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alrighty when we get started  um  so  welcome back nice to see you all  um  and  what have we been doing  in theory of computation  we have been talking about touring  machines  and about uh  the power of touring machines we started  uh at the beginning by  showing um a bunch of decidability  theorems that exhibit the power of  turing machines  to  calculate properties of  finite automata context-free grammars  and so on  in some cases and last lecture we talked  about the limitations of  the power of turing machines by  um  proving undecidability theorems so we  showed that  this language atm  the acceptance problem for turing  machines itself is an undecidable  problem  that was the first of many undecidable  problems that we're going to encounter  and though we proved the undecidability  of atm using the diagonalization method  as you hopefully remember  we're going to introduce a new method  which we kind of basically previewed  last time called the reducibility method  which is the way other problems are  typically shown to be undecidable  um  and so we're going to stick with that uh  for uh this lecture and also next  lecture um we're going to be talking  about um  undecidability and i think there's going  to be a few additional uh discussions  after that but this is one of the  important uh themes of the course is to  understand kind of that threshold  between decidability and undecidability  or the limitations of computation  um  so today um as i mentioned we're going  to talk about the reducibility method  for proving problems undecidable and  also for proving problems  non-touring recognizable uh turning  unrecognizable  we're going to introduce  this notion of a reducibility um in  general and we'll also talk about a very  specific kind of reducibility called the  mapping reducibility so today as  promised we're going to talk about using  reduce abilities  to prove problems are undecidable or  unrecognizable  so that's going to be our general method  oops make myself smaller thank you  i always forget  uh  thank you um  for the reminder  so  uh  so using um reducibilities to prove  problems are undecidable or  unrecognizable  and the basic way that works is we're  going to leverage another some problem  we already know  is undecidable say or unrecognizable to  prove other problems are unrecognizable  so we did a quick example of that last  time we're going to go over that example  again um just to set this set the stage  and then we're going to talk about that  in greater detail  um  so uh  as you recall from last time we had this  problem halt tm  which is the problem of testing for a  given turing machine and an input to  that turing machine whether the turing  machine halts either accepting or  rejecting but just whether it holds um  which is a somewhat different problem  closely related obviously but somewhat  different than the atm problem which is  just testing whether the turing machine  accepts  um you know it's we already showed that  atm is undecidable  um now  conceivably whole tm might be decidable  um you know it's not exactly the same  problem  but we're going to show that whole tm is  likewise undecidable uh we did this last  time but i'm just going over it again uh  i'm going to likewise show that whole tm  is undecidable we could go back to the  um the diagonalization method and do it  from scratch  but uh generally that's not what's done  generally what people do is they use a  reduceability from a known undecidable  problem um so what we're going to show  is a proof by contradiction which says  that  if  um  halt tm were decidable then atm would  also be decidable and we know it isn't  um that and that's by virtue of what we  call a reduceability from atm to whole  tm and i'll explain with the terminology  and and we'll have a chance to play with  the concept all all lecture long um so  we're going to see it in all sorts of  different vari variations um  so  as i said we'll assume whole tm is  decidable and use that to show that atm  is decidable which we know is not true  um  so quickly going through it because we  we did it already once before um  we're gonna assume  you know that whole tm is decidable  let's say turing machine r  is the decider  and now we're going to show that atm is  decidable by constructing a turing  machine s  which uses r  to decide atm  that's going to be our contradiction  so here is the machine s  the machine is you know you have to keep  in mind what the goal of s is go s is  this we're going to design s to solve  atm  which we know is not decidable so that  don't get confused by that we're aiming  for a contradiction  so we're going to use  s is typically  well there might be other variations but  for now s is going to be used to decide  atm  so we can try to figure out how can we  decide atm  and the way we're going to do it is  use our halt tm  tester that we assumed um to have  and we'll first take our  m and w where we're trying to determine  it does m accept w  and we'll first test whether m holds on  w  if it doesn't or done  because it couldn't be accepting w  m couldn't be accepting w if it's not  even this whole thing on w  um  so if it  uh  r reports doesn't halt we can reject  right off  but  um even if r says it does hold  we're still in good shape because now we  can run m on w until completion because  r has promised us that it's going to  halt  r r stated and r is assumed to be  correct  r is stated that m holds on w so now we  don't have to worry about getting into a  loop which we're not allowed to do since  we're making a decider  um we're trying to decide atm here so we  but now we can run them on w to  completion we can find out what what um  m does on w and then we can act  accordingly  so we're using the whole tm decider to  decide atm that's the name of the game  here okay um  and that's a contradiction and so  therefore our assumption that whole tm  was decidable had to be false so it's  undecidable  okay um  important to understand this  uh because this is  um sort of the prototype  for all of the other uh  uh undecidable undecidability uh proofs  that we're gonna do going forward  okay so we can just take a few seconds  here if there's something that you're  not getting about this  it's a good time to ask  not seeing many messages here or any so  why don't we go on  um but if you know if you ask i can get  to it uh next slide too  all right here we go so here's the  concept of reducibility  and i know i've taught this course many  times i know where the bumpy uh places  are in terms of people struggling with  material  the concept of reducibility is um  is a bit tricky  so don't feel bad if you don't get it  right away  you know so that's why i'm going to try  to go slowly in this lecture to make  sure we're all together  on understanding how redu reducibility  works  okay so the concept of reducibility is  that we say one problem is reducible to  another say a reducible to b  it means  that you can use b  to solve a  that's what it means for a to be  reducible to b  okay so uh i'm going to give a bunch of  sort of  informal examples of that or or easy  examples of that and and then we'll  start to use it for real  so example one this is sort of you know  really outside material from the course  but i think it's something uh you can  appreciate  you know everybody knows you can measure  uh the area of a rectangle  by measuring the lengths of the of the  of the two sides  measuring the lengths of its uh it's  measuring the length and width  uh of the rectangle  so in other words if  you had the problem of determining the  area  you could reduce that problem to the  problem of measuring uh the length and  width  of the retaining rectangle  uh so here um we you know we're taking  one problem and reducing it to another  problem you know it's conceivable that  measuring the  um length and width  is easier  um than it would be to measure the area  directly by somehow covering the space  with  uh  you know uh tiles as one way of  measuring it um  but um it tells you you don't have to do  that  the problem of measuring the area is  easier than measure covering with tiles  you can just measure the length and  width and you're done  so reducibility is a way of making  problems easier  by by  translating them into some easier  problem  so here's another example that we've  already seen we didn't talk we didn't  call it a reduceability but  um if you remember back uh a a couple of  weeks ago we were talking about the  languages anfa and adfa the acceptance  problems for you know nfas and dfas  and we gave a way of solving the a d of  a problem as do you remember you know  the turing machine simulated uh the fine  art automaton  and we solved the a nfa problem  not by doing it directly  but by converting the nfa to a dfa  and then using the solution for adfa  in fact in effect what we were doing was  we were reducing the a nfa problem to  the adfa problem  um  uh  um so  um  [Music]  let's do another example  here's a problem you know here's an  example that  you you again probably didn't think  about it this way but from your homework  um  uh  uh we had this pusher problem the  problem of determining whether a  push-down automaton ever  pushes on its stack for any input  i know a bunch of you are struggling  with that problem um working on it  hopefully  hopefully solving it in one way or  another so there's one way to solve it  is an effect by reducing the pusher  problem to the ecfg the emptiness for  cfgs  which is equivalent to the emptiness for  pdas  because  um  you can take your i mean this is the the  solution i had in mind which is a  particularly simple and short solution  of course not the only solution  um you can take your push down automaton  where you're trying to determine if it  ever pushes  and you can take the states  um that are about to make a push  and instead of making them  make a push you make them accept states  and you get rid of the original states  so now you've converted  this  automaton  to one  that  accepts every time the original push  down automaton pushes  and it accepts you know and then it has  to move to the end of the input of  course so um so it goes into an accept  state and moves to the end of the input  so every time the original machine was  about to push the new machine that  you're you're just creating here  is going to go into an except state at  the end of the input  now to test whether the original machine  ever uses stack it's enough to test  whether the new machine ever accepts a  string  okay so that's a way i don't want to  over complicate this right here and get  you thinking about the homework again  but this is a way of  reducing one problem to another problem  and you know if you're  you don't quite get this one just focus  on the other two examples i don't want  to spend time on the on the homework set  too right now so we can address that  offline or separately if you if you want  it's also the solution that's written up  in the um  the solution set that's posted on uh  on the home page by the way  um  okay uh  so getting back to let's see thinking  about uh reducibility  what i have in mind again this is sort  of rephrasing it but i'm trying to  hammer it in  that if a is reducible to b  then solving b gives a solution to a  okay that's what happens in each of  these examples  now that now how we're going to use that  we're going to use that  in the following two ways  one is to observe that if a is reducible  to b  and b is an easy problem  then a is an also then a must also be  easy because we have a way of converting  a problems into b problem you know an a  we have a way of solving a using b  so b is easy  then now you can solve a two easily  because you can solve a using b which is  easy  maybe that's the clearest up here in  example one  where measuring the area might seem at  first glance hard you could have to walk  out over the all the the whole area but  it's not hard because you only have to  measure the length and the width  um  so the fact that b is easy tells you  that a z but actually this is not the  way we're going to be using it most  typically we're going to be most using  it most typically using it in the second  version which is a little bit uh come  more a little bit more convoluted  but this is the way you're gonna have to  get used to this  so if a is reducible to b  and you know a is hard  undecidable unrecognizable whatever the  form of hard you care about  if you know a is hard  and a is reducible to b  then that tells you b also has to be  hard  why because if b were easy then a would  be easy  but we know  by us we're assuming that a is hard so b  also has to be hard  okay so there's a  you know uh um  i'm inverting the logic here but this is  logically equivalent  um so you have to mull that over a bit  um  and um we will um  uh so why don't you think about that  and uh let me just take a few questions  on the chat and don't forget the tas are  there too so you can they're happy to  answer your questions don't  don't make them sit there lonely um  all right  so somebody's asking is it possible  that a is reducible to b and that b is  also reducible to a  so that's a good question uh that can  certainly happen um in that case in a  certain sense a and b are going to be  equivalent  so solving one is going to be just as  easy or hard as solving the other one  okay so they're going to be equivalent  from the perspective of the difficulty  of solving them  so somebody's asking and this is a this  is a perennial confusion  somebody's asking so you know in in the  case for in the previous uh slide here  maybe i'll just flip back to it here  so what which direction are we doing are  we reducing atm to whole tm or whole tmt  atm  the way it's written on the slide is  what i have in mind here we're reducing  atm to haltia  because we're using whole tm to solve  atm  and that's reducing atm to holtia  just like  um you know uh  here  measuring the area  is reducible to measuring the lengths of  the sides we're using measuring the  length of the sides to solve the area  so we're reducing the area to the to the  lengths  the area to the length of the sides  but you know  i know it's  uh  you have to you're going to have to play  with it  digest it get used to it  all right  [Music]  okay so let's continue  okay so  as i said  this latter one because we're the focus  on this course is mainly on the  limitations of computation  so we're going to be looking at  uh ways of showing problems are  difficult  it could be difficult in principle like  undecidable or it could be difficult in  terms of complexity which is what we're  going to focus on in the second half but  in both cases we're going to be using  the concept of reducibility so  reducibility is going to be a theme  you've got to get comfortable with  reducibility  okay so we're going to be focusing more  on the notion that  if you reduce a to b and you know a is  hard that tells you b is also hard  okay so i'm going to try to  i'm going to say that a few times during  the course of today's lecture to try to  help you uh get it  all right here's a check-in  a little bit sort of uh  sort of off to the side but i thought it  was fun a fun check-in more  the question is some people say biology  is reducible to physics well maybe  everything is reducible to physics since  physics is  tells you about the laws of the universe  and biology is in you know part of the  universe  so my question to you is do you think  and there's no right answer here  do you think in your opinion  is biology reducible to physics  maybe yes  or maybe there are some things like  let's consciousness  which cannot be reduced to physics  um  or maybe we don't know  so  curious to know your thoughts  but it does kind of use in a sense  the notion of reducible in the spirit of  what i have in mind here  in the sense that if you could fully  understand physics  would that allow you to fully understand  biology  okay here we are we're  almost  kind of interesting  uh  though not too unexpected i suppose  uh  um so we are i think just about done  five seconds pick anything if you  want to get credit for this and you  don't  haven't uh selected yet  ready to go ending polling  here are the results  and as i say there's no right answer  here  but but  if if i had been  in the class i would have picked b  um  but i'm not surprised  uh that especially in an mit crowd that  a is a winner  all right uh  let's continue  um  okay so now we're going to use  reduceability again um this is going to  be yet another example like the whole tm  example but a little bit more a little  bit uh harder um  and we're going to be doing this you  know the next lecture we're going to be  doing more reducibilities but much  harder  so we really got to get  you know really comfortable  um  [Music]  all right we're going to show etm see  etm is the emptiness problem for touring  machines is this language empty  i'm just going to give you a machine i  want to know is this language empty or  not does it accept something or is its  language empty  um that's going to be undecidable no  surprise  proof by contradiction and we're going  to show that atm is reducible to etm  so  um these things  often take a very similar form and i'm  going to try to use the same form so if  you're feeling shaking on it at least  you'll get the  the form of the way the solution goes  and that will help you maybe plug in um  to solve problems  okay  uh  so uh  proof by contradiction um assume that  etm is decidable opposite of what we're  trying to show  and then show that atm is decidable  which we know is false  um  so  let's say we have a decider for  etm r  using the same letters  on purpose here just to try to get the  pattern for you  so our designing etm  construct s deciding atm  okay so now um  let's think about it together for a  minute before i just put it up there  um so s i'm trying to make a decider  for atm  using my decider  for the emptiness problem  okay so we have r which can tell us  whether the whether m's language is  empty  so why don't we just  i don't know stick m  into that emptiness tester  see what it says  i'm just i'm not saying this is the  solution but this is how one might think  about coming up with the solution  so are you with me we're going to take m  we have an emptiness tester  let's take m  and plug it into r see what r says  r is going to come back and tell us  whether m's language is empty or not  now one of those answers  will make us happy  why  suppose  r  tells us that m's language is empty  why is that good  well now we're done  because what s is trying to figure out  we're trying to figure out  exactly somebody  told me the answer which is correct  because now we can reject  if m's language is empty it's clearly  not accepting w because it's not  accepting anything  so if r says m language is empty then  we're good  the only problem is r may also say m's  language is not empty and then what do  we know  well not much  not much that's useful  for testing whether m accepts w we just  know m accepts something  but that something may or may not be w  okay so what do we do  well the problem is that m  is  possibly accepting all sorts of strings  besides w  which are kind of mucking up the works  they're making  th they're interfering  with the solution that we'd like  uh we'd like to be able to use r  on m  to tell us whether m is accepting w but  m is accepting other things and that's  making  the picture complicated so what i  propose we do  why don't we modify m  so that it never accepts anything  besides w  the very first thing m does in the  modified form  is it looks at its input and sees  whether it's different from w  if it's different from w it immediately  rejects  now we take that modified machine  and we feed it into the emptiness tester  now the emptiness tester is going to  give us the information we're looking  for  because if  the emptiness tester says the modified  machine's language is empty well we know  that  m is not accepting w because we haven't  changed how m behaves when it's when  it's given w  but if  r says m's language is not empty  well then it must be that m is accepting  w  because we've already filtered out all  of the other possibilities in the  modified when we've modified the machine  so let me repeat that on the slide and  write it down a little bit more formally  so what i'm going to do is i'm going to  transform m to a new turing machine i'm  going to call it m sub w  to emphasize the fact that this new  machine depends on w it's going to  actually have w built into as part of  the rules of the machine  so for a different w we're going to end  up with a different machine here so this  is a machine  whose structure is going to depend on  knowing w  and that machine is going to be very  much like the original machine m  except that when it gets an input let's  say it's called x now  it that machine is going to compare x  with w  and reject if it's not equal  if otherwise  if x is equal to w it's going to run m  on w as before so it's not going to  change the behavior  when the input is w it's only going to  change the  behavior when the input is something  different than w and then it's going to  reject  all  right so  let's just um i'm going to look at two  aspects of this first to make let's  understand  the language of this new machine and  then we'll also talk about how we go  about doing this transformation um  so first of all  let just to for  emphasis uh  so mw works just like m it has all the  rules of m in it  except some extra rules  um it always at the very first step  it tests whether um x  is  equal to w or not  and if it's not equal to  it rejects  not equal to w reject so the language of  that new machine  is either going to be just the string w  when m accepts w because everything else  is filtered out  or the empty set if n rejects w  got it so it's important that you  understand  how the behavior at least of this new  machine  it's just like m except filtering out  all of the  um inputs  which are not w those are going to be  all  automatically rejected  now you  so it's also important that s  um  be able to make this transformation  but i claim that you know you'll have to  accept this if you don't uh totally see  it but  the  uh  the transformation is simply taking m  and adding some new rules some new uh  transitions and states  so that the very first thing  that  m sub w does  is it  you know just has a sequence of moves  where it's uh checking that the input  string  is equal to w or not  and if it's not equal to w it just  just rejects  so it's easy to modify m you could  easily write a program which would  modify the you know the states and  transitions of m to make it do that test  at the beginning  so i'm not going to elaborate on those  kinds of things in the future but just  for the very first time i just want to  make sure you understand that we're not  doing anything fishy here this is  completely legitimate  um thing for s to be able to do  so s can modify m  to this new machine mw  which filters that new machine  filters out all strings except for w and  rejects them  now we so s takes that new machine and  what is it going to do with it is it  ever going to run that machine no  this machine is built not for running  this machine is built for feeding into r  because  as you remember feeding m into r had the  problem that m might accept things  besides w and that confuses the result  that we get from r in the sense that  it's not useful  but if we feed m w into r  now now we're good because if r s you  know the answer the information about  whether mw's language is empty  from over here tells us whether or not m  accepts lb  if m's if mw's language is not empty  then m accepts w if m's language is  empty and rejects w  um  okay uh so let me um starting to get  some good questions here uh let me just  finish the description of s  um uh so somebody's asking here so again  this is a good this is an excellent  question um  uh  uh  how do we know that m  w  halts or  you know under on w or whatever we don't  mw may not hold on w we don't care  we're never going to run mw on anything  we're going to take mw as a machine and  we're going to feed it into r  as a description we're going to take the  description of mw and feed it into r  then it's ours problem  but r has been  assumed  to answer  emptiness testing  so we're going to just take the we just  we just took the original machine  modified it so that the only possible  thing it could accept is w  and now feed it into the emptiness  tester to see whether it's language is  empty or not  now if its language is not empty it has  to be accepting w because it's built not  to accept anything else  so we know we don't care whether mw  might end up looping  we're never going to run mw  i i acknowledge  it's a leap for for many of you so  you're going to have to mull it mull it  over  so we're going to use r to test whether  mw um language is empty  if yes  that means that m rejects w so then  we're going to reject if we know that  mw's language is empty  that must have been that m rejected w so  now as an atm decider which is what s is  m is  s is supposed to reject which is what we  we have here in the description and if  no  that means m the language is not empty  so m accepts w and so therefore we're  accepting so there's a little bit of a  twist here also  okay so let's let's take some more um  i'm expecting some questions here  so somebody's asking um how do you  determine if a language is decidable  that's what we're doing  you know  you can show a language is decidable  by exhibiting a turing machine which  decides it and you can show a language  is not decidable which is what we're  doing here by proving that no it's not  possible for a turing machine to decide  it  you know we did that first with atm  we got that contradiction  by  diagonalization and here we're doing a  reduceability um to show as as a method  of proof  um  all right let's let's uh let's continue  so now we're gonna talk about a special  kind so so far we we talked about  reducibility  we didn't define it in a precise way um  because there are several different ways  to get at the notion of reducibility  precisely um  and i'm going to introduce a one version  which is a little bit more restrictive i  mean you know somewhat more restrictive  and a little bit different way of  looking at it than we have been doing so  far  but there are going to be some benefits  to looking at this particular kind of  reducibility which we're calling mapping  reducibility  um it's going to have several benefits  for us uh immediately and down the road  but it's a little  this is also  you know a little technical so you're  going to have to  go don't uh  you know  don't don't  don't don't get scared off  you know we'll will  it it might look complicated at first  we'll um try to unpack it for you  um  okay  so first of all uh  if we have here a um  we have to first of all talk about the  notion of a computable function  so so you know generally when we've had  turing machines  you know they're they're doing yes no  they're doing except reject uh kinds of  things um so it's like a function  just sort of a computing sort of a  binary function  um  you know  for here we're going to want to talk  about turing machines that are computing  some more gener it's a function which  converts one string to another string  um so it's a it's a mapping from strings  to strings  and  um  you know  could be like the function which  reverses the string for example  um that's one uh possible function you  you could be  having here but there of course met  zillions of possible functions here and  we're going to talk about functions that  you can compute with the turing machine  and that basically means you provide the  input to the function as input to the  turing machine  and the output of the function the the  value of the function comes out as the  output of the turing machine  which let's just say it leaves that  value on its tape when it holds it holds  with the value of the function on the  tape  um  but just you know we're thinking about  algorithms here  come up with your favorite method of  thinking about algorithms it has an  input and an output and the algorithm  just computes the function by taking as  input w and the output is f of w it  doesn't have to be turing machines just  any any algorithm that can compute  something is good enough  they're all equivalent  um  