + "Loss: 0.488 Iteration: 37\n", "Loss: 0.484 Iteration: 38\n", "Loss: 0.480 Iteration: 39\n", "Loss: 0.476 Iteration: 40\n", @@ -403,19 +403,19 @@ "Loss: 0.446 Iteration: 47\n", "Loss: 0.442 Iteration: 48\n", "Loss: 0.438 Iteration: 49\n", - "Loss: 0.433 Iteration: 50\n", + "Loss: 0.434 Iteration: 50\n", "Loss: 0.429 Iteration: 51\n", "Loss: 0.425 Iteration: 52\n", "Loss: 0.421 Iteration: 53\n", "Loss: 0.418 Iteration: 54\n", "Loss: 0.421 Iteration: 55\n", - "Loss: 0.412 Iteration: 56\n", - "Loss: 0.404 Iteration: 57\n", + "Loss: 0.413 Iteration: 56\n", + 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QLMIJmo3EOQy3OcLAmyM0oA+xXZ0H6pxg33QXqEk8h2bwIkRXrCHO4uaS1+/h32V3IdJiDY3jRVf3rPQQf3E6h2OEWS0pcuFKe8o7n4YmKTWaF5TNAmCjOTzjx3l+N+lYiGYHDejD8HtlH6Sb13UaIgbXdrk+jm4od2uH7IiIyDtgURARkYJFQUREChYFEREpWBRERKTePuohuuBEf8L9ZWjr7MOgmregQRHLu+34IUDACQwh+tPz52/D89lul1WWEf2Z/ixYIu0MTJN5tonmM1iH7ZMNQnEWBA3l6SB2IUU9zGBwzAyMn2WTH9nboNRQbMUcDKH7fl61/hjWHy9dlWV0CwLXTTCKyDKiKBO6Pw3c5ksYEHMCV4sMGTKB2vC8dcl2eoOmHb/v1/3PhibQYQeWEUW8nOqO8RjsowNYRrTvbg7RFYvx9lEL8Rdj8JeCiIgULAoiIlKwKIiISMGiICIiBYuCiIjU20cXygqCwTnJ4jmDldOBIbO6z3lG82AfTSHj5wh2VE3G0ZVtMKeOkNlEZkZHGTVhfQZZLGQTzWfZNpjCZyba86XqfOaUtwSfuToO93Pf52t4vFBuUdZ1HppgCOVdYJbRGo7lAdbvg8V0D8d31+WDWcE1XC7O420vuN4tGDVkCI01kl7X4Txp3014hvoehuxMp1W2zmma789hPx9tKpEZeIRstx7eifSdcAbLio5lCc/EPAwMm60OP3yPB8f13f+niIj8m8OiICIiBYuCiIgULAoiIlKwKIiISL19dIBMoJRx9Lr9ZjG6I768HdpEVxYP2T6a3oS8D8hmOobjeCvjaANWUjIZKCuIzpOMojQhagYGwgym0dH2NRYC5dzQlDbKW7pZjZ/U1hzytvM+Wx+PZ7CVSDVK+wZzZl2ZT3QbpuOtgzV0ZQV2HBlc6VlBs6fSNCHTJj3PfV+3D1pPKljNcby5DnbPKdiO+6Yuh6iBvCXaPpl6dH9W6/y9N1/tR2fBtfAOXo6jv9qH+/zu/1NERP7NYVEQEZGCRUFERAoWBRERKVgURESkMLpFTZbR9ilnH51Ow10vb3K3ffn4EtdnIePoShuyXo6bPB3r8JJtgy1YRjuYknSqmBKFWTQ0ISrYPR1YKWQC1ZopyfxI09iuXOAzF5XTndJ1We/yI/i4z9f7GAym12MMeUaU/UOT4RYw8Wo5h/MPOVRkZM3e6X4mai0eyrJK2Ve0be2UvnQvaq0pymEiE+gwCcYgvMdTyE8iaibPLckmWubcosV6mHF0pQvvW0/XBL73xuAvBRERKVgURESkYFEQEZGCRUFERAqjuytbaDQfd7nB24WhLyuIrcA4i3VuxPShsXSCOAsaprN9yevH4+yHG7O4DjEX3fQyKvrirT+7J6gRVQMN6mnaY1UUxyo01u5v65qhl/EzgyYt/JOHri01fen80/YkE7ThHr8ZFxHuG21LEsS0sjHbNNPR17s5jxcYftv3jzea6Vmm80/N8LbJX3l03wg69sVy2FSeL/L32ArifVKcxetnhmfofMjfV4enPFxsDP5SEBGRgkVBREQKFgURESlYFEREpGBREBGR74i5AFuHbINFGISz+vAct+3ucxe+AVsn/Qn34WVZddz73eKH/3y9xiZ63R7tlvEDVQg67n5SOwxlvE3VTfsq0+Y9DJSaOA/attYQauBS1Rw7RTRcYDhUimNI0TFXWjK14N7/36T2ftY8y0c6fzCh3uN5a+GZoEiUeYiiWEG8zwIsoylEovThWTnts320/Zpt0TH4S0FERAoWBRERKVgURESkYFEQEZGCRUFEROrto+Mhb0qd9XUwjeYwTAczjg450yTlHJF9tKehOcfxQ3NejzEYK2TfoJUEmUA1uStoGVXYRLWQsVF7nmn7DvZBphbZIOka0nWttYno2iajiIa4nI75/clXKptGZCqdaB0+kyye06kdf+7v8LzREKTLhWyi8Wbg6/7b8dvW5l4tQsbRlXX4PlzejB+a89tB5mM8hu+9HQw523y9nXwv/lIQEZGCRUFERAoWBRERKVgURESkYFEQEZF6+4hMDpqmtvzpabDWPVZmHMH0oMPzcH0Pk9cOkA1SMyHqSjc7jb4mbN+MN2cwgwnMDLREaPxY3aCpfCyV2UKzcA3J4pjNT6Mn+r1+ZldjH1VeQzSKhuvHfZ5ESOZQ3+dXMFlMe3iW94f8mTvY/giT17J9NKmCzK5kGmGOFU3Mo8wqmEYYjcGKd/DKkiwjmJqWTKP5KtuVLXzvUZ5RMixfIOOIrMsx+EtBREQKFgURESlYFEREpGBREBGRgkVBRETq7SPK77j5+C2uzz4Mc46aZTZH+j1ksYQJa5QBQtbHGUwLgjJ3kimRjKQ383xgPdHDpC6avnU511kVF1I83oEGbJB0LFPIMiLLaAZ5MWlaVUv3Eo4vTbZ6+xkaPnPnU53WRfs+HIYGym6f34dnMO+2u/ys7A9wnuGZo+lt7YSMH1ifjreGZvRMTPOxkFGU7KMZmIHL5WF0ltGV1Tp/Hy7C+hSmtJ0gT+64y99l229D02jztKqywMbgLwURESlYFEREpGBREBGRgkVBRETqG823H4exFVcWv8vr04dhw6WZQdPzGzSat/PRjRgaAkTRBTSshQfKpD+ZpyiGumE66TMp5qIWOv+0TlEMtfum/aRzSoNqaNu3PvNdgHsPvdYqQYDOh4bypHiWDbwPz5sci/C0hUYzHOOxItKCWu8zaB534SMX0CDu8+nguzmD9XmISsGG8m2O61nfQIwPNKC70FS+0LAjiLPYveTm8cu39ejn5+YuDzQbg78URESkYFEQEZGCRUFERAoWBRERKVgURESk3j5a//5rXJ/9lLvczfowOs7ivJlX2Ufpz8NrLSOKoqiJvyDLiKIbamIuLmcYQEKGDFBj65yb6bsYP2TanEKkwwHiSWr/TD99JtlhGHMBVs65YsjOmaIycB9gpoQ4k/0h72ML65tzPp8tPEJHiK5IzEDJmsNnrqYhJgYHXeXP7OC9WkCMxGq1H20T3YB9tLrNcRYdDIFK5t0B7LDdJg8R2zwPLaMrxxB9QkOqbh+fJ9+LvxRERKRgURARkYJFQUREChYFEREpWBRERKTePqKMozZkHL0SbIN+m7vwZxgqcYJskJpcoJqhObX7IcuoBcuIso8icHxkzuBuYPt0/qfjpep61+YzpYEyRzBNyHhKBtOVbn8eb3vVGlyUW3RqRxkitO3b17YiawoeK3raatdrIHMozceZk00UBiZdWa9ybtEtGEK3t0Mz8uYOsoxgaE4Hw57IVNvthrlFe7CMti95fQ9GXjImb+7z+dz9IduiY/CXgoiIFCwKIiJSsCiIiEjBoiAiIgWLgoiI1NtH048wyWeVM0AmYerTBe0jsIzA2EgRLWQZzRfZHqidMpYylNrpO1hGANlRF1gffSPfgI6bcntwalrFtU35QW/t+xQygejY6Rq+x/0hc4jsKDruc4XBRdk/s2D6XVleIOMJ8olSnhFFUM3hPyzhWG7mw3flbp3fzdubbALd3eVpZ3d3OednfTvcfhnykK50YDyd4dnfbxej17ebPEltD9YlPbd398PzvP/9l7jtSvtIRETeA4uCiIgULAoiIlKwKIiISH1/srnLDRoiRVqcYWjOOQzNed0HNOFSdAMNvWih8dVDr7GBMhmbP5VxCUiIL7hQQgPGX8Bgn5Qv8Lqf4+gG7BQOJsVWXLlMadBMO7opTfs+VQ78eY+IE9o+xU5QbAU1LImuG96LxSI/43fQlJ/u8nu1hGveJ4GDxAZ4r9bLfIyr5fB5u4OG8hoiJ9Y0CAe2n4fhO/SekPBwgtiSHTSa0/p+n7clbu+y1PPwu2Hz+CasXZn/PscSjcFfCiIiUrAoiIhIwaIgIiIFi4KIiBQsCiIi8h3pCLPL6DiLK5fN0DS6UJzFsS6kYTo7/ZAh8tb6uwByCw3mSGZKC/W6T4rIW5EOEI2Q/j3QNNky6vu8TtEiaOAEo4jiH45gpJHFk/aNA2wq731Lxtc72Ge0j3kY7kLbzrps/KxX8G7Cc1gVrQGxEIt5HoSzXA7XF8tsNC7Ctlfmi8Po4TNkKZ7hu+YAltF+t6iKqEjb0/N2c5NtqoefslF09/vh+uof8rbth7zvMfhLQUREChYFEREpWBRERKRgURARkYJFQURECuO1H8pLeYE8o+dhF/68B/sIhn5QTsksDM7pIfuoFjKE8rZt3fAZyPNJlsQJLImmeR9rKn1mQ9oUMJ1c6iyrYCuRHVVrk0WzqTJXqdZIS1lRdD5tuN5XppQ3NR+uzyuf8drzSdec8rC6YAC+roMJlYbYzEI20VtWGx0LCHmTQ/i+OeznP2wTXdnDd1m65mvIeHr48C2uP/4hD865+eNwvfvdc93wsxH4S0FERAoWBRERKVgURESkYFEQEZGCRUFERL7DPtrBlK2n3J1PU9ZowlqaPHalDdOn/venjjYT3ms6WjKN0D4Cm4pyV050XdJxwLWqzflJE894qhvlKkHmTAemTTiW7lyXq0T3OR07XiuykuAa4n7CejrH1+ODrCCcdhfyfOia1OZe4fbJSINt8f6gfXX54ewoyr0iUy8ZRTQFbU9W0j5bRsR6Ncxzun/IU9Aef58to1uwj+Z/HNpKzW3Og5rAOzsGfymIiEjBoiAiIgWLgoiIFCwKIiJSsCiIiEhhtPbSg2V0el7m9c14+4jsDrJbkpXUwvQlWq/OPgrHSFlGZLdMZ+ONjSPYA3R8lxMYNXE15zP1PRx3pcUyDVPD2CbL23azadWUrZhDBGZP2+Zndg/Tt8huSaDBVWkIpQyhlB/0lglE+UR8XdI1rDPSiPTcnuE9oWl875FbdIDvoMNxfJbRldUq5xndPw5Now9gGd2DZUTT1KYP4TPn8IYf8vszBn8piIhIwaIgIiIFi4KIiBQsCiIiUhjdQTt9Wef1p1Ve3y5GN2YJirnolsM/7Z7CAJIGGnk1DeXftg+xEHB8LTR9LzUN28oIABw+A9EAk+N09La0PoNDpOFI6X7SoBVa7+A+d2F7HAQDDdsuPLNvNTgpFiPu+x0iKmiAzXyRow5mcK2msJ922r/DsCNoHocmPj1X1DjebbMgsKsYhHMMz/1brMJ3zZUHiq74OGwe3//hc9z25h9yo7n78AIHE94JiNTpn/M1HIO/FEREpGBREBGRgkVBREQKFgURESlYFEREpN4+Ony+yetkH4XOPxk/U7BEcD1YFS0YJThsAv7Evq9LxchQ1AHYR2RO1dDT4BgaTBJsEBw+Q1YS2GQYWxKsJLSMFmAlgQ0yW8zGm0pdZVwE2DrHEI1Aw45qh9WkaBGyqcgymsE1RPuIBlVVPRP0DLUVsRWLH7aMXvdfMbwKLaPHbBl9+F2OongM0RW3f8jbzn56jus4OKfCMjr/mm3RMe6VvxRERKRgURARkYJFQUREChYFEREpWBREROQ77KNvuZt9CMN0rpzDYBIaeNNRJhCsV+UCgfHUkyUBA1UuITOFjB+yb94l96nP5kh/ycYC2TCnYGYc4dwPMHzmCHYH5i0FpnCeZJ7NVuNtJbJvOFcJ1l9Woy0ZuiY1RhbZSmQwoe1WMUzndfuQfTSBj+xPTd3zFgbn0LU6Vj5vlGeUrtcSnonHD9/i+k+/y/lED7B+G+yjxe+ywdSmoTlX6HtvG2y3L/nZPPxyG9fHJCL5S0FERAoWBRERKVgURESkYFEQEZGCRUFEROrtox1lHFXki5B91EA+Ea0nKFfpAkbNaZcNh9N2Pvo80zS2t0AbJFgfLU3qgn1QVhBmIgVjI+UhvZVFc9iTDZL3cwn3CDOBaMrYCrKPQnYN5SR1MKlsWjup7Xm4voPpbcm+udKTUBSuC1ptFdMC39pPEw6G8rBo3zRdMeVk0TU50j7gM6fJmro+K7PhO3H/kPOGPnzM+UT3kHF0B3lGy49D06h73MRtmzkErZHVF0yjwy93cdvd52wf5dV/ib8URESkYFEQEZGCRUFERAoWBRERKYzuEu9flnG9ZnBOSw1lirmoaDRTQ/kIjeMjnM/+JTcKj7vhfk7wmQQOVAmNTGySwkAVHuCTG9Dz9fDfAydoEO9hGAo1VWn7FF9Azw89K3T+6Xp10JTulhRzUddoTjJAC/cBG9DwDKVmMA01OlHMQ0WExpXL5TK6oUyfeTqNX8chTfBMdDQECe7P7e3L+IYyrN9+/Da6oXxl9nH4mc0KommO0MSn76BPwzbxjhrNEEs0Bn8piIhIwaIgIiIFi4KIiBQsCiIiUrAoiIjIdwzZCfbNW0bNfHUZHSNA62RPJCPifADrAewjsox2zznOYxcGrbzXQJVkvSxW+7jtYp0Hc8zX+6ohNmkADe17tZ9VGTXbbTa7NsngghgFAofvBPtoCpbRDKykliyjrnIIVAVbMG1SBATFQhD0HJJRRNEqNcOoaMASxWXUPLPzNt/71Xob1+8fh4bQbVi7cvMhx1+sf5ftoznYR806P1uJHgaUHX+5ieu7X4f20fZL3na/ye/mGPylICIiBYuCiIgULAoiIlKwKIiISMGiICIihdE6AxoLMNwlDTKhLJop5fmAhdCH3JULWA9pmMxbA2XIstqHdRo+c641aoLFstztqs6HBq2QlZTMrjnkLS1vst2xhmu1DabWlc1maCU9PcFAHriGlC00C88QWUY0kKiD86fhUDVDZuj55AyhbvS29LyRCXQ+w/nDYKOqfVOeUXg+6V4upjBIKQzNuXJ7P8wbunLz8DLaMlqBTTT/mLdv7/ajv7P6bX7Gz9/ye7IPltGVTRics3teVn2PjcFfCiIiUrAoiIhIwaIgIiIFi4KIiBQsCiIiUm8fUS4KZvTcDu2Z2U02aiijhujPzehpUk2WcjCHiHJX0vaULUPTtMjYSFCu0gUssFqSldRCrtAc7vGKrKTbTVx/CVbSZpsnRB2+ZgOD6LqK6XVgH9H5kx03vxue/+UEk8rgfpIlstv2440fyP06wjNO09HSNaT3hJ79mmccJxHC+hKeQ3rekn20Avto8VNenz7mZ7xZjp+mdnnJ9/jwJT/7mGcUpkXuIX+M7s8Y/KUgIiIFi4KIiBQsCiIiUrAoiIhIwaIgIiL19hFO5XrMuSPz+6ERMLvP+2ggW6aHTJeUwzQ9wkQuyL+5wMSr9yFbBftd/sxjyGGqmVT1ln3VTsHKCrkzaRrb6zrYYavbbGbcglGzeR5el6dgVFx5hqlU5/PdaGtssQQzDiyW6RzO/zZv36a8Jciamm/z+uzlONrAIfMsPT+v21facbNw/mQCUW4RWS/p+exoih6sr+/GW0ZXVo9Do2gJllH34eWHJ6m9sg+ZVU/5Gd9/he8JmP54CFlr9Ex0MEVwDP5SEBGRgkVBREQKFgURESlYFEREpL7RvIaG8gKaPLOHYRNyCg27CTRJ+0PFQBloHDctNGCpyQXRCKlhTfEPs6+5ebh5yo2lTYh/OOzhT+MPef3lCc4TYgrSkB1qVncU8wBN/HWQDK7cbYZNvqfQfH6r0fy8zevTX+6HxwdDWajRjPEXEH2S4lkosoWeqzk0w1MTlu7PEYbvHMOgntf1FhrNYftFGJb1ZgManrfUmKaG8gqkFoqzWD3k9WX4zuo+5G3be/hump9HN5SvXMJAneMTNI5BsjjuafBUMz4SBCJoxuAvBRERKVgURESkYFEQEZGCRUFERAoWBRERqbePUif/yuwxd/O7sN6sYDBFFhYmTdeNL2UU8wBGSbfOxsYFBpAsdsNu/vJlWxUJQtbL7MvwGF/AytmHP3V/00qC/bTBykJTqcnn00I8yRLO/+5haB89BvPqyssmn+enz3n7z9+G289nD1XDgei4Kf5iGa5hsrp+28epyniahe1rB96glTSBYT0VA5zmFAkCxtc02Ud0XWEY1zIMNbqygPiLZEC2d3nfE/huIsiMPL8Mn8MjPMtoGcF9SFEuZLUt4ZqMwV8KIiJSsCiIiEjBoiAiIgWLgoiIFCwKIiJSbx/NwT6iLJHmIXT5YTBHc2rrBnaEDBCsbmA21ZIG/sx32R6YgyVBA3/ScBsakvH0NVtWuy1YSZCh9PIc7CO4P7RO2UeUlbS+Gz5DDx/ycb/AoBHKRPq2Gd6LX2CIyfrnD3H9BrJ16L5Nwz2a3cAAH8j5oWs1mx9GD6WhTCSyWMgySu/blGwqWCf7KJlTczCv0N4DK2l2C9ZYMI2adf7MyQy+KPZwrXb5q/McsrlOZBmB6YgZZCGHqnb42Rj8pSAiIgWLgoiIFCwKIiJSsCiIiEjBoiAiIvX2UfdT7mY3H2DCz/I83gQKZk810LFvZnl9Qjk