
    iΜ              .       z   d dl mZ d dlZd dlmZ ddlmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZ ddgZ G d de      Zd	d
e de
 de de de de dz   e_        dee   dee   dee   dee   dee   dee   dedz  dedz  dededeez  deez  deez  dededededed ed!df(d"Zdee   dee   dee   dee   dee   dee   dedz  dedz  dededeez  deez  deez  dededededed ed!df(d#Z dee   dee   dee   dee   dee   dee   dedz  dedz  dededeez  deez  deez  dededededed ed!df(d$Z! e	e%      	 	 	 	 	 	 	 	 d)dee   dee   dee   dee   dee   dee   d&edz  deded'edz  dedz  dedz  ded ededeez  deez  deez  dededed!df,d(       Z"y)*    )castN)Tensor   )_capturable_doc_default_to_fused_or_foreach_device_dtype_check_for_fused_differentiable_doc_disable_dynamo_if_unsupported_foreach_doc
_fused_doc!_get_capturable_supported_devices_get_scalar_dtype
_get_value_maximize_doc_params_doc_stack_if_compiling
_to_scalar_use_grad_for_differentiable_view_as_real
DeviceDictDeviceDtypeDict	OptimizerParamsTAdamadamc                        e Zd Z	 	 	 	 	 dddddddddedeez  deeez  eez  f   deded	ed
edz  dededededz  deddf fdZ fdZ	d Z
edd       Z xZS )r   FN)foreachmaximize
capturabledifferentiablefuseddecoupled_weight_decayparamslrbetasepsweight_decayamsgradr   r   r   r    r!   r"   returnc                   t        |t              r-|r|	st        d      |j                         dk7  rt        d      d|k  st        d|       d|k  st        d|       d|d   cxk  rdk  sn t        d	|d          d|d   cxk  rdk  sn t        d
|d          d|k  st        d|       t        |d   t              rt        |d   t              s1t        |d   t              rt        |d   t              st        d      t        |d   t              r0|	s|rt        d      |d   j                         dk7  rt        d      t        |d   t              r0|	s|rt        d      |d   j                         dk7  rt        d      t        t        t        |            }||||||||	|
||d}t        | %  ||       |r"|
rt        d      d| _        |rt        d      y y )NElr as a Tensor is not supported for capturable=False and foreach=Truer   Tensor lr must be 1-element        zInvalid learning rate: zInvalid epsilon value: r         ?z#Invalid beta parameter at index 0: z#Invalid beta parameter at index 1: zInvalid weight_decay value: z0betas must be either both floats or both TensorszKbetas[0] as a Tensor is not supported for capturable=False and foreach=Truez!Tensor betas[0] must be 1-elementzKbetas[1] as a Tensor is not supported for capturable=False and foreach=Truez!Tensor betas[1] must be 1-element)r$   r%   r&   r'   r(   r   r   r   r    r!   r"   z)`fused` does not support `differentiable`Tz0`fused` and `foreach` cannot be `True` together.)
isinstancer   
ValueErrornumelfloattuplemapr   super__init__RuntimeError_step_supports_amp_scaling)selfr#   r$   r%   r&   r'   r(   r   r   r   r    r!   r"   defaults	__class__s                 J/var/www/html/engine/venv/lib/python3.12/site-packages/torch/optim/adam.pyr6   zAdam.__init__#   s)     b&!z [  xxzQ !>??by6rd;<<cz6se<==eAh$$B58*MNNeAh$$B58*MNNl";L>JKKa%(Za%-H58V,E!Hf1MOPPeAh'' a  Qx~~1$ !DEEeAh'' a  Qx~~1$ !DEEc*e,- ( $,&<
 	*"#NOO.2D+
 "#UVV      c                    t         |   |       | j                  D ]5  }|j                  dd       |j                  dd       |j                  dd        |j                  dd       |j                  dd       |j                  dd       |j                  dd       }|d	   D ]  }| j                  j                  |g       }t        |      d
k7  s.t        j                  |d         rGt        |d         }|d   s|d   r,t        j                  |t        |      |j                        nt        j                  |t                     |d<    8 y )Nr(   Fr   r   r   r    r"   r!   r#   r   stepis_fuseddtypedevicerC   )r5   __setstate__param_groups
setdefaultstategetlentorch	is_tensorr2   tensorr   rD   )r9   rI   groupr!   pp_statestep_valr;   s          r<   rF   zAdam.__setstate__s   s6   U#&& 	EY.Z/Y-\51-u55u=$$Wd3E8_ **..B/w<1$U__WV_-M$WV_5H !.%. $"3U"C#$88 #\\(:K:MN FO		r=   c                 R   d}|d   D ]  }	|	j                   |t        j                  |	      z  }|j                  |	       |	j                   j                  rt        d      |j                  |	j                          | j                  |	   }
t        |
      dk(  r|d   rt        |	       |d   s|d   r/t        j                  dt        |d         |	j                  	      nt        j                  d
t                     |
d<   t        j                  |	t        j                        |
d<   t        j                  |	t        j                        |
d<   |d   r(t        j                  |	t        j                        |
d<   |j                  |
d          |j                  |
d          |d   r|j                  |
d          |d   r|
d   j                  rt        d      |d   r(t        j                   |d         r|d   st        d      |j                  |
d           |S )NFr#   zJAdam does not support sparse gradients, please consider SparseAdam insteadr   r!   r    r@   rB   r-   rE   r?   )memory_formatexp_avg
exp_avg_sqr(   max_exp_avg_sqr    zB`requires_grad` is not supported for `step` in differentiable moder   r$   r+   )gradrL   
is_complexappend	is_sparser7   rI   rK   r   zerosr   rD   rN   
zeros_likepreserve_formatrequires_gradrM   )r9   rO   params_with_gradgradsexp_avgsexp_avg_sqsmax_exp_avg_sqsstate_stepshas_complexrP   rI   s              r<   _init_groupzAdam._init_group   s    x =	2Avv!u//22 ''*66##&d  QVV$