and now we're going to use this notion  of a function that you can compute  to define a a kind of reducibility  called mapping reducibility i'm going to  say that a is mapping reducible to b  written with this  less than or equal to sub m symbol  you're going to see that a lot it's on  the homework also by the way  if there is some computable function as  i just described  where whenever w is in a  f of w is in b  and the way to think about it is with  this picture  so a and b are languages  written like here's a and here's b  and now there are  strings  so w might be  in a it might be out of a  and you think if you're trying to solve  a  you're trying to have a  you're trying to decide  membership in a  so you want to test whether w is in a or  not  a mapping reducible is a function  which  maps things from this space over to that  space  in a way that strings that are in a get  mapped to strings that are in b  so if you start out with w and a f of w  is in b  and if w is not in a  then f of w is not in b  it's a you know pictorially it's a  simple idea  we'll have to make sure we understand  why this  fits with our  um concept of a re reducibility but  we'll do that but anyway let's first  understand just what we're doing here  we're just coming up with a function  that can do this kind of a mapping  it sort of translates  problems which you know inputs which may  or may not be an a  into um  other strings which may or may not be in  b but sort of maintaining that um uh the  same input  property  uh that's  the same membership property so if you  start out with something in a  when you play f you're going to end up  with something in b  uh and  and conversely if you're not in a then  you won't be in b  okay um uh some somebody's asking  uh  so just a couple of questions here  not necessarily one to one no so the  function doesn't have to be one to one  there could be multiple things that map  to the same point  uh  um  and is it is there any restriction on  the alphabet no  um  so uh  before we actually get into the example  let me try to give you a sense about why  um we call this a reducibility  and the reason is  suppose we have  such an f  which can do the mapping as i described  and we also have a way  of deciding membership in b  so we have so b is decidable  so that's going to tell us right away  that a is decidable  because if you have some  input and you want to know is it an a or  not  you can now apply  f  and test whether f w is in b  so the test of w is an a  you uh you're going to instead test  whether f of w is in b and we'll we're  assuming we have a that that shows that  a is reducible to b so if you could  solve  the b problem that allows gives you a  way to solve the a problem  again we're going to say this several  times in several different ways so if  you didn't quite get it yet  you know don't don't panic  um  so here's going to be an  example sort of building on what we just  showed last time  in the previous slide atm we're going to  show how atm is actually mapping  reducible to the complement of etm  and the complement is necessary here  the computable function that we're going  to give  which is basically if you're going to  the computable function is going to  translate  problems about atm to problems about  uh etm because we're mapping reducing  atm to the complement of etf  so we're going to what we're doing here  is with mapping m and w  to the uh machine mw  kind of in a way we're boiling out the  essence boiling down to the essence of  the proof that we gave in the previous  slide  this is really the the the core of the  proof this translation of mw where you  want to know is m accepting w  to a new machine mw where you're testing  whether  mw's language is empty  and so this is the you know so remember  mw from before it's the machine that  filters out all the non-ws and rejects  them  um and the reason why this reduction  function works  um is that  mw is in atm  if and only if m sub w is in the  complement of etf  so m accepts w exactly when mw's  language is not empty  okay so m accepts w if and only if  the language of mw is not empty  so you have to mull this over a bit  realize it's  you know i i know this is  uh  can be a little tricky  but i think what we're going to do here  i think we're at the uh break the time  for the break so  uh oh no there's one more slide i  apologize so let's let's talk about this  and then we're going to have our coffee  break  uh  uh  so there are um  the reason why so this  these properties are really gonna be  getting at  what makes mapping reducible  mapping reducibility  fit with our  understanding of what a reducibility  should be  so if a is mapping reducible to b and b  is decidable then so is a  um so that  fits with what we want because if a is  reducible to b and b is easy then a is  easy so here easy means decidable  and here's the proof let's take a turing  machine that decides b and construct a  turing machine that decides a  as claimed  s operates like this  it takes its input  computes  f of that input  tests  um  uh  whether that  f  whether f w is in b using the uh r  machine that we were assuming you know  we have r deciding b  and if r  holds then output the same result  so if r accepts we're going to accept if  our holds and rejects we'll reject and  of course we're going to be simula  running r so if r is not going to be  halting we're not going to end up  halting either  okay  so the corollary is and this is the way  we're going to be using it  if a is reducible to b and b and a is  undecidable then so is b  so this is as i mentioned we're going to  be the focus on for us is going to be on  undecidability and you may want to think  about a is like the atm problem  which we know is undecidable we're going  to show the atm is mapping reducible to  some other problem to show that that  other problem is undecidable  um  and the important thing about mapping  reducibility is that also applies to  recognizing to recognizers so if a is  mapping reducible to b and b is turning  recognizable then so is a  so if you map you're reducing a to a  recognizable problem then a is also  recognizable  same proof because you can just  map your w to f of w and feed it into  the recognizer that's going to give you  a recognizer for the original language  um  the corollary is that if a  is  mapping reducible to b and a is  unrecognizable then so is b so this is  again that sort of um  inverted logic  okay so now i think where  uh oops i meant to put this picture up  earlier  uh  okay so here's a check in  um  be more of a check-in for me to see how  well you're following me  so these are some properties of  um i'll give you a minute here to think  about this some properties of mapping  reducibility  um  suppose a is mapping reducible to b what  can we conclude  does that mean that  we can flip it around  if a is mapping reducible to b does that  mean a b is mapping reducible to a  what about this one um if a is mapping  inducible to b  to the is the complement of a mapping  reducible to the complement of b or  maybe neither so you can and you can um  uh check all that apply um  multiple choice  five seconds  sorry to pressure you but  we have to move on here  pick anything  uh if you don't know okay  one two three  the end  um  okay  so  um  well the majority is correct  um  in fact it's only that uh  only b  um now  um  a  really is not in the spirit of  reducibility because um  as suggested even by the inequality sign  there um  a being reducible to b is really a  rather different thing than b being  reducible to a  um  so that that's something to we're not  going to prove that right here but um  that's something that you um could uh  think about  and uh but part b  [Music]  i think you you know if you just look  here  at the definition of mapping  reducibility  it maps strings in  to in and out to out  well that's just going to be if you  exchange in and out as you do when  you're flipping complements on both  sides it's still by the same f gonna  still work as a mapping reduction  okay so uh now we're um at our  co break so we're going to take five  minutes here  and  uh  and i'll be happy to  [Music]  take a questions here but don't forget  the tas they're here too  um  okay  okay so this is a fair question here you  know  so we had this notion of a general  reduction and a mapping reduction  um they're not the same  so  anytime you have a mapping reduction  it's going to be an example of a general  reduction but not not the other way  around  um so you know if you go back and look  at the reduction that we we offered  for halt tm that where we  showed atm is reducible to whole tm  where we started it's actually not a  mapping reduction um  uh because if we're doing something more  complicated than that's translating an  atm problem to a whole tm problem we're  kind of using it using the whole tm  decider in a more complicated way and  there are cases where that that's  actually necessary um  so we won't uh um  not not going to discuss that here but  uh it's actually kind of maybe an  interesting homework problem perhaps or  some kind of a problem to think about  um  so turing machines for fs  does does f have to be a it's not really  a decider but it has to be um well yeah  i guess it does have to be to start in  the way it always holds the turing  machines for f has to always hold it  always has to have an output so  f um  uh for the computing the function always  always has to  always has to hold  um  so someone is asking me uh  can i explain uh the the statement that  if error holds then i'll put the same  result  i just mean that in that previous slide  um or two slides back if r accepts holds  and accepts  then we're gonna hold an accept and if r  holds and rejects then we hold and  reject um so i can i don't know if this  is a good idea but we can just pull that  back here  just that was this statement here if our  holds and output the same result i just  mean that s is going to do the same you  know we're translating  an a problem to a b problem  and then answering the b problem  and we're going to give the same  value the same answer there uh so  whatever r says we're going to say 2.  that's  helpful  um  all right uh  well that's a good question here um  you know  if a is reducible to b uh why can't we  just get b reducible to a by inverting  the function that's a great question i  like that question  um  the reason is is because um  the function that's mapping onto b  uh doesn't have to be on to  surjective i guess um  so you can't always you can you're not  going to be able to if it was  um you know onto so if it covered all of  b  um  then i think then you would get a um an  invertible function and it would they  you would get the  reduction going the other way as well um  but uh though i'm not sure what happens  when you have doesn't matter if you have  collisions  it turns out that's not going to matter  but anyway let's let's not get it too  complicated here but the the problem  with inverting it is that it's not  necessarily on you know onto the whole  range  of b  uh  okay uh  so we're kind of out of time here um  is a reducible to a complement let me  just end with that no not necessarily um  it's reduceable take okay that's we'll  get there it's reducible a is reducible  to a complement um  but not mapping reducible to a  complement but a in is general reducible  to a complement so we'll actually we'll  talk i have a slide on that  uh so let us  move on  okay mapping i think it's actually this  slide mapping versus general  reducibility  so we're going to kind of contrast it to  a bit  so mapping reducibility which is what  we've just been talking about has this  picture which is i think a very useful  picture to remember um  and uh  because  the way i like to think of a mapping  reduction as a problem translator  your problem sort of in the a domain  and the mapping reduction allows you to  translate that problem into the b domain  okay and then if you have a way of  solving it in the b domain  combining that with the reduction you  get a solution to the problem in the a  domain  so that's why if a is mapping reducible  to b  and b is solvable  then a is also solvable  um  so mapping  reduction is a special kind of  reducibility as opposed to the general  notion general reducibility that where  we started  and it's particularly useful to prove  touring unrecognizability so when you  want to prove touring recognizable  unrecognizability  as we'll see the general red  reducibility is not per it's not fine  enough in a way it doesn't sort of um  differentiate things as well as mapping  reducibility does  and and and for that reason it's not  always going to be useful to prove  touring unrecognizability it's better  for proving undecidability  so what we're calling reducibility or  general reducibility  is where we just use a a solver for b to  solve a in sort of a more most general  possible way  so i'm writing that as the picture here  you you want to solve a  you're going to use the b solver as a  subroutine  to solve a  that's the way we did the whole tm a  reduction at the beginning  um  but we didn't necessarily translate an  atm problem to a whole tm problem  a little slightly different uh so you  can go back and look at that  um so i find that people struggle more  with the mapping reducibility concept  and that the general reducibility is  what people naturally gravitate towards  and so in some sense it's conceptually  simpler  and it's useful to proving  undecidability so but you really have to  be comfortable with both and especially  in the complexities  part we're going to be focusing on  mapping  reducibility so one noteworthy  difference here as uh sort of  foreshadowed by uh the  person who made this question which is a  good question  is that a is all is reducible using a  general reduction to a complement which  kind of makes sense  i mean if i can solve a cop you know if  i can test whether things are an a  complement well i can test whether  things are in a you just invert the  answer  but  a may not be mapping reducible to a  complement because there it's a very  special kind of reduction  and you just can't necess you can't you  have to just translate things in the  language to things in the language and  things out of the language of things out  of the language and they don't  necessarily allow you to do that  inversion  so for example atm  complement  is not mapping reducible to atm  because as we pointed out  anything that's reducible to a  recognizable  language is going to be recognizable  anything mapping reducible to a  recognizable languages map is going to  be recognizable  but we know that atm complement is not  recognizable we showed that before  so it couldn't be mapping reducible to  atm  you know coming a little fast i realize  you're gonna have to uh  digest it so here's the last check-in  for today  um  okay we showed that if a is mapping  reducible to b and b is turing  recognizable then so is a  and so let's just say that again  carefully if a is mapping reducible to b  and b is turing recognizable  then so is a and here the difference is  on recognize the emphasis on turing  recognizable as opposed to decidable  is the same true if we use general  reducibility instead of mapping  reducibility  so you got it so we're saying a is  mapping reducible to b using this  picture over here  and we're going to assume that b  is touring recognizable  okay so that we have a  machine which  holds an except  when you're inside b  and you know is going to reject possibly  by looping when you're not inside b  now that allows you to get  a recognizer  for a  if you have a mapping reduction  does it always work to give you a  recognizer if you have just a general  reduction  if you just have a if you just now  assume you have a b solver  and you're going to build an a solver  out of that  um  okay so mull that over while i'm setting  this thing up  well the right answer is winning but not  by much  i suppose i shouldn't be  uh  laughing about it uh but  i i knew that this is going to be  challenging so i think it's the kind of  thing you're going to have to  uh work at  um so let's see we're almost done here  um  five seconds to go  better answered i i could see a few of  you either you've left the  room  or you're uh  okay two seconds  one two three  somebody hasn't answered it  there we go so this is the correct  answer is b  it's not the same  you're not going the reason is that in a  general word i mean the picture's right  here  i mean so you mean you know this is  um  let's see  uh  you know  um how do i explain this so  uh  we know that  uh  a language is going to be um  okay if we're using general reducibility  and a is it's just reducible to b  um  [Music]  so  we know that  a language is always always reducible to  its complement in the using general  reducibility  um  [Music]  so if this were true  um  then  then we would have here  um  um  so um  if this were true when  um a  uh when a language is reducible to its  complement if the complement were  recognizable the language would also be  recognizable  that clearly isn't is not going to be  the case because  you know atm is reducible to the you  know atm complement is reducible to atm  using general reducibility  uh but um  atm complement is not recognizable even  though atm is recognizable so we kind of  have a proof that this has to be no  but as you can see i'm even getting  myself confused so um  you have to you have to stare at it um  so let's let me see we can try to take a  couple of questions see if i can clear  up people's confusion  why again okay so why again is a  reducible to its complement in the  general sense  so i'm saying  if you have a solver if you have a  decider for for for a complement it  gives you a solver for a  you just ask the solver  you know is the string in the language  or not  and now um  you just give the opposite answer if you  want to  solve the the complementary problem so  the a complement is reduced  reducible to a  you just invert the answer for whatever  the solver is doing for a but you can't  just do that inversion when you have a  mapping reduction  it's a much more  um  kind of  specific  translation that's allowed  um  so i mean the fundamental difference  between german disability mapping  disability i'm trying to bring it out  here it's just  it's just a difference in the nature of  the way things are used mapping  reducibility is a special kind of  general reducibility so you know to  answer the question about what's the  fundamental difference  you know one is using the  the problem as a subroutine and the one  is using it as a um  as a  transformation  um  anyway i think we're going to have to uh  move on here and i'm going to have a  couple of examples which may help  and then uh  uh there are also there's office hours  too after after the after the lecture  um  okay oh yeah so i wanted to again to  help you  you know i'm putting these down as sort  of templates for how do you use  reduceability um  i'm not saying you should just  uh  apply things blindly but i think it's  sometimes good just to see the pattern  and then to understand how the pattern  works once you see that once you just  start to understand the pattern of how  things are used  so to show um a language is undecidable  just  to prove a language b is undecidable  show undecidable language is reducible  to be  using just a general reduction is going  to be good enough  um  and and the template for that is assume  we have r deciding b  which you then can use as a subroutine  when you make a machine uh turing  machine or  s deciding a  and that's going to be your  contradiction if a was  originally shown to be known to be  undecidable  um  but now to prove something  unrecognizable  this kind of reduction is not going to  be is not in a sense um  uh  it's it's not  uh as enough  um because this kind of reduction allows  for complementation  which is not going to be  uh satisfactory when you're trying to  prove touring unrecognizable so you're  gonna have to prohibit  that complementation and that's really  one of the effects of the mapping  reducibility if that's sort of getting  at the essence of it  um  so we're going to show an on turing  unrecognizable a is mapping reducible to  b  often you start off with the complement  of atm which is a language we know is  touring uh  unrecognizable as we showed before  um  okay here the template is you give the  reduction function f  that computable function  um  okay so  um  so here are going to be two examples one  showing that etm is touring  unrecognizable we showed it was  undecidable before  now we're going to show it's  even  in a sense worse it's not even  recognizable  and the way we'll do that is to reduce a  a known  unrecognizable language to etm  in the emptiness  language  um  so here is the picture  that we have when we're doing mapping  reductions  we're going to map strings that are in  the complement of atm so strings that  are outside of atm if you wish to  strings where  the language is empty  to machines with the language is empty  and here  um  strings describing machines which  language is empty and here we're going  to take um  uh  atm problems  so and map them to  machines where the language  is not empty  and the thing that's going to do the  trick is going to be that same  reduction function that we saw earlier  um  you know we're going to take that  machine w from before the machine that  filters out all the non w  all the non w's  and we're going to take mw  which is  a  you know um  an atm complement problem  so the so  [Music]  so if m  rejects w then it's in the complement of  atm  and that's supposed to  map to a string a machine which is  uh where  the the language is empty okay so if mw  is in the complement of atm so m rejects  w then mw's language is going to be  empty which is what  you want to have happen  um  let me move on to my last i mean this  example is in a way kind of similar to  the one we did before and i i really  want to get to my the last example here  um  okay so  uh we'll have to just talk through this  uh rather than having it uh uh build um  let's take eqtm  that's the equivalence  problem for turing machines  do they uh  um recognize the same language  um so  this is a this is a an  a language of a new kind for us this is  a language where neither it nor its  complement are going to be recognizable  to recognizable  um  so the way we get that is  um  we're going to reduce the complement the  way we show problems are not  recognizable is re  mapping reduce  a non-recognizable language to a  typically the complement of atm so we're  going to mapping reduce the complement  of atm  to  both  eqtm and to the complement of eqtm to  show that both of those are not  recognizable  and here we're going to introduce a new  uh machine that we're going to be  building inside the reduction function  and that's going to be a  machine i'm going to call t w  and t w is a machine  that  always behaves the way m behaves on w  for every input  so if m accepts w  t is going to accept everything  if m rejects w t is going to reject  everything  so it copies the behavior of m on w onto  all inputs and the way i describe that  machine tw is it ignores its input  whatever the input is it just simulates  m on w  you could easily given m  and w you can build the machine tw  it just always runs mmw no matter what  input it gets  and so now we're going to give a  function which maps atm problems which  have the form mw so it's a atm  complement problem so this is we want to  test if this if m accepts w or not so  that's an atm complement type problem  and i want to map that to an eqtm  problem of the form  you know eqtm problems are pairs of  machines  now and where we're going to be testing  equivalents so i'm just trying to give  you the form of the output of the  reduction function f  and specifically what it's going to look  like is  when we have  m is f is processing on mw  it's going to produce two machines one  of them is going to be tw  which always behaves the way m behaves  on w  but  expanded to all inputs  and then and then  and a machine i'm going to call t reject  which just is designed to reject  everything  now look at just walk through the logic  with me  if m rejects w  tw rejects everything  and so will be equivalent to the machine  t reject  that's what we want  if m rejects w  so we're in the language atm complement  then these two machines that i produce  for you are going to be in  the eqtm language  that's what i want to have happen  for a reduction from atm complement to  eqtm  similarly  to do part two  i'm going to use make here a different f  maybe i should call it f prime  all right and you know f1 and f2 for the  two different parts so these are two  different f's i'm going to make f here  on  instead of generating  t w and t reject i'm going to have t w  and t accept which is a turing machine  that always accepts its input  now  if m rejects w  it's an atm complement  then tw  is going to reject everything and it's  going to be different from  it's companion here t accept  and so won't it'll be in it won't be an  eqtm complement  but if m accepts w  then tw is going to accept everything  and they're going to be equivalent to  t except and you will be  uh  equivalent so the here is where we're  taking  atm complement and mapping it to the  complement of  eqtm  um  too many compliments here i i realize  like compliments are confusing but  anyway why don't you mull this over um  and uh  um  just to summarize  okay yeah  you know we're out of time here but why  do we use reducing when we talk about  reductions  it's because when we reduce a to b  we kind of bring a's difficulty down to  b's difficulty that's where the reducing  comes from  um  or  we bring b's difficulty up to a's  difficulty because it's really a  difficulty relative to b that we're  talking about when we're reducing a to b  so that's why  the term reducing seems  a little out of place when we're proving  things undecidable or unrecognizable but  that's where it's coming from  anyway quick review  um we introduced the ter the  reducibility method  we defined mapping reducibility as a  special kind of reducibility we showed  etm is undecidable and unrecognizable  and that eqtm is both it and its  complement are unrecognizable  so we're out of time um i will uh shut  this down  but i'll take a few questions here  actually you know i'll stick around for  a few questions and then i'll move to  the other chat room for office hours  okay  so  question to go over  the case for the complement of eqtm  so i will do that  so that's in this slide here  okay  so this is the this is proof part two  um for the person who asked me to go  over it but i think it's  helpful for for those of you who are  might be a little bit uh shaky on this  i want a mapping reduce the complement  of atm to the complement of eqtm  by the way i don't know if this is going  to be helpful  but as we pointed out in the check-in a  while back that's completely equivalent  to  having a mapping reduction from atm to  eqtm  you can  complement both sides  and  you get an equivalent statement  maybe let's stick with the compliments  here um though  i hope that doesn't make it too  confusing  okay we're trying to show the complement  of atm is mapping reducible to the  complement of eqtm what does that mean  so that means when m rejects w  so you're in the complement  we want the two turing machines  to be inequivalent  no yeah so we're in the complement of  eqtm  so we're with so in other words we're in  the complement of atm we want the result  of the uh of f to be in  um  in the complement of eq dm  so in other words when m rejects w the  two machines should be in equivalent  right when m accepts w the two machines  should be equivalent  because when we're  not in this language so we're an atm we  want to be not in that language so we  should we should be an eqtm  so when m accepts w  we should be equivalent  when m a rejects w we should be inequal  that's what we want  let's go down here  so if m accepts w  we want  we want them to so when m accepts w want  them to be equivalent so if wham accepts  w  t w accepts everything and it's  equivalent to t except  when m rejects w  t w  um  rejects everything and so it's not  equivalent to the machine that accepts  everything  so this  i hope that's  just go through it just go through the  logic yourself you'll see why it's  working  um  all right see bye bye everyone  you