/ZCGE/U/PYJqss63SgmmSzBTOIeqrTC2ykrabPPWp5jMnk2GW0VtWUrJ4bu/zPh4/UCZSPu59yKLZgTny69fbuH776UNVVlLMnaFJf2TxQH5UspIobyhl4rzFGd63Phx6B9PbZpe6rKB0nnOaRkeT8cgCg/UmTcGjSWrEIRtCPZiH52AaXcCuJJLVdmUW7COaOjeHTLox+EtBREQKFgURESlYFEREpGBREBGR+kZzm2Ir3hpOMQ1dqwPUIGrEUJNn342KoXir8dfktITJ5ALbp8Y5NK0wFoIatmGZzud8ztfkBANVznBtd9thw3YDA28QbEBPRjdmlxBR8PjTt7i+3eRj3IY4j1+/5ib7c4jEuPLly11cv7u/Hz0MBpuE67r4ixR9soDG7CI0IK90Xb5WB0h6SLLCOUTK0LZvRjR0p1FRHq/rqUH8xqCiFrZvlqfR3weTUzP6u4biLK5cwnvYQ6wIDWSawTOxCO/K/B6iWYy5EBGR98CiICIiBYuCiIgULAoiIlKwKIiISL19VGUZXUnWAgym6LcwhAIGqqTOfw+WTYODfcAcWoDhkE6T/mSehtWssiXRhWEgc7AbVjCw4wjr+102cPb74foOtj3DMBAEzJSbEItB9s36PtsTHz5+ieu73fB6HY9gXh3yc/j8kiM0vn3NVtJNOEaK+Gin8KyQrZNiLpbZYFquYCjNPNtHRzLVLmF4FfyzkSwjMu/S0CgaMNR2sE5Dhug9TMcYzvHtOIsur9M1PAYzEt4HiidJw3SuLG6HcSszGOjV3uVnZQz+UhARkYJFQUREChYFEREpWBRERKRgURARke+wj2j4DHTWJ8n8gByRC9hHZ7KPgmmSMkfeooXhJpSj0i660aZSA/uma5UMKRooEge7XM0EGEyyWu9GD9nZbiAraJ8tlhPkMF3I8Ais77JlRGbK3eNTXN+H7KPDMT9Xv35Zx/UTGGwvzzDw59vNYG19u6kySrqQcXRlGgbq0D1ewxAgyok6wuCcZCVNwZqa0tAgMu/CfvAdBKOxBVunoTyj9L5Rzhp8N/X0nQXfN3149injaDqH7CN690P20fQmPxMNmI5j8JeCiIgULAoiIlKwKIiISMGiICIiBYuCiIh8h31EgJSUuvw95YvA+iXkiFw574ZWyRnybGonRLXBbCIbZEr2EUzfovVJmLJGRgVO9gKLhfJy0hSv9jl/5mGTr+0e8pZo2lsNZCWRgfMQrKRDMJLemia2gewnspjSpLpdsLquLMASofuZ1slKWYF9dLPNJtTpOP5+TsEQ6iCHqEUrKdhHNBUR9kFT05Lx87oeDMgGJhr2W7CMdvAMwbOfJibSeZJ91YFhmMxIylNDW3QE/lIQEZGCRUFERAoWBRERKVgURESkYFEQEZHvsI+ofIDJgROO3oFkFF1gOhhmlJCVBOZD281HGUm/rZ/rJkcFO4GMCjIW6FjmYDKkaV1LMJWen7NRs4HpcAewWy6XYKRRdhbYYWTarO6Gps0j2WvwrLRfJ1Uku4nso/V+U5VllSbSzcG8Wt5mE+Z2nw2uMxg43XY5+jmczY51VlLILaKpiGQZ4XdKRZ4R7Bnz1y6UfUSfGZ5bfmfzteogf22a1sGAnEBO1Bj8pSAiIgWLgoiIFCwKIiJSsCiIiEh9o7mnARdNM/rPrBtowOI6DuEI+4bGZGpuXjnTUJ6KBnQLf+qemoSv22OkwWn84BA4TxpKQ9EIKS6CBvKsljBkBobyPMFwpEO45rUxJMQyHPsNRGVQo5mOZQdRB+nZ2lNUxjavL252o8UBusepyX6lBwmEzrML7xs2peHdnMGzn2IuMM6CYitg/QIRN/FdgXO/UGTLHuJz4HslvbdpwNBbcRaxoQyRFvTdacyFiIi8CxYFEREpWBRERKRgURARkYJFQUREviPmYkEDLmBQxiRYCGBDtGEYxpUpDd8JpkALlgBZLGQPUFxGH3ZD4hUOzwB75BJMEzKVcIgJ7JuiEVa3w7iIA1g2OzBnnsOQmSsvYQjSla/Pw/XL5b5uCBINLAnXhQYP3T48V5lq06ebvH0wc07w/NC1PYE5M181o+8xxkUAZLZ14Tk8gpVDzz4NdUpDg/DdJEOIomzg3U+mUa3B1J9rY3J+POYiDdN53XeKtFjmffdL7SMREXkHLAoiIlKwKIiISMGiICIiBYuCiIjU20fnm7osmnZxHm2ONDRQBuyjaTAiyB5o95CrhOZDXJ6cw8AWNBDgWMie6IKV1V2ygUBDNchwmN/sR9tXJxhKczxmA2UbhrJceYHhOy+74fn/8gS5Qv1DpZU0tC0efspTc8hKunt8qvrMfTCKaNsTZG2dwO5JJlQHlhEOtoHtaT1lcB0rcp9e90E5P8mwm9Z9p/SQw3SB55YMw7gPMh3PkHEE9znltZFlVJNx9LrvdchKusnb9mvtIxEReQcsCiIiUrAoiIhIwaIgIiIFi4KIiNTbR6f7uvrR7ofd7+4CNsQRuvCQaTLdDbvwZzBeyLTAqU9AMo1wehtAxkaCc5XguMn6gMlryZ4gm4osjuNhVjWpbBvu5y+bfI9/BiupbR7j+jRclykYWfcfsmU0h0lYt5OcldTNlqMNLrq2dA3PyWDLEUyTKRhpHdgtU7Cv0pS+A0zRO8Nx02TAZDbRRDICc4vgPWwga60m42hCAxDh+6MJRhVaRskmemN9shpewwtYRufb7//C95eCiIgULAoiIlKwKIiISMGiICIiBYuCiIh8h30E3eyGJJ52WG8uwUh63cec1mHS1DzkKlH+C+bCQHYJCAvJHiGbCKe6kX0VTIZka7zu45T33S3B+giZM7ReO8HrAnYH5fzsQ87PZp8frM8wje/PX/MUuLb9MFjrwG6hfJ7bx2wZLdc7+Mzh9Trus61D0LOSJrJRdhbl8JD1QuvJVOvWYB/BdD3MGwrHiPlBlc8hZSKlyWu1ZtOk0gJM3zdTsNpwwhpkH/U3wT4CI+10