1u:?W~5a8 !.%. "3U7^"L#$88 #\\#5F5HI &M (-'7'7)>)>(E)$ +0*:*:)>)>+E,' Y'272B2BU-B-B3./ i 01""5#67##**51A+BC)*uV}/J/J&\  )$d4!,/&_  ""5=1{=	2| r=   c                    | j                          d}|$t        j                         5   |       }ddd       | j                  D ]  }g }g }g }g }g }g }	|d   \  }
}| j	                  |||||||	      }t        ||||||	f|d   ||
||d   |d   |d   |d   |d   |d	   |d
   |d   t        | dd      t        | dd      |d   d  |S # 1 sw Y   xY w)zPerform a single optimization step.

        Args:
            closure (Callable, optional): A closure that reevaluates the model
                and returns the loss.
        Nr%   r(   r$   r'   r&   r   r   r   r    r!   
grad_scale	found_infr"   )r(   rg   beta1beta2r$   r'   r&   r   r   r   r    r!   rj   rk   r"   ) _cuda_graph_capture_health_checkrL   enable_gradrG   rh   r   getattr)r9   closurelossrO   ra   rb   rc   rd   re   rf   rl   rm   rg   s                r<   r?   z	Adam.step   sG    	--/""$ !y! && )	E-/"$E%'H(*K,.O(*K >LE5** K   i(';">2%Lz*i( .$%56Gn"4t<!$T:',-E'F+')	V ]! !s   C

C)gMbP?)g?g+?g:0yE>r   FN)__name__
__module____qualname__r   r2   r   r3   boolr6   rF   rh   r   r?   __classcell__)r;   s   @r<   r   r   "   s    "7CNW  $ $!',NWNW FNNW UV^UV^34	NW
 NW NW NW NW NW NW NW d{NW !%NW 
NW`0IV "9 "9r=   af  Implements Adam algorithm.