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443
00:14:10,959 --> 00:14:11,910


444
00:14:11,910 --> 00:14:14,389

 

445
00:14:14,389 --> 00:14:15,829

 

446
00:14:15,829 --> 00:14:19,590

 

447
00:14:19,590 --> 00:14:21,269

 

448
00:14:21,269 --> 00:14:23,110

 

449
00:14:23,110 --> 00:14:24,629

 

450
00:14:24,629 --> 00:14:26,870

 

451
00:14:26,870 --> 00:14:32,710

 

452
00:14:32,710 --> 00:14:33,990

 

453
00:14:33,990 --> 00:14:36,389

 

454
00:14:36,389 --> 00:14:38,629

 

455
00:14:38,629 --> 00:14:39,990

 

456
00:14:39,990 --> 00:14:42,629

 

457
00:14:42,629 --> 00:14:46,310

 

458
00:14:46,310 --> 00:14:47,350

 

459
00:14:47,350 --> 00:14:51,990

 

460
00:14:51,990 --> 00:14:54,710

 

461
00:14:54,710 --> 00:14:57,110

 

462
00:14:57,110 --> 00:14:58,870

 

463
00:14:58,870 --> 00:15:03,430

 

464
00:15:03,430 --> 00:15:05,030

 

465
00:15:05,030 --> 00:15:08,710

 

466
00:15:08,710 --> 00:15:10,310

 

467
00:15:10,310 --> 00:15:10,320

 

468
00:15:10,320 --> 00:15:12,790


469
00:15:12,790 --> 00:15:14,790

 

470
00:15:14,790 --> 00:15:16,470

 

471
00:15:16,470 --> 00:15:18,069

 

472
00:15:18,069 --> 00:15:20,310

 

473
00:15:20,310 --> 00:15:21,910

 

474
00:15:21,910 --> 00:15:23,509

 

475
00:15:23,509 --> 00:15:25,990

 

476
00:15:25,990 --> 00:15:26,000

 

477
00:15:26,000 --> 00:15:27,189


478
00:15:27,189 --> 00:15:29,509

 

479
00:15:29,509 --> 00:15:32,069

 

480
00:15:32,069 --> 00:15:33,509

 

481
00:15:33,509 --> 00:15:35,110

 

482
00:15:35,110 --> 00:15:37,670

 

483
00:15:37,670 --> 00:15:40,629

 

484
00:15:40,629 --> 00:15:43,110

 

485
00:15:43,110 --> 00:15:44,230

 

486
00:15:44,230 --> 00:15:45,910

 

487
00:15:45,910 --> 00:15:48,629

 

488
00:15:48,629 --> 00:15:51,189

 

489
00:15:51,189 --> 00:15:53,829

 

490
00:15:53,829 --> 00:15:56,069

 

491
00:15:56,069 --> 00:15:58,790

 

492
00:15:58,790 --> 00:16:00,949

 

493
00:16:00,949 --> 00:16:02,790

 

494
00:16:02,790 --> 00:16:02,800

 

495
00:16:02,800 --> 00:16:06,829


496
00:16:06,829 --> 00:16:10,710

 

497
00:16:10,710 --> 00:16:12,150

 

498
00:16:12,150 --> 00:16:13,590

 

499
00:16:13,590 --> 00:16:16,310

 

500
00:16:16,310 --> 00:16:20,150

 

501
00:16:20,150 --> 00:16:21,509

 

502
00:16:21,509 --> 00:16:23,990

 

503
00:16:23,990 --> 00:16:25,670

 

504
00:16:25,670 --> 00:16:28,629

 

505
00:16:28,629 --> 00:16:31,910

 

506
00:16:31,910 --> 00:16:31,920

 

507
00:16:31,920 --> 00:16:34,550


508
00:16:34,550 --> 00:16:38,069

 

509
00:16:38,069 --> 00:16:40,790

 

510
00:16:40,790 --> 00:16:42,550

 

511
00:16:42,550 --> 00:16:44,710

 

512
00:16:44,710 --> 00:16:46,870

 

513
00:16:46,870 --> 00:16:48,870

 

514
00:16:48,870 --> 00:16:52,230

 

515
00:16:52,230 --> 00:16:55,749

 

516
00:16:55,749 --> 00:16:58,069

 

517
00:16:58,069 --> 00:17:00,870

 

518
00:17:00,870 --> 00:17:03,350

 

519
00:17:03,350 --> 00:17:05,429

 

520
00:17:05,429 --> 00:17:07,990

 

521
00:17:07,990 --> 00:17:09,669

 

522
00:17:09,669 --> 00:17:09,679

 

523
00:17:09,679 --> 00:17:10,789


524
00:17:10,789 --> 00:17:13,750

 

525
00:17:13,750 --> 00:17:18,309

 

526
00:17:18,309 --> 00:17:19,750

 

527
00:17:19,750 --> 00:17:21,350

 

528
00:17:21,350 --> 00:17:23,429

 

529
00:17:23,429 --> 00:17:25,590

 

530
00:17:25,590 --> 00:17:28,549

 

531
00:17:28,549 --> 00:17:30,789

 

532
00:17:30,789 --> 00:17:33,750

 

533
00:17:33,750 --> 00:17:35,830

 

534
00:17:35,830 --> 00:17:37,510

 

535
00:17:37,510 --> 00:17:40,150

 

536
00:17:40,150 --> 00:17:40,160

 

537
00:17:40,160 --> 00:17:41,190


538
00:17:41,190 --> 00:17:42,549

 

539
00:17:42,549 --> 00:17:44,390

 

540
00:17:44,390 --> 00:17:46,470

 

541
00:17:46,470 --> 00:17:49,590

 

542
00:17:49,590 --> 00:17:49,600

 

543
00:17:49,600 --> 00:17:52,070


544
00:17:52,070 --> 00:17:55,909

 

545
00:17:55,909 --> 00:17:57,270

 

546
00:17:57,270 --> 00:18:01,110

 

547
00:18:01,110 --> 00:18:01,120

 

548
00:18:01,120 --> 00:18:02,150


549
00:18:02,150 --> 00:18:03,990

 

550
00:18:03,990 --> 00:18:05,430

 

551
00:18:05,430 --> 00:18:07,669

 

552
00:18:07,669 --> 00:18:12,150

 

553
00:18:12,150 --> 00:18:14,470

 

554
00:18:14,470 --> 00:18:14,480

 

555
00:18:14,480 --> 00:18:15,750


556
00:18:15,750 --> 00:18:18,630

 

557
00:18:18,630 --> 00:18:19,909

 

558
00:18:19,909 --> 00:18:21,270

 

559
00:18:21,270 --> 00:18:21,280

 

560
00:18:21,280 --> 00:18:22,870


561
00:18:22,870 --> 00:18:24,630

 

562
00:18:24,630 --> 00:18:25,510

 

563
00:18:25,510 --> 00:18:31,110

 

564
00:18:31,110 --> 00:18:32,320

 

565
00:18:32,320 --> 00:18:32,330

 

566
00:18:32,330 --> 00:18:35,350


567
00:18:35,350 --> 00:18:38,230

 

568
00:18:38,230 --> 00:18:39,430

 

569
00:18:39,430 --> 00:18:41,830

 

570
00:18:41,830 --> 00:18:44,390

 

571
00:18:44,390 --> 00:18:46,230

 

572
00:18:46,230 --> 00:18:48,630

 

573
00:18:48,630 --> 00:18:50,390

 

574
00:18:50,390 --> 00:18:52,390

 

575
00:18:52,390 --> 00:18:52,400

 

576
00:18:52,400 --> 00:18:53,750


577
00:18:53,750 --> 00:18:55,669

 

578
00:18:55,669 --> 00:18:57,990

 

579
00:18:57,990 --> 00:18:59,750

 

580
00:18:59,750 --> 00:19:01,750

 

581
00:19:01,750 --> 00:19:03,669

 

582
00:19:03,669 --> 00:19:05,669

 

583
00:19:05,669 --> 00:19:07,430

 

584
00:19:07,430 --> 00:19:09,750

 

585
00:19:09,750 --> 00:19:09,760

 

586
00:19:09,760 --> 00:19:11,190


587
00:19:11,190 --> 00:19:12,950

 

588
00:19:12,950 --> 00:19:14,630

 

589
00:19:14,630 --> 00:19:16,870

 

590
00:19:16,870 --> 00:19:20,789

 

591
00:19:20,789 --> 00:19:23,590

 

592
00:19:23,590 --> 00:19:25,510

 

593
00:19:25,510 --> 00:19:27,110

 

594
00:19:27,110 --> 00:19:29,510

 

595
00:19:29,510 --> 00:19:31,750

 

596
00:19:31,750 --> 00:19:34,310

 

597
00:19:34,310 --> 00:19:35,909

 

598
00:19:35,909 --> 00:19:41,190

 

599
00:19:41,190 --> 00:19:43,110

 

600
00:19:43,110 --> 00:19:45,110

 

601
00:19:45,110 --> 00:19:46,789

 

602
00:19:46,789 --> 00:19:47,909

 

603
00:19:47,909 --> 00:19:50,230

 

604
00:19:50,230 --> 00:19:53,029

 

605
00:19:53,029 --> 00:19:53,039

 

606
00:19:53,039 --> 00:19:54,070


607
00:19:54,070 --> 00:19:57,190

 

608
00:19:57,190 --> 00:19:59,270

 

609
00:19:59,270 --> 00:20:01,029

 

610
00:20:01,029 --> 00:20:03,430

 

611
00:20:03,430 --> 00:20:04,870

 

612
00:20:04,870 --> 00:20:06,390

 

613
00:20:06,390 --> 00:20:07,990

 

614
00:20:07,990 --> 00:20:10,630

 

615
00:20:10,630 --> 00:20:10,640

 

616
00:20:10,640 --> 00:20:11,510


617
00:20:11,510 --> 00:20:13,590

 

618
00:20:13,590 --> 00:20:13,600

 

619
00:20:13,600 --> 00:20:17,190


620
00:20:17,190 --> 00:20:22,870

 

621
00:20:22,870 --> 00:20:25,830

 

622
00:20:25,830 --> 00:20:28,230

 

623
00:20:28,230 --> 00:20:31,190

 

624
00:20:31,190 --> 00:20:32,549

 

625
00:20:32,549 --> 00:20:34,470

 

626
00:20:34,470 --> 00:20:36,950

 

627
00:20:36,950 --> 00:20:36,960

 

628
00:20:36,960 --> 00:20:42,470


629
00:20:42,470 --> 00:20:45,830

 

630
00:20:45,830 --> 00:20:45,840

 

631
00:20:45,840 --> 00:20:47,270


632
00:20:47,270 --> 00:20:48,710

 

633
00:20:48,710 --> 00:20:48,720

 

634
00:20:48,720 --> 00:20:49,590


635
00:20:49,590 --> 00:20:52,070

 

636
00:20:52,070 --> 00:20:52,080

 

637
00:20:52,080 --> 00:20:55,029


638
00:20:55,029 --> 00:20:59,430

 

639
00:20:59,430 --> 00:21:02,630

 

640
00:21:02,630 --> 00:21:03,909

 

641
00:21:03,909 --> 00:21:03,919

 

642
00:21:03,919 --> 00:21:04,710


643
00:21:04,710 --> 00:21:08,149

 

644
00:21:08,149 --> 00:21:12,630

 

645
00:21:12,630 --> 00:21:17,669

 

646
00:21:17,669 --> 00:21:19,190

 

647
00:21:19,190 --> 00:21:19,200

 

648
00:21:19,200 --> 00:21:19,909


649
00:21:19,909 --> 00:21:21,350

 