k69Jfnv+1XGN2EZERP6dYFEQEZGCRUFERAoWBRERqW80X2bQFIHGUpOajVSCaJ36RKHB11DjB9bxz9Sp+VURC3GGZnADXexTO7wN3Tzfmg4iCqhRlv7s/kob9tOGBv6bA4kodgCeicNh2LTcQsNy++sqrj9DD/JPn4cttK77qWooTQexGDcP0IC+GTagp7O8D4pEoWubhjrRQJ45NXdpyA4cY4pXmELkAg21omE1sQGNsSrjG8RvkfbTwKAvoqWYHJIYQuRIS4OxoKE8WY8fnHNewXdQfn1G4S8FEREpWBRERKRgURARkYJFQUREChYFERGpt4+QPteVNjTQG2i2N0ewDWhIRj/eKmhqh+yADTL2OGqH6VxpT/1og4liBPraz0xWFlgSFNxwQzECsH4Kg1n2EAuxgQFL26ds4HwJpsn0U1YwZt3HvA6GXQdRIau77WBtsdrHbc8dWDlk4FQMdTrTMKoVGE8UrxDufwP2UQ8xJBcaMhSOvadnHOI8KOIFn/2KmAv8nmj6OqsxmF0pluet9cki77sPj34/g+en0rL65/hLQUREChYFEREpWBRERKRgURARkYJFQURE6u2jKWTUTLNsMem+DTvo7QvYAFswFsCqSEM1MPuHsozIVqro2qM5UmkCJdPocgYDA4wsGjTSk8FVMZBoAoM85viZef0xGCiHYCRd2W7zOJDNfjhM58pfDsPP/Bnkjtnf8wktF9lKmkPeVBdMk+XtJu9jTUOTpqMtOBzIA5lIHb0/y+loG6aBZyKZSq/rx9Noo6innCQwmBrYHo2n8F7RO1s78KepWG8gU2tC62RAptsPEmVLRucI/KUgIiIFi4KIiBQsCiIiUrAoiIhIwaIgIiL19tHsS25zT1/y9u3zsN4037Il0X/L+Tf9FrZPFgJJQzVZRpVTn3ro/JPhcAErJ+UwUc4LWUmYiUTbJysJjrsFSyJNb7syux1OJLtycxhOMHsEy+iPm2Vcf9mAlfS328Ha3+H+/BVyexZ/uc/r85z/M18M1zvIT1rCNZmuDj/8HJLBdAJjkCaBJUumJ/uI7JslbH8ebt/DPmh90uTzIS7p6w3eq3ej/fHsNFpvguk53Vzq7KOH//Nh+UtBREQKFgURESlYFEREpGBREBGR72g0/w2apC/wZ/ovw6ZQ/5ybhJfNrOrP1ycp5qJioMabYHRF88MN5Qs0D1OTmAb1UIQExV/QscSoENiWwAEkIf7hymw97JStH7Kp8OHj17j+D8/ruP4SpITtl/y8fYFsgD9B3MryrzlaY7k8jI/EgPUFDPBpKsZf4XMI7895Ox9/P+keTw51g2Ni/ENlo/UMw2qgedyE4VU9iScV7/2b3zfpvQIRgGI+mk1eb9M1PFZEYlz5R1gf8b+KiMi/QywKIiJSsCiIiEjBoiAiIgWLgoiIFEY7Ds2f82CSHoyNy2Y+2npIwzCq/5S8Ihbg9TNhezKEksVzpkE4lcZC2jcO8Kkc7ENDdpIRcTlUKC9vWRU02CeYH908xyKsYFjN40/ZSvrjy2qw9gQxKbt9Pr5vZCV9zRbT+q/DoTyLZZ46NQ+m0lvnPw+mFtleBD0TZxi+E02jSlunvZBNBVbSe1Dz6tcOxmry+V/y7cz3iCJBOojtoIE/4XuymcL9qfw+/Of4S0FERAoWBRERKVgURESkYFEQEZGCRUFERApN3/d1SoOIiPybxV8KIiJSsCiIiEjBoiAiIgWLgoiIFCwKIiJSsCiIiEjBoiAiIgWLgoiIFCwKIiIy+Sf+F1KtwTd/RZntAAAAAElFTkSuQmCC", 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fXWhjn2DfE9j3FBrqNDhnHprEq2t+ru4vef0d/LvsPjSV76BxvABpgsQB4nQO9w1mtaTIhRvTEx3LcL2FZ5YiNGobzW14xo/7/G7WDhOawvYpmodEmj00t+k8U1O5gyFn7cohOyIi8gZYFEREpGBREBGRgkVBREQKFgUREam3j65gBJyeobMeYiH2YVDNa/TQWU+RFt39rsoeOG7mVT89f34c2kfb7WJ0XMCrVkEwGRqIs5j32djowdTqwT5KNsgZjBKiBQNjRtEA4d8gHUQ35AiJyWTRgN1zvYyOreghWuL+mk26h2s2Vj6G9Q9gGT1A/MU9xJmsgmm0RMMs34cOrKQGbvMlvCsnOG6yjzByIjxvXeXzRsN00r5vHLrh/ZztwLqD4z7Du0ycwqAisozOJxiwRNEVyT6iGB/Yxxj8piAiIgWLgoiIFCwKIiJSsCiIiEjBoiAiIvX20WXXjbaMbmxDzhF18qnbvnhYx/X+YTNYm4KZcQLLCDOOIM9oG8ypI+QnYS4MZNf0aRhIW5tlBJZR2DeZHFMwzOh8OshnmoP1chdsi3swgfZg/EBs0eRdGgYD0T8ps+jGCtYf0Eoabv8ANtVDW5dbtJynZ2J8rtDLOjxvZAiNNZJe1uE8ad9NhWlE59POIINrlt/DQ8g5IlOJ8pam8B5e4XzSZ8I5ZUq98m5SJlQfBudQ9tGP4DcFEREpWBRERKRgURARkYJFQUREChYFERGpt48OkAm0+3qXtw/WD3X+aWra/CGvz9JUIbAHjmvIOMIJa6vRJgNlBZGBQUZRm+wjMBDQMqo0UxJ5z2xJzCFv6W6Zr8s5mSwwja6/ZOPnAzyyNMEtMQdzZgnr9w2sB6NoBXbYanGqyrKahVwpupf0vFHWFpGe5ytcVtp3zXQ02pbeK1wHuyfbgTmv7HQ8VV3bM/zNZOrh58Fdti77xT6vh5yjKbyDV5iWOAa/KYiISMGiICIiBYuCiIgULAoiIlKwKIiISL19RJbRFmyd1IVfgGW0/JAzjrowYY1yjo6bnJWzh8lwW7KpYErS8TT6Uk1aMIG6Zrx91IJVQNPOMHOmwkyZwmQrMp6u8zq7JR37Yg+W0T7/e+UAltk5nQ8cXgvnOQc7LOUQ3VjMT6Mn4JFNlu493bday4hsHczmOl9Gb0t/8wLr04rzqc1hOleYNnQ+x2n7/8yyWizBJlrk3KI5TFNrQ0YcTZY8g3U5Br8piIhIwaIgIiIFi4KIiBQsCiIiUhjdPd1Co/m4yw3eths2RZZhOM6N+fu8PrvLDZrrsf3hYTrbdV4/HnPjM/3cPzXPXtYrB96kiIqaBuRr1EQd0PlcYVjLfHqoakyvQvzFA8QFnM/QyKwY1kLXikQAuuY1TX+KcnmL+1bbUJ6GoUavXcOmGd6LC6Sk0P2p+VfmtPKfpDQI5wSP+Ck8W3QfKELkSo1ziuwJERX9PL8nSxBv0jCdG0143s6H/Hl1eMqCzRj8piAiIgWLgoiIFCwKIiJSsCiIiEjBoiAiIt8RcwG2DnXn58EcWkCcRQvDdJoud/jPz8PDPqwXVce9382rfjKf5qyQTTQFW4esnGmFxVL7s/srWCI1VlLtcJdpn4eHNCFeojaeg6iJhaBrm+7D9xxLjTlDJlAa4kLPJkZOQJzHZPzcJaQ2cqPmGtI1oSFQyTKqjdbIT+yELaN5Xu9DFMXqHqxLsIxmEIlyDc/QCWJiNl/vJ9+L3xRERKRgURARkYJFQUREChYFEREpWBRERKTePjoe8qbLu2wOrT4+D9b6j9k+mq5yNsj1kK2ClHNE9tEehuacjuMHc5CB04JlNINhLWgrgeGQwPwbMDDeAsyLgfNswbJKGUJt7bUCQyhdw7cym9DuCZYMGUInGNJ0Au0l3U8cEAPPMg2Gomcl5RnR36RhOkQygc75Fr9yf8gMHH+fKW+J3sEFmEAp4+jG6m5oGi0qhua8QIZU+NzbwZCz7WPOqhuD3xRERKRgURARkYJFQUREChYFEREpWBRERKTePqLu/AryjBY/PQ3W2veQcQSTsM6PObfo8Dw0jfYwee0A2SA4fQryYtrpafQ1IfuGbJ2Uq5Qmvb1mt9RMJCPIKJlVWjxkDnXBPiKLo+vpGtJ6sI8qrK5XLSOYYJaMomPl83a55O1PYbrgHva9P+Tph3swBo/0DCX76A0sIwKtITKEKrOsZvFdzs9mD5bRAi2j/Fm2vB+aRv0y25VT+Dw4wTTL/Xr4Gbf5ljOOdmBjjsFvCiIiUrAoiIhIwaIgIiIFi4KIiBQsCiIiUm8fLUJX/cbqp8e43n8aZh81lHG0g1yY0G2nDJDjvq+cpFZnzqTtadsWTIaafaMd1fx4Pg9t/1b/QiCDK9lXdK06yIXpejI5xk+vo2yZC2UCVeRknYM19D2ZVck02kCO12abn/0N2ErHIxzLZbxpRM8hGUKzcJpTeE46zLcCM7AFay4Yg3Ow2pbLOsto9Y6mqQ0/J2cwifAEdtgBTMrd8zDnaPO0rLo/Y/CbgoiIFCwKIiJSsCiIiEjBoiAiIvWN5ntoKC9+HsZZ3Jg+DBsuDQyluezgp/7QQDuGn4HTECBq8NGwFiJtTwNi0jCZ1xrNCW4052tIsRh0/vFvnt/m3wi0n7RO214vdeeTrktTe4/hj14od6HiPtD9JBHicEyN5vw+PK7z+hqGVO1CnMXLsYQ1OnN6qjpoBvdhvYPPg2v+OJjMSeAAoWAeZIXFIosKq/vcOL6DdRou1oam8gXkgwPEWexCjM+NTWg0k6hw/zAUfcbiNwURESlYFEREpGBREBGRgkVBREQKFgUREam3j+5++RbX2095yE5zN+zyX7dZKzhv+ir7KP08/Fpp68zATKH1FJlAlhEN2aGf6SeuYMJgdMMbcG5mP2wwvWbaHIOFQRYY3TciHeOMbCo6HfiTaZgOmR9kg1wgQoK2P4ZojT3EbeyO+TzXYBnt4TyP4QJM4WLRBwdFZaTVFt4HimjouvysLBc5RuIuRE7c3a/rLKN7sozyO34JNhkNR9ptxltGN46H4X6Wq3x8dx+0j0RE5A2wKIiISMGiICIiBYuCiIgULAoiIlJvH/WUcfQ+D99JugHaR2QZQdc+5uWArUKGEA2CIZL1Q1lGszDw5c9/s8Icqsj4eSua4/WHB/W8tp5yfg4wHOkKFssJsoK6YINMK4YavXo+ZFMFC+4EOTeUcXSinKjwN3GQEt6HyeiMo5f95L3A1pApBlvPwuZ9l/e9BLNntciDcO4ghyiZRnfv6rKMZmASUmZXGva1W4NltM4Dcg7wuZee8buHfD7v/pBt0TH4TUFERAoWBRERKVgURESkYFEQEZGCRUFEROrto9lPOTNksgCXYTvc9YUyjmAC0RmyXuLxgWmSOvYv259/fPIa2USUT1RjveDEODi+GRkoZF+FY6FspnPFJLVaK+l0rMsKohyiw/4y/j5g5k6dlZTOP+U7vZZxRKRjaSEnqof1OVhTE7i2l2AU0fPWw39YwrHchc+J+1XOLHp3l43GdzQd7V3+bFoFo2i+3FcZg2e4b5RbtN/OB2vbTbaM9vC5R89tOp+HX77mbbWPRETkLbAoiIhIwaIgIiIFi4KIiNQ3mpuH4dCc17iu+9HDdM4hLuDVwTmhUUhDL6YzaB5Cn5maiqnx19AMl+oYhev45mb+k5NpyhF45Qbn84GBRNBQrh0okxqzFKFBcRGnY8X5VEaCvMVgH7omFHNBdN2wMbuY52ecnpV2n//mgYYPBWZwTXoYeLPos/BxtzyMGoLzsg6DbVKj9eVvLvN++vlx9D1OkSU3TmGwzY1daCjT+n6XtyUePuRIoYefh83jO2god394nHwvflMQEZGCRUFERAoWBRERKVgURESkYFEQEZF6+2gCP1+frGEQzma4ft7BthVxFi+HEqIbyCoguwWpEFBoEEzt8JlLMFYukB5C51m7Pgv3k35ef5nlaziDg6T4i2Tm0NAcHFZDxlOF2VTLWww2wtgSML76brw500OUyd2qzg6ridZIdtSNeZ8txcViuD6HoTnzsO2Nfn4Y/SwTZBMdKi2jPRhFu7BO9+0+DAG68eGnHF3x8Icvg7XF32T7aPopm1pj8JuCiIgULAoiIlKwKIiISMGiICIiBYuCiIh8h31EA1Uoz2g97MKf97nDf4V90xCbmHME2Ue15tCkwhwii4POp27QSt72ev1xE4azgvK20ymoUBOwj+C6pPOfTtu6/Kg97DtYTEcwm2qHA9WYXZS1NYNnmdbbMJRmfoXgJ4DOh0j2WRoudaNt8/vWggnVtufR29LALLTj4Hk7HvvR1hANvNnT9vBZVpPl9OFTzid6+CUbRXfBNGp/yTlJk0Xd5+E/xW8KIiJSsCiIiEjBoiAiIgWLgoiIFCwKIiLyHfbRNm96ecrd+VOFfUQZNbMWMk2a8w9n/xA1uUWX03R0ltGNKWQ8Nc3wupxg0N3lDEZJ7bS3sDnaR2CgkB1G07ra62mUlfKyD1inrKCa54omj50rs5Km8TzhfGDXdJ7JwCH7htZpkh69E+na1v5NelbS9rUTCk+n/Bl0hNyiZBTV2kSH43jLiKbJffiUbaL3v+SMo3f/bphxdKP/2+F+mvu6iZhj8JuCiIgULAoiIlKwKIiISMGiICIiBYuCiIjU20eXb4u4fnpc5vVNsI8qJ6xNKQMlWElTyFEhQwah6WjBTLlStg5YSee2HW191JoZdblKeXv+m3kfbXetum/JJrtCZlULzwpl7sTcHjRn6gyUt5jgxsYPGFzhGrYw7YyuSY3ZVPscktlUkzVWO3WPp6MtRk9Bo3t8rPxsursbWkY33n8c5hl9+DlbRu//NltGOE3tffibHXy+7caLpYO/893/p4iI/NVhURARkYJFQUREChYFEREpjO5GnL6s4vrhKTeaj9vhT8wv8DN1imhIDeUbs/nwp92z+eltYi6gqdiEaIQrNOyaFuIsKC4irdfGVlzqIjeuoZlHDT6KLiBwONI0xFzANezyzJNJR43p0ITFgS+4Pq+KUThVNOsxigK2T03irstDdvrwPuAwqtcazWFAEB0fxa2Q8HA6d6Oft912XtlQhgE5h350Q5nOc7Xcx/UPoaF84+PPw+bx+z/kRvPqb/J6+3ET1yfpM+4A7zfED43BbwoiIlKwKIiISMGiICIiBYuCiIgULAoiIlJvHx2+3uX1J4i/CD8nJ3OGLAmKrkim0RR+0j+BwTETkJLoGGtAAwUtnnCedBwVQ4BunCFy43gY3vrjBSwbsMYuMKyGiNENZMhAdEM7zwZOFwycFmwdioWggT9pWAtdF4rEqI+5uIy3puAa9nCtMD4mHAu+D82s6llJkRYUW7Hfz3/YMqqNrlgussH1EQbkfKToimAa3UOcRffzc1xv7vej3/3rMzybv+fP6zFXxG8KIiJSsCiIiEjBoiAiIgWLgoiIFCwKIiJSbx/tv0H2EeSUXIOZQoYQZeXg9hV5RlfIaLlCRssZskQuIaeF8oZqacIhTtG+qbOPaODP6Tg0Pw57MBnA4qB1yr9J5zmjwTE9WUZ5fbIM9hFsS7YODbGZVVhJlOdDzCqecRx4Q+9DbQ5TyD6agNRHzz6tp+tCmVJkJR3CM/uyb3jG03WpzTL69Eu2jD78IRtF74Jp1P+ULaPpO7CMgOt6eP5nsIwOn+/j+phEJL8piIhIwaIgIiIFi4KIiBQsCiIiUrAoiIjId9hHz3nC2ilk6LwQOv89ZLfQhDXMLRppO904w/GdKM8G1s/BtKHsn2YKlgjl3ITzrzWyWpi+1YGZ0Uf7CLJo4JocMHOmG21IkTlDhlAHGTXJSuKcpDorCXOY2mHu1343H539Q0YWgVP33ignK5lGlOWEk9fIdguZSJiTBFYbZqfB58e8Hz4r7z88VVlGDz/l7KP7n7OtNA+m0ezDNm47gSy06za/P5evw8/g/W/v4ra7L9lKylv/c/ymICIiBYuCiIgULAoiIlKwKIiIyHc0mjcQZ3GB5k9o5qWG6o0GGi7UhEwNpws0p45w3Id1Hg50oO1Ds7V2oEoaMkMNztqIhmmKKHhpzOb9XM67UYN3Xmue7rZwDSHq4QzN1sQMpIQ0TOdGv9qPj7OAazujRjMNewqxGGk4zo0dxMFQszU94xQfcobrfQJZgUhyA8VW0LHQ+aQGdM3zcKOF96eD+/bwMGwqf/w5N47ffcqN4/tf8vbLX/L27cf1YK3p83FfKVLnW36v9r8O28Q7iLPYPuZYojH4TUFERAoWBRERKVgURESkYFEQEZGCRUFEROrtoyMMYGk7sGSCmUGDY8juICspRVqcIaLhuM3HvQf7aLdejravKLqAoOEmKXZhsRraQTfmd7uq+Aca4tKH7elvHuHaklGzhfWn8AydcCDPtWoQTjp/NLju8nCTGWw/BetlCnEmVREVW4iLCNeldoDPFQ7vcgGDLdlHcNxkPJFRlEy92nvczvIzvlzlGIn3H4f20T3EXNx9yuvLn/J6+2loGd1olsNn6AoS2OUZTMffcxjFNqxvvt1Vfb6NwW8KIiJSsCiIiEjBoiAiIgWLgoiIFCwKIiJSqNMZRua/3OiWh1FrL/uA7JI0qOfG5TR+4M350FUZNSnjiEybA+y7dvhOF+yrE+0bsmjIEiEraRr+JplNNEiJso82m2xwbeI1HJ/981p+VNdXPG+QB9XC9nTfEhfIArvg8JnxGUI0fOZMzz7suzsfq65t/pvjLSOCzDg05sI9vnH/kE2gu/fDgTerD8O1l3UYmtOHoTk3pvfZYGvC6V/W+V0+fcn5RJhnFEyjXe3wsxH4TUFERAoWBRERKVgURESkYFEQEZGCRUFERAqjW9QzyC2a3+fckfm7zWCte7cbbcK8NvXpGsyHJksfaDBRDlGD69fRhszxWGcOHfaX0VYK5dkQmC8Tcn5oUtkcsoLudsN7fGO7yVbS8/NwfQ2T7k7n+6rz6frjqGlsr9lu/cO2ykqKEwBh8hjZZAeYarffXcdPaTvCcwjPMj1bbbB+6D2hZ5lMqBrbidZX8Flz/x7so4/BPoIsI7SMHvJnFk5T2w3v0Tk89zf2X3Ju0fZrXk+mEVmUP4LfFEREpGBREBGRgkVBREQKFgURESlYFEREpN4+Wj5k02T5YT3a5JiBxTKBbJkrZL1cQ47MLNgnrxkoEzCHKOeGrJe4a8i/ORxyrlKaqEVmE0H2FVpWYXu6hvNlvoanYJjduIfJa+sw1Y7so6f1vC7jKdhxPUxSwyl1YCWRfZTWuwNMzIMJgLs5ZFOFa0XGzxHMJoIspjZcw5amIsL7QPcnPYf0rs3hmqzu8/O2ChlHN5bBSuo/5s+r9v129CS1F8Cyuu6G9+L0DaY5PsLUNLD3Up4RXe80WXEsflMQEZGCRUFERAoWBRERKVgURETkOxrNFQ3llx2H9Sk1bYBL+Mk4NXJbaO42s0tVU5EGs/RhnZo5fZ8bSJvQPKRYiNR8vrGHWIQpNO2mcP5pfU6RIDD0ZEGxA/DT+3SezzAkZAP7+Pacz7+dfRis9dCwnK9yM5hiPmqeoRQf8tpz1cH2qcFLzd0jDt/J61MYwNKH86GBPKkp/ZrYkJ63NFzqxhKGPS3f5edtAevz8JmFDeU7aMx2+XyuB7jm4fk8POVn/AjyAQ3ISU1len6WIIGMwW8KIiJSsCiIiEjBoiAiIgWLgoiIFCwKIiJSbx/NYZBFB1bS7P1u/GCKY65N04poCfrJ/GwBNghEblzA5JiHn68voMNPVs78Sx4c0z0O1zdg5VBUxn6X16fTVV4Pg0zoGvYQc0G2DlkiD9vhgJPNOh8fxV98fc7n+XuIEuj7T/n4wD6iOI9pl5/beYh+IVMLY1jAYOsq7COKv9iDxTKFfwrSfmrouuNoO67WDiOjJt0HMo2mMOhrMj9VxeFM9vnankM8y6nSMiLS+0bPLMUSjcFvCiIiUrAoiIhIwaIgIiIFi4KIiBQsCiIiUhjd/u4/gWX0KXe5m/vxQx6a2ayq8z8N65RPg/ZAJd1peIzzTbYKOshuoeEuySqgbJnnp5yrdNjDEBcYeJNMFrJbaJ3Oh4yau2Cwfdh+i9uuYdDIBqyPbcii+f1LvlarVbaSVmCNUZ5RMo1asN3IYCKDqw22Ej0TtVbSMQyp+vP2FVlGsE72UTp2yu1ZgH3U03sFJmEa6tUswTKagem4h2sF2VznsH6GHDO6P3RtZ+EZwtyn99pHIiLyBlgURESkYFEQEZGCRUFERAoWBRERqbePZh/BMnq/Hz+xCDKOEJimFqFdN7mT30BGTQOTllIO0/U+2xDTVbZvZpCvkqwCMhCIJ7CsyEpKU+Bq7aOcWvSKVXI3NCUePj6OntJ2YwM5MofPw6N53ubH+/OXd3H9/n44va1+UtumziiBTKR0DXu4rrMWpoPBM3E+08syvF7tKe+7v4DFA8zC+0bn068gawusthm8b02a9AjvN3IAc2gL9lGw4C54vSejPw9uzIN9tYBMuv5jXh+D3xRERKRgURARkYJFQUREChYFERGpbzQ3D9BQXuSmyCT1cyiJAhrQVxh4cw3NnCs0pTH+YgZNbGq2hgFBNDSImtXUsE1RHFdoTtFP48/nfK1O8BP742HYKHsKw35ea1jS+oqGnoSm6goGp3z4lOMvNps8fGgX4gUe17kZ+LTOzeqvXx7i+v1DbtqlASezMBznZZ3iL6BJnBrN80V+B3uIlpiFQUo3jiGy5cYlvEP0vF3g3tMzno6FYlJmEP1BosYUGtbx/aR38AzP+A4azRC3cgnvGzWa06CrGy01mkMMS/8A0SwfjLkQEZE3wKIgIiIFi4KIiBQsCiIiUrAoiIhIvX00AdOGu/mh3kDH/go/GaefkqfOP9k6Ddgd0xOYDDSUJw32oWsCERoUf9EFW2e+y+e+guEeh102ava7+ej4i+02R0ucwVYh+4hYhoEgKf7gxj38fP/T9mtc34frcjrnOIsTPCuPzzm44/Fr3s/qfjPaqJnDe4LDauaH0cOLFsscwzEPUSY3jid4D+FVHhv78rIOtl8yamYwNIgMLhpUhO9hOkZ6ZoPRWGsZvayHZ6uZXqsGLHVLGF4VYnVm7yBqp2LI2eD//e7/U0RE/uqwKIiISMGiICIiBYuCiIgULAoiIvId9tGsLjMkdfMpR+QKps15k42ac9j+ChktlMVCJsMUhmrMghGA1kPlgJy0nxYMBDITFjAIZrHZjR6ys93OR5s9r+Ut1WQlUfYRWTw0lOcQjvEA9/LxeVGVCfQMVtImrC9g8BKZJjRkJw1aSVlLN5Zh+MqNFdz7E+Vknaaj85NwaBDYRynnh4YDka2DOWYVmWKTA+SskRl5ACuJctlCflRD16rNx93RkKG7kLUV1l6AnKgx+E1BREQKFgURESlYFEREpGBREBGRgkVBRES+wz4iyD4K09Swk3+oyxc5h6lhZAMQaASAaXMJxlPTV2a0kD0R8lKmkAnUwpQpspLIWElTvNbPyyr7CK0kmtYF64nl3bbKskqT2o7HrsqOOsDztg85UTfWT0P76O7d+Cltr97n8Gz1sI+UwXRjD3lYZB8dw3tI2VS0TlZSWqd3kN6TmsmFONGRpjxizlqX18FUS8dCltUUsp/oHU/T+xqyjOizZgR+UxARkYJFQUREChYFEREpWBRERKRgURARkTe0j/5fQrJBMJ5wElLIc3mN0w5MgW5ocsz6t5kcNQlZLylD5c/7gGlNYCzwtK6hyTKHfaw3OStos+2rLJ4LmWoVkH20ClPdPhyHRtJrk+Qen+6qbKX9fpgVtYNrtdxvq0yTZCX1YJiRqXUkcwYmz+1g8l6i68CQIVspPPs0pY3ATC0wipo0oRHeK5zyeIBMJPpcCYZUyn26MQNzKFlGL/tZVOSvUVbdCPymICIiBYuCiIgULAoiIlKwKIiIyHc0mrtLXV0J21NTZFodFzG+iULRCtSApmbWNDSDaxvKNdvjoBGIBqCGJQ9mGTYnV3ebqkbz8yYP5XlcQ7zC6f3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