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \gamma \text{ (lr)}, \beta_1, \beta_2
                \text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)}          \\
            &\hspace{13mm}      \lambda \text{ (weight decay)},  \: \textit{amsgrad},
                \:\textit{maximize},  \: \epsilon \text{ (epsilon)}                              \\
            &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                v_0\leftarrow 0 \text{ (second moment)},\: v_0^{max}\leftarrow 0          \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do}                         \\

            &\hspace{5mm}\textbf{if} \: \textit{maximize}:                                       \\
            &\hspace{10mm}g_t           \leftarrow   -\nabla_{\theta} f_t (\theta_{t-1})         \\
            &\hspace{5mm}\textbf{else}                                                           \\
            &\hspace{10mm}g_t           \leftarrow   \nabla_{\theta} f_t (\theta_{t-1})          \\
            &\hspace{5mm}\textbf{if} \: \lambda \neq 0                                           \\
            &\hspace{10mm} g_t \leftarrow g_t + \lambda  \theta_{t-1}                            \\
            &\hspace{5mm}m_t           \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t          \\
            &\hspace{5mm}v_t           \leftarrow   \beta_2 v_{t-1} + (1-\beta_2) g^2_t          \\
            &\hspace{5mm}\widehat{m_t} \leftarrow   m_t/\big(1-\beta_1^t \big)                   \\
            &\hspace{5mm}\textbf{if} \: amsgrad                                                  \\
            &\hspace{10mm} v_t^{max} \leftarrow \mathrm{max}(v_{t-1}^{max},v_t)                  \\
            &\hspace{10mm}\widehat{v_t} \leftarrow v_t^{max}/\big(1-\beta_2^t \big)              \\
            &\hspace{5mm}\textbf{else}                                                           \\
            &\hspace{10mm}\widehat{v_t} \leftarrow   v_t/\big(1-\beta_2^t \big)                  \\
            &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
                \big(\sqrt{\widehat{v_t}} + \epsilon \big)                                       \\
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
            &\bf{return} \:  \theta_t                                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
       \end{aligned}

    For further details regarding the algorithm we refer to `Adam: A Method for Stochastic Optimization`_.
    z
    Args:
        aG  
        lr (float, Tensor, optional): learning rate (default: 1e-3). A tensor LR
            is not yet supported for all our implementations. Please use a float
            LR if you are not also specifying fused=True or capturable=True.
        betas (tuple[Union[float, Tensor], Union[float, Tensor]], optional):
            coefficients used for computing running averages of gradient and
            its square. If a tensor is provided, must be 1-element. (default: (0.9, 0.999))
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-8)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
        decoupled_weight_decay (bool, optional): if True, this optimizer is
            equivalent to AdamW and the algorithm will not accumulate weight
            decay in the momentum nor variance. (default: False)
        amsgrad (bool, optional): whether to use the AMSGrad variant of this
            algorithm from the paper `On the Convergence of Adam and Beyond`_
            (default: False)
        z	
        a=  
    .. Note::
        A prototype implementation of Adam and AdamW for MPS supports `torch.float32` and `torch.float16`.
    .. _Adam\: A Method for Stochastic Optimization:
        https://arxiv.org/abs/1412.6980
    .. _On the Convergence of Adam and Beyond:
        https://openreview.net/forum?id=ryQu7f-RZ