650
00:21:21,350 --> 00:21:23,110

 

651
00:21:23,110 --> 00:21:27,830

 

652
00:21:27,830 --> 00:21:27,840

 

653
00:21:27,840 --> 00:21:28,789


654
00:21:28,789 --> 00:21:30,390

 

655
00:21:30,390 --> 00:21:33,669

 

656
00:21:33,669 --> 00:21:36,310

 

657
00:21:36,310 --> 00:21:39,110

 

658
00:21:39,110 --> 00:21:41,110

 

659
00:21:41,110 --> 00:21:41,120

 

660
00:21:41,120 --> 00:21:44,390


661
00:21:44,390 --> 00:21:46,070

 

662
00:21:46,070 --> 00:21:48,630

 

663
00:21:48,630 --> 00:21:50,789

 

664
00:21:50,789 --> 00:21:52,070

 

665
00:21:52,070 --> 00:21:55,270

 

666
00:21:55,270 --> 00:21:56,310

 

667
00:21:56,310 --> 00:21:57,830

 

668
00:21:57,830 --> 00:21:59,270

 

669
00:21:59,270 --> 00:21:59,280

 

670
00:21:59,280 --> 00:22:00,789


671
00:22:00,789 --> 00:22:02,470

 

672
00:22:02,470 --> 00:22:04,870

 

673
00:22:04,870 --> 00:22:04,880

 

674
00:22:04,880 --> 00:22:05,250


675
00:22:05,250 --> 00:22:05,260

 

676
00:22:05,260 --> 00:22:07,990


677
00:22:07,990 --> 00:22:09,190

 

678
00:22:09,190 --> 00:22:10,870

 

679
00:22:10,870 --> 00:22:13,669

 

680
00:22:13,669 --> 00:22:14,870

 

681
00:22:14,870 --> 00:22:16,310

 

682
00:22:16,310 --> 00:22:18,149

 

683
00:22:18,149 --> 00:22:19,830

 

684
00:22:19,830 --> 00:22:21,750

 

685
00:22:21,750 --> 00:22:21,760

 

686
00:22:21,760 --> 00:22:23,669


687
00:22:23,669 --> 00:22:25,430

 

688
00:22:25,430 --> 00:22:31,669

 

689
00:22:31,669 --> 00:22:31,679

 

690
00:22:31,679 --> 00:22:32,549


691
00:22:32,549 --> 00:22:35,029

 

692
00:22:35,029 --> 00:22:37,430

 

693
00:22:37,430 --> 00:22:39,430

 

694
00:22:39,430 --> 00:22:41,110

 

695
00:22:41,110 --> 00:22:43,270

 

696
00:22:43,270 --> 00:22:45,430

 

697
00:22:45,430 --> 00:22:47,590

 

698
00:22:47,590 --> 00:22:50,390

 

699
00:22:50,390 --> 00:22:50,400

 

700
00:22:50,400 --> 00:22:51,270


701
00:22:51,270 --> 00:22:51,280

 

702
00:22:51,280 --> 00:22:52,230


703
00:22:52,230 --> 00:22:54,710

 

704
00:22:54,710 --> 00:22:57,350

 

705
00:22:57,350 --> 00:22:59,669

 

706
00:22:59,669 --> 00:23:00,789

 

707
00:23:00,789 --> 00:23:02,390

 

708
00:23:02,390 --> 00:23:05,029

 

709
00:23:05,029 --> 00:23:05,039

 

710
00:23:05,039 --> 00:23:06,070


711
00:23:06,070 --> 00:23:06,080

 

712
00:23:06,080 --> 00:23:06,870


713
00:23:06,870 --> 00:23:09,510

 

714
00:23:09,510 --> 00:23:11,750

 

715
00:23:11,750 --> 00:23:13,590

 

716
00:23:13,590 --> 00:23:16,310

 

717
00:23:16,310 --> 00:23:18,070

 

718
00:23:18,070 --> 00:23:19,909

 

719
00:23:19,909 --> 00:23:24,870

 

720
00:23:24,870 --> 00:23:28,230

 

721
00:23:28,230 --> 00:23:30,710

 

722
00:23:30,710 --> 00:23:34,830

 

723
00:23:34,830 --> 00:23:39,510

 

724
00:23:39,510 --> 00:23:41,269

 

725
00:23:41,269 --> 00:23:44,310

 

726
00:23:44,310 --> 00:23:48,549

 

727
00:23:48,549 --> 00:23:50,310

 

728
00:23:50,310 --> 00:23:52,470

 

729
00:23:52,470 --> 00:23:52,480

 

730
00:23:52,480 --> 00:23:54,789


731
00:23:54,789 --> 00:23:56,710

 

732
00:23:56,710 --> 00:23:58,950

 

733
00:23:58,950 --> 00:24:01,590

 

734
00:24:01,590 --> 00:24:03,029

 

735
00:24:03,029 --> 00:24:04,630

 

736
00:24:04,630 --> 00:24:06,390

 

737
00:24:06,390 --> 00:24:11,029

 

738
00:24:11,029 --> 00:24:14,470

 

739
00:24:14,470 --> 00:24:17,190

 

740
00:24:17,190 --> 00:24:18,470

 

741
00:24:18,470 --> 00:24:21,830

 

742
00:24:21,830 --> 00:24:23,990

 

743
00:24:23,990 --> 00:24:28,070

 

744
00:24:28,070 --> 00:24:31,350

 

745
00:24:31,350 --> 00:24:35,909

 

746
00:24:35,909 --> 00:24:35,919

 

747
00:24:35,919 --> 00:24:37,269


748
00:24:37,269 --> 00:24:37,279

 

749
00:24:37,279 --> 00:24:38,950


750
00:24:38,950 --> 00:24:38,960

 

751
00:24:38,960 --> 00:24:41,029


752
00:24:41,029 --> 00:24:45,430

 

753
00:24:45,430 --> 00:24:48,070

 

754
00:24:48,070 --> 00:24:50,549

 

755
00:24:50,549 --> 00:24:52,310

 

756
00:24:52,310 --> 00:24:54,870

 

757
00:24:54,870 --> 00:24:56,630

 

758
00:24:56,630 --> 00:24:58,390

 

759
00:24:58,390 --> 00:25:00,789

 

760
00:25:00,789 --> 00:25:02,470

 

761
00:25:02,470 --> 00:25:04,390

 

762
00:25:04,390 --> 00:25:07,269

 

763
00:25:07,269 --> 00:25:09,830

 

764
00:25:09,830 --> 00:25:11,909

 

765
00:25:11,909 --> 00:25:14,230

 

766
00:25:14,230 --> 00:25:15,750

 

767
00:25:15,750 --> 00:25:16,789

 

768
00:25:16,789 --> 00:25:18,230

 

769
00:25:18,230 --> 00:25:19,830

 

770
00:25:19,830 --> 00:25:21,990

 

771
00:25:21,990 --> 00:25:23,990

 

772
00:25:23,990 --> 00:25:32,070

 

773
00:25:32,070 --> 00:25:35,269

 

774
00:25:35,269 --> 00:25:37,830

 

775
00:25:37,830 --> 00:25:37,840

 

776
00:25:37,840 --> 00:25:38,789


777
00:25:38,789 --> 00:25:41,669

 

778
00:25:41,669 --> 00:25:43,750

 

779
00:25:43,750 --> 00:25:45,430

 

780
00:25:45,430 --> 00:25:46,549

 

781
00:25:46,549 --> 00:25:48,630

 

782
00:25:48,630 --> 00:25:50,789

 

783
00:25:50,789 --> 00:25:53,750

 

784
00:25:53,750 --> 00:25:55,430

 

785
00:25:55,430 --> 00:25:58,230

 

786
00:25:58,230 --> 00:25:59,750

 

787
00:25:59,750 --> 00:25:59,760

 

788
00:25:59,760 --> 00:26:00,789


789
00:26:00,789 --> 00:26:02,470

 

790
00:26:02,470 --> 00:26:04,310

 

791
00:26:04,310 --> 00:26:07,110

 

792
00:26:07,110 --> 00:26:08,950

 

793
00:26:08,950 --> 00:26:10,710

 

794
00:26:10,710 --> 00:26:12,710

 

795
00:26:12,710 --> 00:26:14,230

 

796
00:26:14,230 --> 00:26:15,990

 

797
00:26:15,990 --> 00:26:17,990

 

798
00:26:17,990 --> 00:26:19,510

 

799
00:26:19,510 --> 00:26:19,520

 

800
00:26:19,520 --> 00:26:22,710


801
00:26:22,710 --> 00:26:25,190

 

802
00:26:25,190 --> 00:26:30,789

 

803
00:26:30,789 --> 00:26:32,789

 

804
00:26:32,789 --> 00:26:34,310

 

805
00:26:34,310 --> 00:26:34,320

 

806
00:26:34,320 --> 00:26:35,190


807
00:26:35,190 --> 00:26:36,390

 

808
00:26:36,390 --> 00:26:38,789

 

809
00:26:38,789 --> 00:26:41,110

 

810
00:26:41,110 --> 00:26:41,120

 

811
00:26:41,120 --> 00:26:41,909


812
00:26:41,909 --> 00:26:45,350

 

813
00:26:45,350 --> 00:26:47,909

 

814
00:26:47,909 --> 00:26:49,430

 

815
00:26:49,430 --> 00:26:50,390

 

816
00:26:50,390 --> 00:26:56,230

 

817
00:26:56,230 --> 00:26:57,909

 

818
00:26:57,909 --> 00:26:57,919

 

819
00:26:57,919 --> 00:26:58,789


820
00:26:58,789 --> 00:27:00,549

 

821
00:27:00,549 --> 00:27:02,310

 

822
00:27:02,310 --> 00:27:06,070

 

823
00:27:06,070 --> 00:27:09,029

 

824
00:27:09,029 --> 00:27:11,669

 

825
00:27:11,669 --> 00:27:13,110

 

826
00:27:13,110 --> 00:27:15,269

 

827
00:27:15,269 --> 00:27:17,750

 

828
00:27:17,750 --> 00:27:19,590

 

829
00:27:19,590 --> 00:27:21,430

 

830
00:27:21,430 --> 00:27:23,669

 

831
00:27:23,669 --> 00:27:26,630

 

832
00:27:26,630 --> 00:27:28,149

 

833
00:27:28,149 --> 00:27:29,510

 

834
00:27:29,510 --> 00:27:30,789

 

835
00:27:30,789 --> 00:27:33,190

 

836
00:27:33,190 --> 00:27:36,950

 

837
00:27:36,950 --> 00:27:38,870

 

838
00:27:38,870 --> 00:27:41,269

 

839
00:27:41,269 --> 00:27:43,430

 

840
00:27:43,430 --> 00:27:45,350

 

841
00:27:45,350 --> 00:27:47,510

 

842
00:27:47,510 --> 00:27:50,630

 

843
00:27:50,630 --> 00:27:54,870

 

844
00:27:54,870 --> 00:27:57,190

 

845
00:27:57,190 --> 00:28:00,310

 

846
00:28:00,310 --> 00:28:02,149

 

847
00:28:02,149 --> 00:28:04,070

 

848
00:28:04,070 --> 00:28:06,230

 

849
00:28:06,230 --> 00:28:07,269

 

850
00:28:07,269 --> 00:28:09,029

 

851
00:28:09,029 --> 00:28:10,789

 

852
00:28:10,789 --> 00:28:10,799

 

853
00:28:10,799 --> 00:28:13,990


854
00:28:13,990 --> 00:28:14,000

 

855
00:28:14,000 --> 00:28:14,830


856
00:28:14,830 --> 00:28:18,389

 

857
00:28:18,389 --> 00:28:20,789

 

858
00:28:20,789 --> 00:28:22,870

 

859
00:28:22,870 --> 00:28:22,880

 

860
00:28:22,880 --> 00:28:23,990


861
00:28:23,990 --> 00:28:25,669

 

862
00:28:25,669 --> 00:28:27,830

 

863
00:28:27,830 --> 00:28:30,950

 

864
00:28:30,950 --> 00:28:32,870

 

865
00:28:32,870 --> 00:28:34,470

 

866
00:28:34,470 --> 00:28:35,990

 

867
00:28:35,990 --> 00:28:38,470

 

868
00:28:38,470 --> 00:28:39,990

 

869
00:28:39,990 --> 00:28:41,750

 

870
00:28:41,750 --> 00:28:45,750

 

871
00:28:45,750 --> 00:28:49,350

 

872
00:28:49,350 --> 00:28:49,360

 

873
00:28:49,360 --> 00:28:50,310


874
00:28:50,310 --> 00:28:53,190

 

875
00:28:53,190 --> 00:28:55,110

 

876
00:28:55,110 --> 00:28:56,310

 

877
00:28:56,310 --> 00:28:58,230

 

878
00:28:58,230 --> 00:28:59,590

 

879
00:28:59,590 --> 00:29:02,310

 

880
00:29:02,310 --> 00:29:04,230

 

881
00:29:04,230 --> 00:29:05,750

 

882
00:29:05,750 --> 00:29:10,470

 

883
00:29:10,470 --> 00:29:12,549

 

884
00:29:12,549 --> 00:29:12,559

 

885
00:29:12,559 --> 00:29:13,750


886
00:29:13,750 --> 00:29:15,990

 

887
00:29:15,990 --> 00:29:16,000

 

888
00:29:16,000 --> 00:29:18,549


889
00:29:18,549 --> 00:29:21,510

 

890
00:29:21,510 --> 00:29:22,630

 

891
00:29:22,630 --> 00:29:24,389

 

892
00:29:24,389 --> 00:29:26,070

 

893
00:29:26,070 --> 00:29:26,080

 

894
00:29:26,080 --> 00:29:26,710


895
00:29:26,710 --> 00:29:28,630

 

896
00:29:28,630 --> 00:29:30,070

 

897
00:29:30,070 --> 00:29:34,310

 

898
00:29:34,310 --> 00:29:34,320

 

899
00:29:34,320 --> 00:29:35,350


900
00:29:35,350 --> 00:29:38,389

 

901
00:29:38,389 --> 00:29:41,110

 

902
00:29:41,110 --> 00:29:43,510

 

903
00:29:43,510 --> 00:29:44,389

 

904
00:29:44,389 --> 00:29:44,399

 

905
00:29:44,399 --> 00:29:45,350


906
00:29:45,350 --> 00:29:45,360

 

907
00:29:45,360 --> 00:29:46,230


908
00:29:46,230 --> 00:29:49,430

 

909
00:29:49,430 --> 00:29:52,549

 

910
00:29:52,549 --> 00:29:54,630

 

911
00:29:54,630 --> 00:29:56,630

 

912
00:29:56,630 --> 00:29:56,640

 

913
00:29:56,640 --> 00:29:57,590


914
00:29:57,590 --> 00:29:59,669

 

915
00:29:59,669 --> 00:30:00,950

 

916
00:30:00,950 --> 00:30:03,669

 

917
00:30:03,669 --> 00:30:05,909

 

918
00:30:05,909 --> 00:30:05,919

 

919
00:30:05,919 --> 00:30:07,029


920
00:30:07,029 --> 00:30:08,950

 

921
00:30:08,950 --> 00:30:11,350

 

922
00:30:11,350 --> 00:30:13,590

 

923
00:30:13,590 --> 00:30:15,750

 

924
00:30:15,750 --> 00:30:17,350

 

925
00:30:17,350 --> 00:30:19,430

 

926
00:30:19,430 --> 00:30:23,669

 

927
00:30:23,669 --> 00:30:25,909

 

928
00:30:25,909 --> 00:30:27,909

 

929
00:30:27,909 --> 00:30:30,230

 

930
00:30:30,230 --> 00:30:31,590

 

931
00:30:31,590 --> 00:30:33,510

 

932
00:30:33,510 --> 00:30:35,190

 

933
00:30:35,190 --> 00:30:36,870

 

934
00:30:36,870 --> 00:30:41,430

 

935
00:30:41,430 --> 00:30:44,149

 

936
00:30:44,149 --> 00:30:46,789

 

937
00:30:46,789 --> 00:30:48,870

 

938
00:30:48,870 --> 00:30:52,470

 

939
00:30:52,470 --> 00:30:54,389

 

940
00:30:54,389 --> 00:30:56,870

 

941
00:30:56,870 --> 00:30:58,549

 

942
00:30:58,549 --> 00:31:01,509

 

943
00:31:01,509 --> 00:31:04,710

 

944
00:31:04,710 --> 00:31:11,430

 

945
00:31:11,430 --> 00:31:11,440

 

946
00:31:11,440 --> 00:31:12,470


947
00:31:12,470 --> 00:31:14,950

 

948
00:31:14,950 --> 00:31:16,630

 

949
00:31:16,630 --> 00:31:19,110

 

950
00:31:19,110 --> 00:31:20,710

 

951
00:31:20,710 --> 00:31:22,070

 

952
00:31:22,070 --> 00:31:25,669

 

953
00:31:25,669 --> 00:31:28,789

 

954
00:31:28,789 --> 00:31:30,630

 

955
00:31:30,630 --> 00:31:33,190

 

956
00:31:33,190 --> 00:31:35,590

 

957
00:31:35,590 --> 00:31:38,549

 

958
00:31:38,549 --> 00:31:41,430

 

959
00:31:41,430 --> 00:31:43,909

 

960
00:31:43,909 --> 00:31:47,430

 

961
00:31:47,430 --> 00:31:47,440

 

962
00:31:47,440 --> 00:31:51,509


963
00:31:51,509 --> 00:31:54,389

 

964
00:31:54,389 --> 00:31:56,470

 

965
00:31:56,470 --> 00:31:58,630

 

966
00:31:58,630 --> 00:32:02,549

 

967
00:32:02,549 --> 00:32:03,909

 

968
00:32:03,909 --> 00:32:05,269

 

969
00:32:05,269 --> 00:32:05,279

 

970
00:32:05,279 --> 00:32:07,750


971
00:32:07,750 --> 00:32:07,760

 

972
00:32:07,760 --> 00:32:08,549


973
00:32:08,549 --> 00:32:10,230

 

974
00:32:10,230 --> 00:32:10,240

 

975
00:32:10,240 --> 00:32:11,430


976
00:32:11,430 --> 00:32:13,190

 

977
00:32:13,190 --> 00:32:16,549

 

978
00:32:16,549 --> 00:32:20,549

 

979
00:32:20,549 --> 00:32:26,630

 

980
00:32:26,630 --> 00:32:28,710

 

981
00:32:28,710 --> 00:32:30,549

 

982
00:32:30,549 --> 00:32:32,230

 

983
00:32:32,230 --> 00:32:34,470

 

984
00:32:34,470 --> 00:32:36,870

 

985
00:32:36,870 --> 00:32:38,630

 

986
00:32:38,630 --> 00:32:38,640

 

987
00:32:38,640 --> 00:32:39,830


988
00:32:39,830 --> 00:32:41,110

 

989
00:32:41,110 --> 00:32:43,350

 

990
00:32:43,350 --> 00:32:45,110

 

991
00:32:45,110 --> 00:32:47,509

 

992
00:32:47,509 --> 00:32:49,990

 

993
00:32:49,990 --> 00:32:51,990

 

994
00:32:51,990 --> 00:32:53,430

 

995
00:32:53,430 --> 00:32:55,669

 

996
00:32:55,669 --> 00:32:57,590

 

997
00:32:57,590 --> 00:32:59,590

 

998
00:32:59,590 --> 00:33:01,909

 

999
00:33:01,909 --> 00:33:03,990

 

1000
00:33:03,990 --> 00:33:06,470

 

1001
00:33:06,470 --> 00:33:09,029

 

1002
00:33:09,029 --> 00:33:13,190

 

1003
00:33:13,190 --> 00:33:15,110

 

1004
00:33:15,110 --> 00:33:17,509

 

1005
00:33:17,509 --> 00:33:19,430

 

1006
00:33:19,430 --> 00:33:19,440

 

1007
00:33:19,440 --> 00:33:21,350


1008
00:33:21,350 --> 00:33:23,430

 

1009
00:33:23,430 --> 00:33:26,789

 

1010
00:33:26,789 --> 00:33:28,149

 

1011
00:33:28,149 --> 00:33:29,990

 

1012
00:33:29,990 --> 00:33:31,509

 

1013
00:33:31,509 --> 00:33:33,509

 

1014
00:33:33,509 --> 00:33:36,470

 

1015
00:33:36,470 --> 00:33:40,549

 

1016
00:33:40,549 --> 00:33:41,909

 

1017
00:33:41,909 --> 00:33:43,909

 

1018
00:33:43,909 --> 00:33:46,149

 

1019
00:33:46,149 --> 00:33:46,159

 

1020
00:33:46,159 --> 00:33:47,029


1021
00:33:47,029 --> 00:33:49,669

 

1022
00:33:49,669 --> 00:33:52,149

 

1023
00:33:52,149 --> 00:33:53,669

 

1024
00:33:53,669 --> 00:33:55,430

 

1025
00:33:55,430 --> 00:34:01,350

 

1026
00:34:01,350 --> 00:34:03,669

 

1027
00:34:03,669 --> 00:34:06,630

 

1028
00:34:06,630 --> 00:34:10,550

 

1029
00:34:10,550 --> 00:34:12,950

 

1030
00:34:12,950 --> 00:34:14,230

 

1031
00:34:14,230 --> 00:34:16,550

 

1032
00:34:16,550 --> 00:34:18,389

 

1033
00:34:18,389 --> 00:34:21,030

 

1034
00:34:21,030 --> 00:34:22,950

 

1035
00:34:22,950 --> 00:34:25,589

 

1036
00:34:25,589 --> 00:34:27,270

 

1037
00:34:27,270 --> 00:34:27,280

 

1038
00:34:27,280 --> 00:34:28,149


1039
00:34:28,149 --> 00:34:30,389

 

1040
00:34:30,389 --> 00:34:32,149

 

1041
00:34:32,149 --> 00:34:32,159

 

1042
00:34:32,159 --> 00:34:32,829


1043
00:34:32,829 --> 00:34:34,710

 

1044
00:34:34,710 --> 00:34:38,310

 

1045
00:34:38,310 --> 00:34:40,629

 

1046
00:34:40,629 --> 00:34:40,639

 

1047
00:34:40,639 --> 00:34:42,950


1048
00:34:42,950 --> 00:34:45,430

 

1049
00:34:45,430 --> 00:34:48,230

 

1050
00:34:48,230 --> 00:34:50,389

 

1051
00:34:50,389 --> 00:34:50,399

 

1052
00:34:50,399 --> 00:34:52,149


1053
00:34:52,149 --> 00:34:54,869

 

1054
00:34:54,869 --> 00:34:57,030

 

1055
00:34:57,030 --> 00:34:59,030

 

1056
00:34:59,030 --> 00:35:01,109

 

1057
00:35:01,109 --> 00:35:03,430

 

1058
00:35:03,430 --> 00:35:05,270

 

1059
00:35:05,270 --> 00:35:06,790

 

1060
00:35:06,790 --> 00:35:07,750

 

1061
00:35:07,750 --> 00:35:09,829

 

1062
00:35:09,829 --> 00:35:09,839

 

1063
00:35:09,839 --> 00:35:11,109


1064
00:35:11,109 --> 00:35:13,030

 

1065
00:35:13,030 --> 00:35:14,950

 

1066
00:35:14,950 --> 00:35:16,550

 

1067
00:35:16,550 --> 00:35:16,560

 

1068
00:35:16,560 --> 00:35:18,069


1069
00:35:18,069 --> 00:35:19,750

 

1070
00:35:19,750 --> 00:35:23,190

 

1071
00:35:23,190 --> 00:35:24,630

 

1072
00:35:24,630 --> 00:35:26,150

 

1073
00:35:26,150 --> 00:35:27,750

 

1074
00:35:27,750 --> 00:35:29,190

 

1075
00:35:29,190 --> 00:35:31,030

 

1076
00:35:31,030 --> 00:35:32,470

 

1077
00:35:32,470 --> 00:35:33,990

 

1078
00:35:33,990 --> 00:35:35,910

 

1079
00:35:35,910 --> 00:35:37,270

 

1080
00:35:37,270 --> 00:35:39,190

 

1081
00:35:39,190 --> 00:35:41,430

 

1082
00:35:41,430 --> 00:35:41,440

 

1083
00:35:41,440 --> 00:35:42,310


1084
00:35:42,310 --> 00:35:42,320

 

1085
00:35:42,320 --> 00:35:43,589


1086
00:35:43,589 --> 00:35:46,390

 

1087
00:35:46,390 --> 00:35:49,430

 

1088
00:35:49,430 --> 00:35:51,190

 

1089
00:35:51,190 --> 00:35:53,670

 

1090
00:35:53,670 --> 00:35:55,109

 

1091
00:35:55,109 --> 00:35:56,630

 

1092
00:35:56,630 --> 00:35:58,790

 

1093
00:35:58,790 --> 00:36:01,109

 

1094
00:36:01,109 --> 00:36:03,430

 

1095
00:36:03,430 --> 00:36:04,790

 

1096
00:36:04,790 --> 00:36:06,230

 

1097
00:36:06,230 --> 00:36:06,240

 

1098
00:36:06,240 --> 00:36:07,430


1099
00:36:07,430 --> 00:36:08,230

 

1100
00:36:08,230 --> 00:36:09,670

 

1101
00:36:09,670 --> 00:36:11,990

 

1102
00:36:11,990 --> 00:36:14,390

 

1103
00:36:14,390 --> 00:36:17,190

 

1104
00:36:17,190 --> 00:36:19,750

 

1105
00:36:19,750 --> 00:36:22,710

 

1106
00:36:22,710 --> 00:36:22,720

 

1107
00:36:22,720 --> 00:36:23,510


1108
00:36:23,510 --> 00:36:23,520

 

1109
00:36:23,520 --> 00:36:25,109


1110
00:36:25,109 --> 00:36:26,470

 

1111
00:36:26,470 --> 00:36:27,829

 

1112
00:36:27,829 --> 00:36:30,230

 

1113
00:36:30,230 --> 00:36:33,190

 

1114
00:36:33,190 --> 00:36:34,390

 

1115
00:36:34,390 --> 00:36:35,990

 

1116
00:36:35,990 --> 00:36:38,150

 

1117
00:36:38,150 --> 00:36:40,230

 

1118
00:36:40,230 --> 00:36:42,550

 

1119
00:36:42,550 --> 00:36:44,710

 

1120
00:36:44,710 --> 00:36:46,230

 

1121
00:36:46,230 --> 00:36:47,349

 

1122
00:36:47,349 --> 00:36:49,030

 

1123
00:36:49,030 --> 00:36:50,790

 

1124
00:36:50,790 --> 00:36:52,390

 

1125
00:36:52,390 --> 00:36:54,230

 

1126
00:36:54,230 --> 00:36:56,950

 

1127
00:36:56,950 --> 00:36:58,310

 

1128
00:36:58,310 --> 00:36:58,320

 

1129
00:36:58,320 --> 00:36:59,510


1130
00:36:59,510 --> 00:36:59,520

 

1131
00:36:59,520 --> 00:37:01,750


1132
00:37:01,750 --> 00:37:02,950

 

1133
00:37:02,950 --> 00:37:04,870

 

1134
00:37:04,870 --> 00:37:06,550

 

1135
00:37:06,550 --> 00:37:08,390

 

1136
00:37:08,390 --> 00:37:10,470

 

1137
00:37:10,470 --> 00:37:13,430

 

1138
00:37:13,430 --> 00:37:16,230

 

1139
00:37:16,230 --> 00:37:17,990

 

1140
00:37:17,990 --> 00:37:19,829

 

1141
00:37:19,829 --> 00:37:21,910

 

1142
00:37:21,910 --> 00:37:24,069

 

1143
00:37:24,069 --> 00:37:24,079

 

1144
00:37:24,079 --> 00:37:24,950


1145
00:37:24,950 --> 00:37:26,390

 

1146
00:37:26,390 --> 00:37:28,710

 

1147
00:37:28,710 --> 00:37:31,109

 

1148
00:37:31,109 --> 00:37:33,109

 

1149
00:37:33,109 --> 00:37:36,470

 

1150
00:37:36,470 --> 00:37:38,069

 

1151
00:37:38,069 --> 00:37:40,790

 

1152
00:37:40,790 --> 00:37:42,230

 

1153
00:37:42,230 --> 00:37:45,589

 

1154
00:37:45,589 --> 00:37:47,430

 

1155
00:37:47,430 --> 00:37:49,750

 

1156
00:37:49,750 --> 00:37:52,870

 

1157
00:37:52,870 --> 00:37:58,390

 

1158
00:37:58,390 --> 00:37:59,829

 

1159
00:37:59,829 --> 00:38:01,510

 

1160
00:38:01,510 --> 00:38:03,589

 

1161
00:38:03,589 --> 00:38:07,670

 

1162
00:38:07,670 --> 00:38:09,109

 

1163
00:38:09,109 --> 00:38:09,119

 

1164
00:38:09,119 --> 00:38:12,230


1165
00:38:12,230 --> 00:38:14,790

 

1166
00:38:14,790 --> 00:38:18,950

 

1167
00:38:18,950 --> 00:38:21,589

 

1168
00:38:21,589 --> 00:38:21,599

 

1169
00:38:21,599 --> 00:38:22,390


1170
00:38:22,390 --> 00:38:25,349

 

1171
00:38:25,349 --> 00:38:27,430

 

1172
00:38:27,430 --> 00:38:28,790

 

1173
00:38:28,790 --> 00:38:31,349

 

1174
00:38:31,349 --> 00:38:31,359

 

1175
00:38:31,359 --> 00:38:34,150


1176
00:38:34,150 --> 00:38:36,950

 

1177
00:38:36,950 --> 00:38:36,960

 

1178
00:38:36,960 --> 00:38:40,950


1179
00:38:40,950 --> 00:38:43,349

 

1180
00:38:43,349 --> 00:38:43,359

 

1181
00:38:43,359 --> 00:38:44,470


1182
00:38:44,470 --> 00:38:47,990

 

1183
00:38:47,990 --> 00:38:51,190

 

1184
00:38:51,190 --> 00:38:53,990

 

1185
00:38:53,990 --> 00:38:55,829

 

1186
00:38:55,829 --> 00:38:57,990

 

1187
00:38:57,990 --> 00:39:02,230

 

1188
00:39:02,230 --> 00:39:04,550

 

1189
00:39:04,550 --> 00:39:06,069

 

1190
00:39:06,069 --> 00:39:07,750

 

1191
00:39:07,750 --> 00:39:09,270

 

1192
00:39:09,270 --> 00:39:10,550

 

1193
00:39:10,550 --> 00:39:13,829

 

1194
00:39:13,829 --> 00:39:15,750

 

1195
00:39:15,750 --> 00:39:17,829

 

1196
00:39:17,829 --> 00:39:20,069

 

1197
00:39:20,069 --> 00:39:22,150

 

1198
00:39:22,150 --> 00:39:24,150

 

1199
00:39:24,150 --> 00:39:26,710

 

1200
00:39:26,710 --> 00:39:28,710

 

1201
00:39:28,710 --> 00:39:31,349

 

1202
00:39:31,349 --> 00:39:33,109

 

1203
00:39:33,109 --> 00:39:37,510

 

1204
00:39:37,510 --> 00:39:38,710

 

1205
00:39:38,710 --> 00:39:38,720

 

1206
00:39:38,720 --> 00:39:39,750


1207
00:39:39,750 --> 00:39:40,870

 

1208
00:39:40,870 --> 00:39:42,390

 

1209
00:39:42,390 --> 00:39:44,470

 

1210
00:39:44,470 --> 00:39:45,910

 

1211
00:39:45,910 --> 00:39:47,430

 

1212
00:39:47,430 --> 00:39:48,870

 

1213
00:39:48,870 --> 00:39:51,270

 

1214
00:39:51,270 --> 00:39:54,310

 

1215
00:39:54,310 --> 00:39:58,790

 

1216
00:39:58,790 --> 00:39:58,800

 

1217
00:39:58,800 --> 00:39:59,589


1218
00:39:59,589 --> 00:40:01,510

 

1219
00:40:01,510 --> 00:40:03,990

 

1220
00:40:03,990 --> 00:40:05,589

 

1221
00:40:05,589 --> 00:40:07,270

 

1222
00:40:07,270 --> 00:40:09,190

 

1223
00:40:09,190 --> 00:40:09,200

 

1224
00:40:09,200 --> 00:40:10,550


1225
00:40:10,550 --> 00:40:10,560

 

1226
00:40:10,560 --> 00:40:11,510


1227
00:40:11,510 --> 00:40:13,349

 

1228
00:40:13,349 --> 00:40:15,510

 

1229
00:40:15,510 --> 00:40:15,520

 

1230
00:40:15,520 --> 00:40:18,309


1231
00:40:18,309 --> 00:40:22,390

 

1232
00:40:22,390 --> 00:40:24,150

 

1233
00:40:24,150 --> 00:40:27,190

 

1234
00:40:27,190 --> 00:40:30,230

 

1235
00:40:30,230 --> 00:40:32,309

 

1236
00:40:32,309 --> 00:40:34,470

 

1237
00:40:34,470 --> 00:40:36,069

 

1238
00:40:36,069 --> 00:40:39,270

 

1239
00:40:39,270 --> 00:40:42,069

 

1240
00:40:42,069 --> 00:40:44,790

 

1241
00:40:44,790 --> 00:40:48,390

 

1242
00:40:48,390 --> 00:40:49,589

 

1243
00:40:49,589 --> 00:40:51,030

 

1244
00:40:51,030 --> 00:40:52,710

 

1245
00:40:52,710 --> 00:40:54,550

 

1246
00:40:54,550 --> 00:40:54,560

 

1247
00:40:54,560 --> 00:40:55,990


1248
00:40:55,990 --> 00:40:58,950

 

1249
00:40:58,950 --> 00:40:58,960

 

1250
00:40:58,960 --> 00:41:00,790


1251
00:41:00,790 --> 00:41:05,270

 

1252
00:41:05,270 --> 00:41:07,910

 

1253
00:41:07,910 --> 00:41:10,309

 

1254
00:41:10,309 --> 00:41:12,710

 

1255
00:41:12,710 --> 00:41:14,710

 

1256
00:41:14,710 --> 00:41:16,470

 

1257
00:41:16,470 --> 00:41:16,480

 

1258
00:41:16,480 --> 00:41:18,230


1259
00:41:18,230 --> 00:41:19,910

 

1260
00:41:19,910 --> 00:41:22,870

 

1261
00:41:22,870 --> 00:41:24,710

 

1262
00:41:24,710 --> 00:41:26,150

 

1263
00:41:26,150 --> 00:41:28,150

 

1264
00:41:28,150 --> 00:41:30,069

 

1265
00:41:30,069 --> 00:41:30,079

 

1266
00:41:30,079 --> 00:41:30,950


1267
00:41:30,950 --> 00:41:32,829

 

1268
00:41:32,829 --> 00:41:35,829

 

1269
00:41:35,829 --> 00:41:37,109

 

1270
00:41:37,109 --> 00:41:39,349

 

1271
00:41:39,349 --> 00:41:41,430

 

1272
00:41:41,430 --> 00:41:45,510

 

1273
00:41:45,510 --> 00:41:50,550

 

1274
00:41:50,550 --> 00:41:52,069

 

1275
00:41:52,069 --> 00:41:53,030

 

1276
00:41:53,030 --> 00:41:56,150

 

1277
00:41:56,150 --> 00:41:58,069

 

1278
00:41:58,069 --> 00:41:58,079

 

1279
00:41:58,079 --> 00:41:59,750


1280
00:41:59,750 --> 00:42:03,510

 

1281
00:42:03,510 --> 00:42:06,550

 

1282
00:42:06,550 --> 00:42:09,670

 

1283
00:42:09,670 --> 00:42:11,750

 

1284
00:42:11,750 --> 00:42:14,309

 

1285
00:42:14,309 --> 00:42:20,390

 

1286
00:42:20,390 --> 00:42:23,030

 

1287
00:42:23,030 --> 00:42:25,510

 

1288
00:42:25,510 --> 00:42:27,030

 

1289
00:42:27,030 --> 00:42:27,040

 

1290
00:42:27,040 --> 00:42:28,309


1291
00:42:28,309 --> 00:42:30,790

 

1292
00:42:30,790 --> 00:42:33,990

 

1293
00:42:33,990 --> 00:42:36,870

 