    r#   rb   rc   rd   re   rf   rj   rk   r(   rg   rl   rm   r$   r'   r&   r   r   r    r"   r)   c          
         ||t        d      t        j                  j                         rut	        |t
              st        dt        |             t	        |
t
              st        dt        |
             t	        |t
              s8t        dt        |             t        |      }t        |
      }
t        |      }t	        |
t              r|
j                  |
j                  f|
i}nd }t        |       D ]  \  }}|s||   n||    }||   }||   }||   }t        j                  j                         s`|r^t               }|j                  j                  |j                  j                  k(  r|j                  j                  |v st        d| d      |dz  }|dk7  r|r|j                  d||z  z
         nf|rQt	        |t              rA|j                   r!|j#                  |j%                         |      }n'|j'                  ||	      }n|j'                  ||	      }t        j(                  |      rqt        j*                  |      }t        j*                  |      }t        j*                  |      }|rt        j*                  ||         ||<   t        j*                  |      }|j                  }|1|j                  }||f}||vr|
j-                  ||d
      ||<   ||   }n|
}|j/                  |d|z
         |r{t	        |t              rk|j                   r*|j/                  t        j0                  |      d|z
         n[|j                  |      j#                  ||t3        t
        d|z
               n&|j                  |      j#                  ||d|z
         |s|r|}|r<t	        |
t              r,|
j                   rd|
|j%                         z  z
  } nd|
|z  z
  } nd|
|z  z
  } |r<t	        |t              r,|j                   rd||j%                         z  z
  }!nd||z  z
  }!nd||z  z
  }!|| z  }"|"j5                         }#|!j7                         }$|ro|r||   j%                         }%n||   }%||   j9                  t        j:                  |%|             ||   j7                         |$|#z  z  j=                  ||#z        }&n(|j7                         |$|#z  z  j=                  ||#z        }&|r!|j?                  |j%                         |&       n|j?                  ||&       ntA        |      }d|
|z  z
  } d||z  z
  }!|| z  }"|!dz  }$|rDt        j:                  ||   |||          ||   j7                         |$z  j=                  |      }&n"|j7                         |$z  j=                  |      }&|j?                  ||&|"        |st        j(                  | |         st        jB                  ||         ||<    y )N,Expected grad_scale and found_inf to be Nonez#Expected lr to be a float, but got z&Expected beta1 to be a float, but got z&Expected beta2 to be a float, but got IIf capturable=True, params and state_steps must be on supported devices: .r   r   alphaT)rD   rC   non_blocking)weight)value      ?)out)"AssertionErrorrL   jitis_scriptingr/   r2   typer   r   rD   rC   	enumeratecompileris_compilingr   mul_r`   addcmul_cloneaddrZ   view_as_realtolerp_squarer   negsqrtcopy_maximumadd_addcdiv_r   view_as_complex)'r#   rb   rc   rd   re   rf   rj   rk   r(   rg   rl   rm   r$   r'   r&   r   r   r    r"   
beta1_dictiparamrY   rV   rW   step_tcapturable_supported_devicesrD   rC   keydevice_beta1r?   bias_correction1bias_correction2	step_sizestep_size_negbias_correction2_sqrtrX   denoms'                                          r<   _single_tensor_adamr   [  s   , !6KLLyy "e$ #FtBxj!QRR%' #I$u+!WXX%' #I$u+!WXX^5!5! % /4||U[[.I5-Q