1294
00:42:36,870 --> 00:42:39,589

 

1295
00:42:39,589 --> 00:42:39,599

 

1296
00:42:39,599 --> 00:42:40,510


1297
00:42:40,510 --> 00:42:43,270

 

1298
00:42:43,270 --> 00:42:45,990

 

1299
00:42:45,990 --> 00:42:47,750

 

1300
00:42:47,750 --> 00:42:51,030

 

1301
00:42:51,030 --> 00:42:51,040

 

1302
00:42:51,040 --> 00:42:53,109


1303
00:42:53,109 --> 00:42:55,349

 

1304
00:42:55,349 --> 00:42:56,710

 

1305
00:42:56,710 --> 00:42:58,390

 

1306
00:42:58,390 --> 00:43:00,630

 

1307
00:43:00,630 --> 00:43:03,190

 

1308
00:43:03,190 --> 00:43:06,309

 

1309
00:43:06,309 --> 00:43:09,990

 

1310
00:43:09,990 --> 00:43:15,910

 

1311
00:43:15,910 --> 00:43:18,550

 

1312
00:43:18,550 --> 00:43:20,790

 

1313
00:43:20,790 --> 00:43:22,550

 

1314
00:43:22,550 --> 00:43:23,750

 

1315
00:43:23,750 --> 00:43:26,390

 

1316
00:43:26,390 --> 00:43:26,400

 

1317
00:43:26,400 --> 00:43:27,349


1318
00:43:27,349 --> 00:43:28,950

 

1319
00:43:28,950 --> 00:43:30,230

 

1320
00:43:30,230 --> 00:43:32,550

 

1321
00:43:32,550 --> 00:43:34,069

 

1322
00:43:34,069 --> 00:43:36,390

 

1323
00:43:36,390 --> 00:43:38,390

 

1324
00:43:38,390 --> 00:43:39,430

 

1325
00:43:39,430 --> 00:43:39,440

 

1326
00:43:39,440 --> 00:43:40,470


1327
00:43:40,470 --> 00:43:40,480

 

1328
00:43:40,480 --> 00:43:42,150


1329
00:43:42,150 --> 00:43:42,160

 

1330
00:43:42,160 --> 00:43:43,349


1331
00:43:43,349 --> 00:43:46,069

 

1332
00:43:46,069 --> 00:43:48,790

 

1333
00:43:48,790 --> 00:43:50,230

 

1334
00:43:50,230 --> 00:43:51,270

 

1335
00:43:51,270 --> 00:43:54,390

 

1336
00:43:54,390 --> 00:43:56,470

 

1337
00:43:56,470 --> 00:43:57,589

 

1338
00:43:57,589 --> 00:43:59,030

 

1339
00:43:59,030 --> 00:44:00,150

 

1340
00:44:00,150 --> 00:44:02,470

 

1341
00:44:02,470 --> 00:44:05,270

 

1342
00:44:05,270 --> 00:44:06,710

 

1343
00:44:06,710 --> 00:44:08,390

 

1344
00:44:08,390 --> 00:44:10,390

 

1345
00:44:10,390 --> 00:44:13,829

 

1346
00:44:13,829 --> 00:44:15,750

 

1347
00:44:15,750 --> 00:44:17,910

 

1348
00:44:17,910 --> 00:44:20,309

 

1349
00:44:20,309 --> 00:44:22,870

 

1350
00:44:22,870 --> 00:44:24,470

 

1351
00:44:24,470 --> 00:44:26,069

 

1352
00:44:26,069 --> 00:44:26,079

 

1353
00:44:26,079 --> 00:44:27,109


1354
00:44:27,109 --> 00:44:28,870

 

1355
00:44:28,870 --> 00:44:28,880

 

1356
00:44:28,880 --> 00:44:30,150


1357
00:44:30,150 --> 00:44:30,160

 

1358
00:44:30,160 --> 00:44:31,670


1359
00:44:31,670 --> 00:44:31,680

 

1360
00:44:31,680 --> 00:44:32,950


1361
00:44:32,950 --> 00:44:33,990

 

1362
00:44:33,990 --> 00:44:34,000

 

1363
00:44:34,000 --> 00:44:34,710


1364
00:44:34,710 --> 00:44:38,390

 

1365
00:44:38,390 --> 00:44:40,470

 

1366
00:44:40,470 --> 00:44:43,190

 

1367
00:44:43,190 --> 00:44:44,390

 

1368
00:44:44,390 --> 00:44:47,349

 

1369
00:44:47,349 --> 00:44:49,510

 

1370
00:44:49,510 --> 00:44:51,670

 

1371
00:44:51,670 --> 00:44:53,349

 

1372
00:44:53,349 --> 00:44:55,589

 

1373
00:44:55,589 --> 00:44:56,710

 

1374
00:44:56,710 --> 00:44:58,470

 

1375
00:44:58,470 --> 00:44:58,480

 

1376
00:44:58,480 --> 00:44:59,670


1377
00:44:59,670 --> 00:45:01,990

 

1378
00:45:01,990 --> 00:45:07,190

 

1379
00:45:07,190 --> 00:45:10,069

 

1380
00:45:10,069 --> 00:45:15,109

 

1381
00:45:15,109 --> 00:45:16,630

 

1382
00:45:16,630 --> 00:45:18,790

 

1383
00:45:18,790 --> 00:45:21,510

 

1384
00:45:21,510 --> 00:45:24,950

 

1385
00:45:24,950 --> 00:45:27,190

 

1386
00:45:27,190 --> 00:45:29,510

 

1387
00:45:29,510 --> 00:45:30,870

 

1388
00:45:30,870 --> 00:45:35,030

 

1389
00:45:35,030 --> 00:45:35,040

 

1390
00:45:35,040 --> 00:45:37,030


1391
00:45:37,030 --> 00:45:38,230

 

1392
00:45:38,230 --> 00:45:40,470

 

1393
00:45:40,470 --> 00:45:43,589

 

1394
00:45:43,589 --> 00:45:45,349

 

1395
00:45:45,349 --> 00:45:47,910

 

1396
00:45:47,910 --> 00:45:50,309

 

1397
00:45:50,309 --> 00:45:52,069

 

1398
00:45:52,069 --> 00:45:52,079

 

1399
00:45:52,079 --> 00:45:53,510


1400
00:45:53,510 --> 00:45:56,390

 

1401
00:45:56,390 --> 00:45:59,589

 

1402
00:45:59,589 --> 00:46:01,670

 

1403
00:46:01,670 --> 00:46:05,990

 

1404
00:46:05,990 --> 00:46:06,000

 

1405
00:46:06,000 --> 00:46:06,870


1406
00:46:06,870 --> 00:46:09,270

 

1407
00:46:09,270 --> 00:46:09,280

 

1408
00:46:09,280 --> 00:46:10,150


1409
00:46:10,150 --> 00:46:12,109

 

1410
00:46:12,109 --> 00:46:14,630

 

1411
00:46:14,630 --> 00:46:16,870

 

1412
00:46:16,870 --> 00:46:18,710

 

1413
00:46:18,710 --> 00:46:20,470

 

1414
00:46:20,470 --> 00:46:22,790

 

1415
00:46:22,790 --> 00:46:22,800

 

1416
00:46:22,800 --> 00:46:24,230


1417
00:46:24,230 --> 00:46:24,240

 

1418
00:46:24,240 --> 00:46:25,030


1419
00:46:25,030 --> 00:46:27,430

 

1420
00:46:27,430 --> 00:46:27,440

 

1421
00:46:27,440 --> 00:46:28,950


1422
00:46:28,950 --> 00:46:30,950

 

1423
00:46:30,950 --> 00:46:34,390

 

1424
00:46:34,390 --> 00:46:37,030

 

1425
00:46:37,030 --> 00:46:38,790

 

1426
00:46:38,790 --> 00:46:41,190

 

1427
00:46:41,190 --> 00:46:41,200

 

1428
00:46:41,200 --> 00:46:42,470


1429
00:46:42,470 --> 00:46:42,480

 

1430
00:46:42,480 --> 00:46:43,670


1431
00:46:43,670 --> 00:46:45,670

 

1432
00:46:45,670 --> 00:46:48,630

 

1433
00:46:48,630 --> 00:46:50,150

 

1434
00:46:50,150 --> 00:46:52,069

 

1435
00:46:52,069 --> 00:46:53,750

 

1436
00:46:53,750 --> 00:46:56,470

 

1437
00:46:56,470 --> 00:46:58,870

 

1438
00:46:58,870 --> 00:47:00,309

 

1439
00:47:00,309 --> 00:47:02,069

 

1440
00:47:02,069 --> 00:47:03,829

 

1441
00:47:03,829 --> 00:47:07,510

 

1442
00:47:07,510 --> 00:47:12,790

 

1443
00:47:12,790 --> 00:47:16,550

 

1444
00:47:16,550 --> 00:47:20,230

 

1445
00:47:20,230 --> 00:47:22,549

 

1446
00:47:22,549 --> 00:47:24,470

 

1447
00:47:24,470 --> 00:47:25,910

 

1448
00:47:25,910 --> 00:47:28,069

 

1449
00:47:28,069 --> 00:47:29,670

 

1450
00:47:29,670 --> 00:47:31,030

 

1451
00:47:31,030 --> 00:47:31,040

 

1452
00:47:31,040 --> 00:47:32,549


1453
00:47:32,549 --> 00:47:32,559

 

1454
00:47:32,559 --> 00:47:33,750


1455
00:47:33,750 --> 00:47:33,760

 

1456
00:47:33,760 --> 00:47:34,790


1457
00:47:34,790 --> 00:47:34,800

 

1458
00:47:34,800 --> 00:47:36,630


1459
00:47:36,630 --> 00:47:38,470

 

1460
00:47:38,470 --> 00:47:38,480

 

1461
00:47:38,480 --> 00:47:40,309


1462
00:47:40,309 --> 00:47:43,349

 

1463
00:47:43,349 --> 00:47:45,109

 

1464
00:47:45,109 --> 00:47:47,030

 

1465
00:47:47,030 --> 00:47:47,040

 

1466
00:47:47,040 --> 00:47:49,829


1467
00:47:49,829 --> 00:47:49,839

 

1468
00:47:49,839 --> 00:47:50,710


1469
00:47:50,710 --> 00:47:51,990

 

1470
00:47:51,990 --> 00:47:54,630

 

1471
00:47:54,630 --> 00:47:57,589

 

1472
00:47:57,589 --> 00:47:59,670

 

1473
00:47:59,670 --> 00:48:01,510

 

1474
00:48:01,510 --> 00:48:03,109

 

1475
00:48:03,109 --> 00:48:05,190

 

1476
00:48:05,190 --> 00:48:05,200

 

1477
00:48:05,200 --> 00:48:07,750


1478
00:48:07,750 --> 00:48:09,589

 

1479
00:48:09,589 --> 00:48:12,470

 

1480
00:48:12,470 --> 00:48:15,190

 

1481
00:48:15,190 --> 00:48:16,390

 

1482
00:48:16,390 --> 00:48:18,520

 

1483
00:48:18,520 --> 00:48:18,530

 

1484
00:48:18,530 --> 00:48:19,990


1485
00:48:19,990 --> 00:48:21,670

 

1486
00:48:21,670 --> 00:48:21,680

 

1487
00:48:21,680 --> 00:48:22,470


1488
00:48:22,470 --> 00:48:24,309

 

1489
00:48:24,309 --> 00:48:24,319

 

1490
00:48:24,319 --> 00:48:26,150


1491
00:48:26,150 --> 00:48:27,990

 

1492
00:48:27,990 --> 00:48:30,549

 

1493
00:48:30,549 --> 00:48:32,230

 

1494
00:48:32,230 --> 00:48:34,069

 

1495
00:48:34,069 --> 00:48:35,910

 

1496
00:48:35,910 --> 00:48:38,710

 

1497
00:48:38,710 --> 00:48:41,910

 

1498
00:48:41,910 --> 00:48:45,910

 

1499
00:48:45,910 --> 00:48:47,750

 

1500
00:48:47,750 --> 00:48:49,030

 

1501
00:48:49,030 --> 00:48:49,040

 

1502
00:48:49,040 --> 00:48:51,990


1503
00:48:51,990 --> 00:48:52,000

 

1504
00:48:52,000 --> 00:48:54,710


1505
00:48:54,710 --> 00:48:56,050

 

1506
00:48:56,050 --> 00:48:56,060

 

1507
00:48:56,060 --> 00:49:00,549


1508
00:49:00,549 --> 00:49:03,109

 

1509
00:49:03,109 --> 00:49:05,030

 

1510
00:49:05,030 --> 00:49:05,040

 

1511
00:49:05,040 --> 00:49:08,230


1512
00:49:08,230 --> 00:49:08,240

 

1513
00:49:08,240 --> 00:49:19,270


1514
00:49:19,270 --> 00:49:21,109

 

1515
00:49:21,109 --> 00:49:21,119

 

1516
00:49:21,119 --> 00:49:21,829


1517
00:49:21,829 --> 00:49:23,670

 

1518
00:49:23,670 --> 00:49:25,750

 

1519
00:49:25,750 --> 00:49:27,589

 

1520
00:49:27,589 --> 00:49:27,599

 

1521
00:49:27,599 --> 00:49:28,390


1522
00:49:28,390 --> 00:49:29,990

 

1523
00:49:29,990 --> 00:49:31,829

 

1524
00:49:31,829 --> 00:49:33,589

 

1525
00:49:33,589 --> 00:49:33,599

 

1526
00:49:33,599 --> 00:49:34,470


1527
00:49:34,470 --> 00:49:36,790

 

1528
00:49:36,790 --> 00:49:39,190

 

1529
00:49:39,190 --> 00:49:43,030

 

1530
00:49:43,030 --> 00:49:45,030

 

1531
00:49:45,030 --> 00:49:46,950

 

1532
00:49:46,950 --> 00:49:49,270

 

1533
00:49:49,270 --> 00:49:50,870

 

1534
00:49:50,870 --> 00:49:53,030

 

1535
00:49:53,030 --> 00:49:54,950

 

1536
00:49:54,950 --> 00:49:57,349

 

1537
00:49:57,349 --> 00:49:59,670

 

1538
00:49:59,670 --> 00:50:01,190

 

1539
00:50:01,190 --> 00:50:03,270

 

1540
00:50:03,270 --> 00:50:06,710

 

1541
00:50:06,710 --> 00:50:08,710

 

1542
00:50:08,710 --> 00:50:09,990

 

1543
00:50:09,990 --> 00:50:11,750

 

1544
00:50:11,750 --> 00:50:14,549

 

1545
00:50:14,549 --> 00:50:14,559

 

1546
00:50:14,559 --> 00:50:17,349


1547
00:50:17,349 --> 00:50:19,430

 

1548
00:50:19,430 --> 00:50:22,069

 

1549
00:50:22,069 --> 00:50:24,470

 

1550
00:50:24,470 --> 00:50:25,670

 

1551
00:50:25,670 --> 00:50:27,030

 

1552
00:50:27,030 --> 00:50:29,030

 

1553
00:50:29,030 --> 00:50:31,349

 

1554
00:50:31,349 --> 00:50:32,710

 

1555
00:50:32,710 --> 00:50:35,270

 

1556
00:50:35,270 --> 00:50:36,470

 

1557
00:50:36,470 --> 00:50:37,990

 

1558
00:50:37,990 --> 00:50:38,000

 

1559
00:50:38,000 --> 00:50:41,670


1560
00:50:41,670 --> 00:50:44,069

 

1561
00:50:44,069 --> 00:50:46,710

 

1562
00:50:46,710 --> 00:50:48,549

 

1563
00:50:48,549 --> 00:50:48,559

 

1564
00:50:48,559 --> 00:50:49,510


1565
00:50:49,510 --> 00:50:52,309

 

1566
00:50:52,309 --> 00:50:55,990

 

1567
00:50:55,990 --> 00:50:57,190

 

1568
00:50:57,190 --> 00:50:59,030

 

1569
00:50:59,030 --> 00:51:00,470

 

1570
00:51:00,470 --> 00:51:03,349

 

1571
00:51:03,349 --> 00:51:05,349

 

1572
00:51:05,349 --> 00:51:06,390

 

1573
00:51:06,390 --> 00:51:08,470

 

1574
00:51:08,470 --> 00:51:10,630

 

1575
00:51:10,630 --> 00:51:13,109

 

1576
00:51:13,109 --> 00:51:14,950

 

1577
00:51:14,950 --> 00:51:18,710

 

1578
00:51:18,710 --> 00:51:21,030

 

1579
00:51:21,030 --> 00:51:22,470

 

1580
00:51:22,470 --> 00:51:25,829

 

1581
00:51:25,829 --> 00:51:29,910

 

1582
00:51:29,910 --> 00:51:29,920

 

1583
00:51:29,920 --> 00:51:31,270


1584
00:51:31,270 --> 00:51:31,280

 

1585
00:51:31,280 --> 00:51:32,950


1586
00:51:32,950 --> 00:51:32,960

 

1587
00:51:32,960 --> 00:51:34,309


1588
00:51:34,309 --> 00:51:37,430

 

1589
00:51:37,430 --> 00:51:41,670

 

1590
00:51:41,670 --> 00:51:42,630

 

1591
00:51:42,630 --> 00:51:45,430

 

1592
00:51:45,430 --> 00:51:47,349

 

1593
00:51:47,349 --> 00:51:49,190

 

1594
00:51:49,190 --> 00:51:50,630

 

1595
00:51:50,630 --> 00:51:50,640

 

1596
00:51:50,640 --> 00:51:52,230


1597
00:51:52,230 --> 00:51:55,030

 

1598
00:51:55,030 --> 00:51:57,430

 

1599
00:51:57,430 --> 00:51:59,270

 

1600
00:51:59,270 --> 00:52:01,430

 

1601
00:52:01,430 --> 00:52:03,270

 

1602
00:52:03,270 --> 00:52:05,109

 

1603
00:52:05,109 --> 00:52:08,230

 

1604
00:52:08,230 --> 00:52:08,240

 

1605
00:52:08,240 --> 00:52:08,950


1606
00:52:08,950 --> 00:52:08,960

 

1607
00:52:08,960 --> 00:52:09,910


1608
00:52:09,910 --> 00:52:12,710

 

1609
00:52:12,710 --> 00:52:14,309

 

1610
00:52:14,309 --> 00:52:15,750

 

1611
00:52:15,750 --> 00:52:18,470

 

1612
00:52:18,470 --> 00:52:20,870

 

1613
00:52:20,870 --> 00:52:23,030

 

1614
00:52:23,030 --> 00:52:23,040

 

1615
00:52:23,040 --> 00:52:24,309


1616
00:52:24,309 --> 00:52:25,510

 

1617
00:52:25,510 --> 00:52:27,270

 

1618
00:52:27,270 --> 00:52:29,670

 

1619
00:52:29,670 --> 00:52:31,829

 

1620
00:52:31,829 --> 00:52:33,910

 

1621
00:52:33,910 --> 00:52:33,920

 

1622
00:52:33,920 --> 00:52:35,109


1623
00:52:35,109 --> 00:52:37,109

 

1624
00:52:37,109 --> 00:52:37,119

 

1625
00:52:37,119 --> 00:52:39,190


1626
00:52:39,190 --> 00:52:42,549

 

1627
00:52:42,549 --> 00:52:47,430

 

1628
00:52:47,430 --> 00:52:49,190

 

1629
00:52:49,190 --> 00:52:52,630

 

1630
00:52:52,630 --> 00:52:54,549

 

1631
00:52:54,549 --> 00:52:56,549

 

1632
00:52:56,549 --> 00:52:58,470

 

1633
00:52:58,470 --> 00:53:00,470

 

1634
00:53:00,470 --> 00:53:03,430

 

1635
00:53:03,430 --> 00:53:05,349

 

1636
00:53:05,349 --> 00:53:07,030

 

1637
00:53:07,030 --> 00:53:09,750

 

1638
00:53:09,750 --> 00:53:11,829

 

1639
00:53:11,829 --> 00:53:13,270

 

1640
00:53:13,270 --> 00:53:14,710

 

1641
00:53:14,710 --> 00:53:14,720

 

1642
00:53:14,720 --> 00:53:16,549


1643
00:53:16,549 --> 00:53:18,309

 

1644
00:53:18,309 --> 00:53:19,349

 

1645
00:53:19,349 --> 00:53:20,950

 

1646
00:53:20,950 --> 00:53:22,309

 

1647
00:53:22,309 --> 00:53:23,910

 

1648
00:53:23,910 --> 00:53:27,109

 

1649
00:53:27,109 --> 00:53:29,589

 

1650
00:53:29,589 --> 00:53:29,599

 

1651
00:53:29,599 --> 00:53:32,150


1652
00:53:32,150 --> 00:53:33,829

 

1653
00:53:33,829 --> 00:53:37,510

 

1654
00:53:37,510 --> 00:53:39,990

 

1655
00:53:39,990 --> 00:53:42,069

 

1656
00:53:42,069 --> 00:53:45,829

 

1657
00:53:45,829 --> 00:53:47,190

 

1658
00:53:47,190 --> 00:53:49,589

 

1659
00:53:49,589 --> 00:53:51,109

 

1660
00:53:51,109 --> 00:53:53,109

 

1661
00:53:53,109 --> 00:53:53,119

 

1662
00:53:53,119 --> 00:53:55,430


1663
00:53:55,430 --> 00:53:58,150

 

1664
00:53:58,150 --> 00:53:59,270

 

1665
00:53:59,270 --> 00:54:00,790

 

1666
00:54:00,790 --> 00:54:02,870

 

1667
00:54:02,870 --> 00:54:02,880

 

1668
00:54:02,880 --> 00:54:04,549


1669
00:54:04,549 --> 00:54:06,069

 

1670
00:54:06,069 --> 00:54:07,510

 

1671
00:54:07,510 --> 00:54:09,750

 

1672
00:54:09,750 --> 00:54:11,349

 

1673
00:54:11,349 --> 00:54:12,870

 

1674
00:54:12,870 --> 00:54:15,190

 

1675
00:54:15,190 --> 00:54:17,270

 

1676
00:54:17,270 --> 00:54:19,030

 

1677
00:54:19,030 --> 00:54:19,040

 

1678
00:54:19,040 --> 00:54:22,470


1679
00:54:22,470 --> 00:54:25,109

 

1680
00:54:25,109 --> 00:54:27,910

 

1681
00:54:27,910 --> 00:54:30,150

 

1682
00:54:30,150 --> 00:54:32,549

 

1683
00:54:32,549 --> 00:54:34,069

 

1684
00:54:34,069 --> 00:54:36,870

 

1685
00:54:36,870 --> 00:54:39,030

 

1686
00:54:39,030 --> 00:54:41,750

 

1687
00:54:41,750 --> 00:54:47,030

 

1688
00:54:47,030 --> 00:54:49,270

 

1689
00:54:49,270 --> 00:54:51,829

 

1690
00:54:51,829 --> 00:54:54,390

 

1691
00:54:54,390 --> 00:54:56,789

 

1692
00:54:56,789 --> 00:54:58,150

 

1693
00:54:58,150 --> 00:55:00,230

 

1694
00:55:00,230 --> 00:55:02,390

 

1695
00:55:02,390 --> 00:55:04,309

 

1696
00:55:04,309 --> 00:55:04,319

 

1697
00:55:04,319 --> 00:55:05,510


1698
00:55:05,510 --> 00:55:07,910

 

1699
00:55:07,910 --> 00:55:09,910

 

1700
00:55:09,910 --> 00:55:11,829

 

1701
00:55:11,829 --> 00:55:11,839

 

1702
00:55:11,839 --> 00:55:13,030


1703
00:55:13,030 --> 00:55:15,349

 

1704
00:55:15,349 --> 00:55:18,710

 

1705
00:55:18,710 --> 00:55:20,789

 

1706
00:55:20,789 --> 00:55:22,549

 

1707
00:55:22,549 --> 00:55:26,470

 

1708
00:55:26,470 --> 00:55:28,870

 

1709
00:55:28,870 --> 00:55:30,630

 

1710
00:55:30,630 --> 00:55:33,510

 

1711
00:55:33,510 --> 00:55:35,030

 

1712
00:55:35,030 --> 00:55:35,040

 

1713
00:55:35,040 --> 00:55:36,230


1714
00:55:36,230 --> 00:55:37,349

 

1715
00:55:37,349 --> 00:55:39,109

 

1716
00:55:39,109 --> 00:55:41,430

 

1717
00:55:41,430 --> 00:55:42,789

 

1718
00:55:42,789 --> 00:55:44,549

 

1719
00:55:44,549 --> 00:55:44,559

 

1720
00:55:44,559 --> 00:55:46,829


1721
00:55:46,829 --> 00:55:48,950

 

1722
00:55:48,950 --> 00:55:51,670

 

1723
00:55:51,670 --> 00:55:53,990

 

1724
00:55:53,990 --> 00:55:55,270

 

1725
00:55:55,270 --> 00:55:56,390

 

1726
00:55:56,390 --> 00:55:59,510

 

1727
00:55:59,510 --> 00:56:01,829

 

1728
00:56:01,829 --> 00:56:03,109

 

1729
00:56:03,109 --> 00:56:05,670

 

1730
00:56:05,670 --> 00:56:07,829

 

1731
00:56:07,829 --> 00:56:09,670

 

1732
00:56:09,670 --> 00:56:10,870

 

1733
00:56:10,870 --> 00:56:10,880

 

1734
00:56:10,880 --> 00:56:13,510


1735
00:56:13,510 --> 00:56:13,520

 

1736
00:56:13,520 --> 00:56:15,030


1737
00:56:15,030 --> 00:56:17,109

 

1738
00:56:17,109 --> 00:56:18,789

 

1739
00:56:18,789 --> 00:56:20,630

 

1740
00:56:20,630 --> 00:56:22,630

 

1741
00:56:22,630 --> 00:56:24,789

 

1742
00:56:24,789 --> 00:56:26,309

 

1743
00:56:26,309 --> 00:56:27,670

 

1744
00:56:27,670 --> 00:56:28,789

 

1745
00:56:28,789 --> 00:56:30,150

 

1746
00:56:30,150 --> 00:56:30,160

 

1747
00:56:30,160 --> 00:56:31,910


1748
00:56:31,910 --> 00:56:34,549

 

1749
00:56:34,549 --> 00:56:34,559

 

1750
00:56:34,559 --> 00:56:35,829


1751
00:56:35,829 --> 00:56:38,710

 

1752
00:56:38,710 --> 00:56:41,750

 

1753
00:56:41,750 --> 00:56:43,270

 

1754
00:56:43,270 --> 00:56:43,280

 

1755
00:56:43,280 --> 00:56:44,470


1756
00:56:44,470 --> 00:56:46,710

 

1757
00:56:46,710 --> 00:56:48,470

 

1758
00:56:48,470 --> 00:56:50,470

 

1759
00:56:50,470 --> 00:56:52,390

 

1760
00:56:52,390 --> 00:56:54,470

 

1761
00:56:54,470 --> 00:56:56,789

 

1762
00:56:56,789 --> 00:56:58,950

 

1763
00:56:58,950 --> 00:56:58,960

 

1764
00:56:58,960 --> 00:57:01,990


1765
00:57:01,990 --> 00:57:03,910

 

1766
00:57:03,910 --> 00:57:06,150

 

1767
00:57:06,150 --> 00:57:09,510

 

1768
00:57:09,510 --> 00:57:11,349

 

1769
00:57:11,349 --> 00:57:11,359

 

1770
00:57:11,359 --> 00:57:16,230


1771
00:57:16,230 --> 00:57:18,230

 

1772
00:57:18,230 --> 00:57:20,390

 

1773
00:57:20,390 --> 00:57:23,510

 

1774
00:57:23,510 --> 00:57:25,349

 

1775
00:57:25,349 --> 00:57:28,789

 

1776
00:57:28,789 --> 00:57:31,910

 

1777
00:57:31,910 --> 00:57:34,549

 

1778
00:57:34,549 --> 00:57:36,549

 

1779
00:57:36,549 --> 00:57:40,870

 

1780
00:57:40,870 --> 00:57:42,470

 

1781
00:57:42,470 --> 00:57:43,990

 

1782
00:57:43,990 --> 00:57:44,000

 

1783
00:57:44,000 --> 00:57:47,510


1784
00:57:47,510 --> 00:57:49,750

 

1785
00:57:49,750 --> 00:57:51,750

 

1786
00:57:51,750 --> 00:57:53,430

 

1787
00:57:53,430 --> 00:57:55,510

 

1788
00:57:55,510 --> 00:57:59,190

 

1789
00:57:59,190 --> 00:58:00,870

 

1790
00:58:00,870 --> 00:58:02,390

 

1791
00:58:02,390 --> 00:58:03,829

 

1792
00:58:03,829 --> 00:58:06,309

 

1793
00:58:06,309 --> 00:58:08,549

 

1794
00:58:08,549 --> 00:58:10,710

 

1795
00:58:10,710 --> 00:58:13,109

 

1796
00:58:13,109 --> 00:58:15,030

 

1797
00:58:15,030 --> 00:58:16,069

 

1798
00:58:16,069 --> 00:58:18,549

 

1799
00:58:18,549 --> 00:58:20,069

 

1800
00:58:20,069 --> 00:58:21,910

 

1801
00:58:21,910 --> 00:58:21,920

 

1802
00:58:21,920 --> 00:58:22,950


1803
00:58:22,950 --> 00:58:25,109

 

1804
00:58:25,109 --> 00:58:27,109

 

1805
00:58:27,109 --> 00:58:28,630

 

1806
00:58:28,630 --> 00:58:30,870

 

1807
00:58:30,870 --> 00:58:30,880

 

1808
00:58:30,880 --> 00:58:32,470


1809
00:58:32,470 --> 00:58:34,069

 

1810
00:58:34,069 --> 00:58:37,510

 

1811
00:58:37,510 --> 00:58:39,510

 

1812
00:58:39,510 --> 00:58:42,069

 

1813
00:58:42,069 --> 00:58:44,309

 

1814
00:58:44,309 --> 00:58:44,319

 

1815
00:58:44,319 --> 00:58:45,670


1816
00:58:45,670 --> 00:58:48,069

 

1817
00:58:48,069 --> 00:58:49,670

 

1818
00:58:49,670 --> 00:58:51,109

 

1819
00:58:51,109 --> 00:58:52,630

 

1820
00:58:52,630 --> 00:58:54,470

 

1821
00:58:54,470 --> 00:58:58,470

 

1822
00:58:58,470 --> 00:58:58,480

 

1823
00:58:58,480 --> 00:58:59,750


1824
00:58:59,750 --> 00:59:01,589

 

1825
00:59:01,589 --> 00:59:03,190

 

1826
00:59:03,190 --> 00:59:05,670

 

1827
00:59:05,670 --> 00:59:05,680

 

1828
00:59:05,680 --> 00:59:06,710


1829
00:59:06,710 --> 00:59:09,030

 

1830
00:59:09,030 --> 00:59:10,789

 

1831
00:59:10,789 --> 00:59:12,710

 

1832
00:59:12,710 --> 00:59:18,470

 

1833
00:59:18,470 --> 00:59:20,069

 

1834
00:59:20,069 --> 00:59:21,349

 

1835
00:59:21,349 --> 00:59:22,870

 

1836
00:59:22,870 --> 00:59:25,270

 

1837
00:59:25,270 --> 00:59:27,109

 

1838
00:59:27,109 --> 00:59:27,119

 

1839
00:59:27,119 --> 00:59:28,789


1840
00:59:28,789 --> 00:59:33,270

 

1841
00:59:33,270 --> 00:59:33,280

 

1842
00:59:33,280 --> 00:59:35,190


1843
00:59:35,190 --> 00:59:36,470

 

1844
00:59:36,470 --> 00:59:36,480

 

1845
00:59:36,480 --> 00:59:40,549


1846
00:59:40,549 --> 00:59:45,270

 

1847
00:59:45,270 --> 00:59:48,390

 

1848
00:59:48,390 --> 00:59:48,400

 

1849
00:59:48,400 --> 00:59:51,510


1850
00:59:51,510 --> 00:59:53,589

 

1851
00:59:53,589 --> 00:59:53,599

 

1852
00:59:53,599 --> 00:59:54,470


1853
00:59:54,470 --> 00:59:57,829

 

1854
00:59:57,829 --> 01:00:00,789

 

1855
01:00:00,789 --> 01:00:04,150

 

1856
01:00:04,150 --> 01:00:04,160

 

1857
01:00:04,160 --> 01:00:07,130


1858
01:00:07,130 --> 01:00:07,140

 

1859
01:00:07,140 --> 01:00:09,109


1860
01:00:09,109 --> 01:00:09,119

 

1861
01:00:09,119 --> 01:00:11,349


1862
01:00:11,349 --> 01:00:13,109

 

1863
01:00:13,109 --> 01:00:14,950

 

1864
01:00:14,950 --> 01:00:16,789

 

1865
01:00:16,789 --> 01:00:16,799

 

1866
01:00:16,799 --> 01:00:18,309


1867
01:00:18,309 --> 01:00:18,319

 

1868
01:00:18,319 --> 01:00:18,670


1869
01:00:18,670 --> 01:00:18,680

 

1870
01:00:18,680 --> 01:00:19,829


1871
01:00:19,829 --> 01:00:22,950

 

1872
01:00:22,950 --> 01:00:22,960

 

1873
01:00:22,960 --> 01:00:24,230


1874
01:00:24,230 --> 01:00:24,240

 

1875
01:00:24,240 --> 01:00:27,430


1876
01:00:27,430 --> 01:00:29,190

 

1877
01:00:29,190 --> 01:00:29,200

 

1878
01:00:29,200 --> 01:00:31,510


1879
01:00:31,510 --> 01:00:31,520

 

1880
01:00:31,520 --> 01:00:33,430


1881
01:00:33,430 --> 01:00:34,950

 

1882
01:00:34,950 --> 01:00:37,430

 

1883
01:00:37,430 --> 01:00:39,270

 

1884
01:00:39,270 --> 01:00:41,349

 

1885
01:00:41,349 --> 01:00:43,270

 

1886
01:00:43,270 --> 01:00:45,109

 

1887
01:00:45,109 --> 01:00:45,119

 

1888
01:00:45,119 --> 01:00:46,710


1889
01:00:46,710 --> 01:00:48,390

 

1890
01:00:48,390 --> 01:00:49,910

 

1891
01:00:49,910 --> 01:00:52,549

 

1892
01:00:52,549 --> 01:00:56,230

 

1893
01:00:56,230 --> 01:00:58,230

 

1894
01:00:58,230 --> 01:01:00,630

 

1895
01:01:00,630 --> 01:01:02,630

 

1896
01:01:02,630 --> 01:01:04,549

 

1897
01:01:04,549 --> 01:01:06,870

 

1898
01:01:06,870 --> 01:01:08,789

 

1899
01:01:08,789 --> 01:01:11,670

 

1900
01:01:11,670 --> 01:01:13,990

 

1901
01:01:13,990 --> 01:01:16,710

 

1902
01:01:16,710 --> 01:01:18,309

 

1903
01:01:18,309 --> 01:01:20,870

 

1904
01:01:20,870 --> 01:01:23,349

 

1905
01:01:23,349 --> 01:01:24,789

 

1906
01:01:24,789 --> 01:01:26,870

 

1907
01:01:26,870 --> 01:01:28,150

 

1908
01:01:28,150 --> 01:01:30,150

 

1909
01:01:30,150 --> 01:01:33,349

 

1910
01:01:33,349 --> 01:01:35,510

 

1911
01:01:35,510 --> 01:01:37,670

 

1912
01:01:37,670 --> 01:01:39,510

 

1913
01:01:39,510 --> 01:01:40,789

 

1914
01:01:40,789 --> 01:01:43,589

 

1915
01:01:43,589 --> 01:01:45,349

 

1916
01:01:45,349 --> 01:01:46,230

 

1917
01:01:46,230 --> 01:01:48,549

 

1918
01:01:48,549 --> 01:01:51,670

 

1919
01:01:51,670 --> 01:01:53,109

 

1920
01:01:53,109 --> 01:01:55,190

 

1921
01:01:55,190 --> 01:01:57,510

 

1922
01:01:57,510 --> 01:01:58,950

 

1923
01:01:58,950 --> 01:02:01,270

 