f% [K5'uQxeAhY1+ ^
Q ~~**,+L+N(!!V]]%7%77LL%%)EE$_`|_}}~ 
 	!1%

1rL001 "jv&F#11#}}U[[]LI  $xx\xB88E8>DE"%%d+D((1G++J7J%*%7%78J%K"&&u-E!KKE 5/C*$"'((!T #+ #
3 ,6c?L L 	dA,- j7""   d!3AI F&//$d5!e)&< 0  OOE"++D$a%i+HD *UF";&&'(5DJJL+@'@$'(5$;$#$ud{?  *UF";&&'(5DJJL+@'@$'(5$;$#$ud{? --I%MMOM$4$9$9$;!!%4Q%7%=%=%?N%4Q%7N"((~z)RS $A&++-1F1VW$s]*+ 
 OO%)>)NO$s]*+  w}}6w.f%D 5$; 5$;--I$4c$9!oa0*/RSBTU )+0025JJPPQTU#*-BBHHMNN7E)N< u''q	2!&!6!6q7I!JOAw[Kr=   c          
      V  - t        |       dk(  ry t        |t              r+|st        d      |j	                         dk7  rt        d      t        |
t              r+|st        d      |
j	                         dk7  rt        d      t        |t              r+|st        d      |j	                         dk7  rt        d      t        j                  j                         s=|r;t        d	
      -t        -fdt        | |d      D              st        d- d      ||t        d      |rt        d      t        |      }t        |
      }
t        |      }t        j                  | |||||g      }t        |
t              r&t!        |
j"                        dk7  r|
j"                  |
ind }|j%                         D ]  \  \  }}}}}}}t'        t(        t           |      }t'        t(        t           |      }t'        t(        t           |      }t'        t(        t           |      }t'        t(        t           |      } |d   j"                  }!||!|vr|
j+                  |!d      ||!<   |r||!   n|
}"|	r7|r't'        t(        t           |      }#t-        |||||#       nt-        ||||       |rt        j.                  |      }t        j                  j                         s=| d   j0                  r.t        j2                  | t        j4                  dd      d       nt        j2                  | d       |dk7  rR|rt        j6                  |d||z  z
         n3|rt        j2                  |||       nt        j8                  |||      }t        j:                  ||t'        t<        d|"z
               t        j6                  ||       t        |t        j                        rt        j>                  |d|z
        }$d}%n|}$d|z
  }%t        j@                  ||$||%       ~~$|rft        jB                  |
|       }&t        jB                  ||       }'t        jD                  |&d       t        jD                  |'d       t        jF                  |'       t        jH                  |&|       t        jJ                  |&       t        jL                  |'       |&}(|'})|rCt'        t(        t           |      }#t        jN                  |#|       t        jP                  |#      }*nt        jP                  |      }*t        jH                  |*|)       t        j2                  |*|       t        jH                  |*|(       t        jR                  |||*       | D +cg c]  }+d|
tU        |+      z  z
   }&}+| D +cg c]  }+d|tU        |+      z  z
   }'}+tW        |&D ,cg c]
  },||,z  dz   c},      }(|'D ,cg c]  },|,dz  	 })},|rCt'        t(        t           |      }#t        jN                  |#|       t        jP                  |#      }*nt        jP                  |      }*t        jH                  |*|)       t        j2                  |*|       t        jR                  |||*|(        y c c}+w c c}+w c c},w c c},w )Nr   r+   r   r,   zHbeta1 as a Tensor is not supported for capturable=False and foreach=TruezTensor beta1 must be 1-elementzHbeta2 as a Tensor is not supported for capturable=False and foreach=TruezTensor beta2 must be 1-elementF)supports_xlac              3      K   | ]N  \  }}|j                   j                  |j                   j                  k(  xr |j                   j                  v  P y wrs   )rD   r   ).0rP   r?   r   s      r<   	<genexpr>z%_multi_tensor_adam.<locals>.<genexpr>`  sQ      
 4 HHMMT[[--- >!==>
s   AAT)strictr{   r|   rz   z#_foreach ops don't support autogradcpurD   r   r.   )rD   r}   r   ),rK   r/   r   r7   r1   r0   rL   r   r   r   allzipr   r   r   "_group_tensors_by_device_and_dtypestrrD   valuesr   listr   r   _foreach_negis_cpu_foreach_add_rN   _foreach_mul__foreach_add_foreach_lerp_r2   _foreach_mul_foreach_addcmul__foreach_pow_foreach_sub__foreach_neg__foreach_div__foreach_reciprocal__foreach_sqrt__foreach_maximum__foreach_sqrt_foreach_addcdiv_r   r   ).r#   rb   rc   rd   re   rf   rj   rk   r(   rg   rl   rm   r$   r'   r&   r   r   r    r"   grouped_tensorsr   device_params_device_grads_device_exp_avgs_device_exp_avg_sqs_device_max_exp_avg_sqs_device_state_steps__device_paramsdevice_gradsdevice_exp_avgsdevice_exp_avg_sqsdevice_state_stepsrD   r   device_max_exp_avg_sqsscaled_device_gradsr   r   r   r   r   exp_avg_sq_sqrtr?   bcr   s.                                                @r<   _multi_tensor_adamr   *  sq   , 6{a"fW  88:?:;;% Z  ;;=A=>>% Z  ;;=A=>> >>&&(Z'H(
$  
 v{4@
 

 ![\x[yyz{  !6KLLBCC	BBuEuEBB	+LO eV$U\\):e)C 
u  ""$a 		 	T&\>:DL-8tF|-=>!$v,0CD!$v,0CDq!((!fJ&>!&d!KJv-7z&)U )-d6l<S)T&! #&* !<BT  --l;L ~~**,1CA1F1M1M"ELLU$C3  2A61%##M1rL7H3HI ''m<X#(#5#5$m<$L 	\4q<7G+H	
 	.6 eU\\*"'"4"4\1u9"ME".IE 3\5	

  $11%9KL$11%9KL 0!4 0!4 01  0"5&&'78  !12
 )I$4!)-d6l<S)T&''(>@RS #("5"56L"M"'"5"56H"I1FG5; ##M?OT ;M 26EZ---    ;M 26EZ---    ,FV,Wb2g^,WXI7G$HRW$H!$H)-d6l<S)T&''(>@RS #("5"56L"M"'"5"56H"I1FG5##	yaJ   -X$Hs   Z*ZZ!
'Z&c                >   | sy |rt        d      t        |
      }
t        |      }||j                  |ini }||j                  |ini }t        |t              r&t        |j                        dk7  r|j                  |ind }t        j                  | |||||g      }|j                         D ]l  \  \  }}\  \  }}}}}}}t        t        t           |      }t        t        t           |      } t        t        t           |      }!t        t        t           |      }"t        t        t           |      }#d\  }$}%|#|j                  ||j                  |d            }$|#|j                  ||j                  |d            }%|||vr|j                  |d      ||<   ||   }t        j                  |#d       |st        j                  nt        j                   }& |&|| |!|"||#|||
|||||$|%       |%Jt        j"                  |#|%gt%        |#      z         o y )	Nz9Adam with fused=True does not support differentiable=Truer   )NNT)r   r   r   )	r(   r$   rl   rm   r'   r&   r   rj   rk   )r7   r   rD   r/   r   r   r   r   itemsr   r   rH   r   rL   r   _fused_adam__fused_adamw_r   rK   )'r#   rb   rc   rd   re   rf   rj   rk   r(   rg   rl   rm   r$   r'   r&   r   r   r    r"   grad_scale_dictfound_inf_dictlr_dictr   rD   r   r   r   r   r   r   r   r   r   r   r   r   device_grad_scaledevice_found_inffuncs'                                          r<   _fused_adamr   #  s_   , VWWuEuE ,6+A		J'r  *3)>		9%B  &b&1c"))n6MBSW   BB	+LO 
			 3 
	 
	
"	T&\>:DL-8tF|-=>!$v,0CD!$v,0CD.8++! / : :
f4@!  -88	V$?  6#8 ee6eEGFOB.2)?u!!UEXEX"%(&	
" '"%5$6=O9P$Pc3r=   )single_tensor_fnr   r!   c                h   |	)|'t        | |d      \  }}|rt        |t              r|sd}|	d}	|d}t        j                  j                         st        d |D              st        d      |r)t        j                  j                         rt        d      |	r)t        j                  j                         rt        d      |	r%t        j                  j                         st        }n-|r%t        j                  j                         st        }nt        } || |||||f|||||||||||
||d y)	znFunctional API that performs Adam algorithm computation.

    See :class:`~torch.optim.Adam` for details.
    NF)	use_fusedc              3   P   K   | ]  }t        |t        j                           y wrs   )r/   rL   r   )r   ts     r<   r   zadam.<locals>.<genexpr>  s       5()
1ell#5s   $&zPAPI has changed, `state_steps` argument must contain a list of singleton tensorsz6torch.jit.script not supported with foreach optimizersz4torch.jit.script not supported with fused optimizers)r(   rg   rl   rm   r$   r'   r&   r   r   r    rj   rk   r"   )r   r/   r   rL   r   r   r   r7   r   r   r   r   r   )r#   rb   rc   rd   re   rf   r   r   r    r!   rj   rk   rg   r"   r(   rl   rm   r$   r'   r&   r   r   r   s                          r<   r   r     s=   F }1Ne

7 z"f-jG} >>&&( 5-85 2 ^
 	
 599))+STT'')QRRUYY++-	//1!" !%5'r=   )NFFNNNFF)#typingr   rL   r   	optimizerr   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   __all__r   __doc__r   rw   r2   r   r   r   r   rT   r=   r<   <module>r      s5          0 6
n9 nd$J		 	  
 		 		 		 		 -KC PLKLLK<LK 6lLK f	LK
 &\LK fLK LK }LK LK LK 6>LK 6>LK 	LK LK  
!LK" #LK$ %LK& 'LK( !)LK* 
+LK^vLv<v 6lv f	v
 &\v fv v }v v v 6>v 6>v 	v v  
!v" #v$ %v& 'v( !)v* 
+vr`L`<` 6l` f	`
 &\` f` ` }` ` ` 6>` 6>` 	` `  
!`" #`$ %`& '`( !)`* 
+`F  1DE    $##(!WLW<W 6lW f	W
 &\W fW D[W W W $;W W }W W  !!W$ %W& 6>'W( 6>)W* 	+W, -W. 
/W0 1W2 
3W FWr=   