1924
01:02:01,270 --> 01:02:02,710

 

1925
01:02:02,710 --> 01:02:02,720

 

1926
01:02:02,720 --> 01:02:03,910


1927
01:02:03,910 --> 01:02:05,349

 

1928
01:02:05,349 --> 01:02:05,359

 

1929
01:02:05,359 --> 01:02:06,870


1930
01:02:06,870 --> 01:02:09,029

 

1931
01:02:09,029 --> 01:02:09,039

 

1932
01:02:09,039 --> 01:02:10,710


1933
01:02:10,710 --> 01:02:12,710

 

1934
01:02:12,710 --> 01:02:14,390

 

1935
01:02:14,390 --> 01:02:15,750

 

1936
01:02:15,750 --> 01:02:17,510

 

1937
01:02:17,510 --> 01:02:19,029

 

1938
01:02:19,029 --> 01:02:21,029

 

1939
01:02:21,029 --> 01:02:22,950

 

1940
01:02:22,950 --> 01:02:25,430

 

1941
01:02:25,430 --> 01:02:27,029

 

1942
01:02:27,029 --> 01:02:28,789

 

1943
01:02:28,789 --> 01:02:30,789

 

1944
01:02:30,789 --> 01:02:32,710

 

1945
01:02:32,710 --> 01:02:36,630

 

1946
01:02:36,630 --> 01:02:37,510

 

1947
01:02:37,510 --> 01:02:37,520

 

1948
01:02:37,520 --> 01:02:39,270


1949
01:02:39,270 --> 01:02:39,280

 

1950
01:02:39,280 --> 01:02:42,069


1951
01:02:42,069 --> 01:02:45,109

 

1952
01:02:45,109 --> 01:02:47,190

 

1953
01:02:47,190 --> 01:02:49,510

 

1954
01:02:49,510 --> 01:02:50,870

 

1955
01:02:50,870 --> 01:02:53,270

 

1956
01:02:53,270 --> 01:02:56,150

 

1957
01:02:56,150 --> 01:02:56,160

 

1958
01:02:56,160 --> 01:02:57,589


1959
01:02:57,589 --> 01:02:59,990

 

1960
01:02:59,990 --> 01:03:01,670

 

1961
01:03:01,670 --> 01:03:03,589

 

1962
01:03:03,589 --> 01:03:04,870

 

1963
01:03:04,870 --> 01:03:07,109

 

1964
01:03:07,109 --> 01:03:09,029

 

1965
01:03:09,029 --> 01:03:09,039

 

1966
01:03:09,039 --> 01:03:09,829


1967
01:03:09,829 --> 01:03:12,069

 

1968
01:03:12,069 --> 01:03:14,309

 

1969
01:03:14,309 --> 01:03:15,750

 

1970
01:03:15,750 --> 01:03:18,230

 

1971
01:03:18,230 --> 01:03:19,589

 

1972
01:03:19,589 --> 01:03:21,029

 

1973
01:03:21,029 --> 01:03:24,470

 

1974
01:03:24,470 --> 01:03:24,480

 

1975
01:03:24,480 --> 01:03:26,230


1976
01:03:26,230 --> 01:03:28,710

 

1977
01:03:28,710 --> 01:03:30,950

 

1978
01:03:30,950 --> 01:03:32,789

 

1979
01:03:32,789 --> 01:03:34,390

 

1980
01:03:34,390 --> 01:03:35,829

 

1981
01:03:35,829 --> 01:03:35,839

 

1982
01:03:35,839 --> 01:03:36,870


1983
01:03:36,870 --> 01:03:39,270

 

1984
01:03:39,270 --> 01:03:41,750

 

1985
01:03:41,750 --> 01:03:43,670

 

1986
01:03:43,670 --> 01:03:46,630

 

1987
01:03:46,630 --> 01:03:48,150

 

1988
01:03:48,150 --> 01:03:49,670

 

1989
01:03:49,670 --> 01:03:50,390

 

1990
01:03:50,390 --> 01:03:52,870

 

1991
01:03:52,870 --> 01:03:54,630

 

1992
01:03:54,630 --> 01:03:54,640

 

1993
01:03:54,640 --> 01:03:57,109


1994
01:03:57,109 --> 01:03:57,119

 

1995
01:03:57,119 --> 01:03:59,510


1996
01:03:59,510 --> 01:04:00,750

 

1997
01:04:00,750 --> 01:04:00,760

 

1998
01:04:00,760 --> 01:04:02,630


1999
01:04:02,630 --> 01:04:04,470

 

2000
01:04:04,470 --> 01:04:07,109

 

2001
01:04:07,109 --> 01:04:07,119

 

2002
01:04:07,119 --> 01:04:08,710


2003
01:04:08,710 --> 01:04:11,190

 

2004
01:04:11,190 --> 01:04:13,270

 

2005
01:04:13,270 --> 01:04:16,230

 

2006
01:04:16,230 --> 01:04:18,069

 

2007
01:04:18,069 --> 01:04:19,589

 

2008
01:04:19,589 --> 01:04:21,349

 

2009
01:04:21,349 --> 01:04:24,069

 

2010
01:04:24,069 --> 01:04:26,150

 

2011
01:04:26,150 --> 01:04:27,910

 

2012
01:04:27,910 --> 01:04:29,109

 

2013
01:04:29,109 --> 01:04:30,470

 

2014
01:04:30,470 --> 01:04:32,150

 

2015
01:04:32,150 --> 01:04:32,160

 

2016
01:04:32,160 --> 01:04:33,430


2017
01:04:33,430 --> 01:04:35,670

 

2018
01:04:35,670 --> 01:04:37,990

 

2019
01:04:37,990 --> 01:04:38,000

 

2020
01:04:38,000 --> 01:04:38,789


2021
01:04:38,789 --> 01:04:40,470

 

2022
01:04:40,470 --> 01:04:43,109

 

2023
01:04:43,109 --> 01:04:44,549

 

2024
01:04:44,549 --> 01:04:47,589

 

2025
01:04:47,589 --> 01:04:47,599

 

2026
01:04:47,599 --> 01:04:50,230


2027
01:04:50,230 --> 01:04:51,990

 

2028
01:04:51,990 --> 01:04:53,589

 

2029
01:04:53,589 --> 01:04:55,910

 

2030
01:04:55,910 --> 01:04:55,920

 

2031
01:04:55,920 --> 01:04:57,270


2032
01:04:57,270 --> 01:04:58,710

 

2033
01:04:58,710 --> 01:04:58,720

 

2034
01:04:58,720 --> 01:05:00,390


2035
01:05:00,390 --> 01:05:02,789

 

2036
01:05:02,789 --> 01:05:05,029

 

2037
01:05:05,029 --> 01:05:06,549

 

2038
01:05:06,549 --> 01:05:08,390

 

2039
01:05:08,390 --> 01:05:10,470

 

2040
01:05:10,470 --> 01:05:10,480

 

2041
01:05:10,480 --> 01:05:11,270


2042
01:05:11,270 --> 01:05:13,029

 

2043
01:05:13,029 --> 01:05:13,039

 

2044
01:05:13,039 --> 01:05:15,990


2045
01:05:15,990 --> 01:05:21,349

 

2046
01:05:21,349 --> 01:05:22,589

 

2047
01:05:22,589 --> 01:05:26,630

 

2048
01:05:26,630 --> 01:05:27,910

 

2049
01:05:27,910 --> 01:05:27,920

 

2050
01:05:27,920 --> 01:05:29,270


2051
01:05:29,270 --> 01:05:29,280

 

2052
01:05:29,280 --> 01:05:30,870


2053
01:05:30,870 --> 01:05:32,870

 

2054
01:05:32,870 --> 01:05:34,230

 

2055
01:05:34,230 --> 01:05:34,240

 

2056
01:05:34,240 --> 01:05:36,870


2057
01:05:36,870 --> 01:05:42,069

 

2058
01:05:42,069 --> 01:05:44,390

 

2059
01:05:44,390 --> 01:05:46,789

 

2060
01:05:46,789 --> 01:05:48,470

 

2061
01:05:48,470 --> 01:05:51,109

 

2062
01:05:51,109 --> 01:05:52,950

 

2063
01:05:52,950 --> 01:05:53,990

 

2064
01:05:53,990 --> 01:05:54,000

 

2065
01:05:54,000 --> 01:05:55,109


2066
01:05:55,109 --> 01:05:56,950

 

2067
01:05:56,950 --> 01:05:58,470

 

2068
01:05:58,470 --> 01:05:59,990

 

2069
01:05:59,990 --> 01:06:00,000

 

2070
01:06:00,000 --> 01:06:01,829


2071
01:06:01,829 --> 01:06:04,069

 

2072
01:06:04,069 --> 01:06:06,069

 

2073
01:06:06,069 --> 01:06:07,990

 

2074
01:06:07,990 --> 01:06:09,750

 

2075
01:06:09,750 --> 01:06:10,870

 

2076
01:06:10,870 --> 01:06:12,950

 

2077
01:06:12,950 --> 01:06:15,589

 

2078
01:06:15,589 --> 01:06:15,599

 

2079
01:06:15,599 --> 01:06:18,390


2080
01:06:18,390 --> 01:06:20,470

 

2081
01:06:20,470 --> 01:06:23,109

 

2082
01:06:23,109 --> 01:06:25,990

 

2083
01:06:25,990 --> 01:06:27,829

 

2084
01:06:27,829 --> 01:06:30,870

 

2085
01:06:30,870 --> 01:06:32,390

 

2086
01:06:32,390 --> 01:06:32,400

 

2087
01:06:32,400 --> 01:06:33,349


2088
01:06:33,349 --> 01:06:35,510

 

2089
01:06:35,510 --> 01:06:37,829

 

2090
01:06:37,829 --> 01:06:38,700

 

2091
01:06:38,700 --> 01:06:38,710

 

2092
01:06:38,710 --> 01:06:40,069


2093
01:06:40,069 --> 01:06:41,670

 

2094
01:06:41,670 --> 01:06:43,990

 

2095
01:06:43,990 --> 01:06:44,000

 

2096
01:06:44,000 --> 01:06:45,109


2097
01:06:45,109 --> 01:06:47,430

 

2098
01:06:47,430 --> 01:06:52,950

 

2099
01:06:52,950 --> 01:06:57,430

 

2100
01:06:57,430 --> 01:07:01,430

 

2101
01:07:01,430 --> 01:07:03,510

 

2102
01:07:03,510 --> 01:07:05,990

 

2103
01:07:05,990 --> 01:07:07,670

 

2104
01:07:07,670 --> 01:07:09,670

 

2105
01:07:09,670 --> 01:07:09,680

 

2106
01:07:09,680 --> 01:07:11,349


2107
01:07:11,349 --> 01:07:13,270

 

2108
01:07:13,270 --> 01:07:14,789

 

2109
01:07:14,789 --> 01:07:16,710

 

2110
01:07:16,710 --> 01:07:18,950

 

2111
01:07:18,950 --> 01:07:18,960

 

2112
01:07:18,960 --> 01:07:20,309


2113
01:07:20,309 --> 01:07:21,910

 

2114
01:07:21,910 --> 01:07:24,230

 

2115
01:07:24,230 --> 01:07:29,349

 

2116
01:07:29,349 --> 01:07:31,510

 

2117
01:07:31,510 --> 01:07:33,430

 

2118
01:07:33,430 --> 01:07:35,670

 

2119
01:07:35,670 --> 01:07:37,589

 

2120
01:07:37,589 --> 01:07:41,190

 

2121
01:07:41,190 --> 01:07:43,029

 

2122
01:07:43,029 --> 01:07:45,670

 

2123
01:07:45,670 --> 01:07:47,750

 

2124
01:07:47,750 --> 01:07:50,069

 

2125
01:07:50,069 --> 01:07:52,150

 

2126
01:07:52,150 --> 01:07:55,349

 

2127
01:07:55,349 --> 01:07:55,359

 

2128
01:07:55,359 --> 01:07:58,150


2129
01:07:58,150 --> 01:08:01,430

 

2130
01:08:01,430 --> 01:08:01,440

 

2131
01:08:01,440 --> 01:08:02,549


2132
01:08:02,549 --> 01:08:04,150

 

2133
01:08:04,150 --> 01:08:05,349

 

2134
01:08:05,349 --> 01:08:07,670

 

2135
01:08:07,670 --> 01:08:09,990

 

2136
01:08:09,990 --> 01:08:11,910

 

2137
01:08:11,910 --> 01:08:14,150

 

2138
01:08:14,150 --> 01:08:15,829

 

2139
01:08:15,829 --> 01:08:17,030

 

2140
01:08:17,030 --> 01:08:17,040

 

2141
01:08:17,040 --> 01:08:18,550


2142
01:08:18,550 --> 01:08:18,560

 

2143
01:08:18,560 --> 01:08:19,510


2144
01:08:19,510 --> 01:08:23,269

 

2145
01:08:23,269 --> 01:08:24,870

 

2146
01:08:24,870 --> 01:08:24,880

 

2147
01:08:24,880 --> 01:08:26,789


2148
01:08:26,789 --> 01:08:29,189

 

2149
01:08:29,189 --> 01:08:30,470

 

2150
01:08:30,470 --> 01:08:35,110

 

2151
01:08:35,110 --> 01:08:36,870

 

2152
01:08:36,870 --> 01:08:39,590

 

2153
01:08:39,590 --> 01:08:41,669

 

2154
01:08:41,669 --> 01:08:41,679

 

2155
01:08:41,679 --> 01:08:42,950


2156
01:08:42,950 --> 01:08:45,829

 

2157
01:08:45,829 --> 01:08:48,630

 

2158
01:08:48,630 --> 01:08:50,870

 

2159
01:08:50,870 --> 01:08:53,349

 

2160
01:08:53,349 --> 01:08:55,669

 

2161
01:08:55,669 --> 01:08:55,679

 

2162
01:08:55,679 --> 01:08:57,669


2163
01:08:57,669 --> 01:09:01,990

 

2164
01:09:01,990 --> 01:09:03,910

 

2165
01:09:03,910 --> 01:09:06,390

 

2166
01:09:06,390 --> 01:09:08,630

 

2167
01:09:08,630 --> 01:09:11,749

 

2168
01:09:11,749 --> 01:09:14,070

 

2169
01:09:14,070 --> 01:09:16,709

 

2170
01:09:16,709 --> 01:09:19,030

 

2171
01:09:19,030 --> 01:09:22,550

 

2172
01:09:22,550 --> 01:09:23,910

 

2173
01:09:23,910 --> 01:09:26,149

 

2174
01:09:26,149 --> 01:09:28,950

 

2175
01:09:28,950 --> 01:09:31,030

 

2176
01:09:31,030 --> 01:09:33,590

 

2177
01:09:33,590 --> 01:09:36,709

 

2178
01:09:36,709 --> 01:09:38,550

 

2179
01:09:38,550 --> 01:09:40,709

 

2180
01:09:40,709 --> 01:09:42,950

 

2181
01:09:42,950 --> 01:09:42,960

 

2182
01:09:42,960 --> 01:09:43,990


2183
01:09:43,990 --> 01:09:45,749

 

2184
01:09:45,749 --> 01:09:46,950

 

2185
01:09:46,950 --> 01:09:48,870

 

2186
01:09:48,870 --> 01:09:52,070

 

2187
01:09:52,070 --> 01:09:53,829

 

2188
01:09:53,829 --> 01:09:54,950

 

2189
01:09:54,950 --> 01:09:56,790

 

2190
01:09:56,790 --> 01:10:00,070

 

2191
01:10:00,070 --> 01:10:01,669

 

2192
01:10:01,669 --> 01:10:05,030

 

2193
01:10:05,030 --> 01:10:07,430

 

2194
01:10:07,430 --> 01:10:08,470

 

2195
01:10:08,470 --> 01:10:08,480

 

2196
01:10:08,480 --> 01:10:09,270


2197
01:10:09,270 --> 01:10:11,510

 

2198
01:10:11,510 --> 01:10:13,350

 

2199
01:10:13,350 --> 01:10:15,830

 

2200
01:10:15,830 --> 01:10:18,229

 

2201
01:10:18,229 --> 01:10:18,239

 

2202
01:10:18,239 --> 01:10:21,990


2203
01:10:21,990 --> 01:10:24,229

 

2204
01:10:24,229 --> 01:10:25,590

 

2205
01:10:25,590 --> 01:10:29,430

 

2206
01:10:29,430 --> 01:10:32,310

 

2207
01:10:32,310 --> 01:10:35,110

 

2208
01:10:35,110 --> 01:10:37,110

 

2209
01:10:37,110 --> 01:10:38,630

 

2210
01:10:38,630 --> 01:10:40,630

 

2211
01:10:40,630 --> 01:10:43,990

 

2212
01:10:43,990 --> 01:10:45,510

 

2213
01:10:45,510 --> 01:10:47,270

 

2214
01:10:47,270 --> 01:10:50,229

 

2215
01:10:50,229 --> 01:10:52,470

 

2216
01:10:52,470 --> 01:10:54,709

 

2217
01:10:54,709 --> 01:10:54,719

 

2218
01:10:54,719 --> 01:10:57,590


2219
01:10:57,590 --> 01:10:57,600

 

2220
01:10:57,600 --> 01:10:59,510


2221
01:10:59,510 --> 01:11:02,229

 

2222
01:11:02,229 --> 01:11:04,709

 

2223
01:11:04,709 --> 01:11:06,709

 

2224
01:11:06,709 --> 01:11:08,790

 

2225
01:11:08,790 --> 01:11:10,470

 

2226
01:11:10,470 --> 01:11:14,229

 

2227
01:11:14,229 --> 01:11:14,239

 

2228
01:11:14,239 --> 01:11:16,390


2229
01:11:16,390 --> 01:11:18,229

 

2230
01:11:18,229 --> 01:11:20,790

 

2231
01:11:20,790 --> 01:11:22,709

 

2232
01:11:22,709 --> 01:11:25,990

 

2233
01:11:25,990 --> 01:11:26,000

 

2234
01:11:26,000 --> 01:11:27,030


2235
01:11:27,030 --> 01:11:30,070

 

2236
01:11:30,070 --> 01:11:32,709

 

2237
01:11:32,709 --> 01:11:34,390

 

2238
01:11:34,390 --> 01:11:35,910

 

2239
01:11:35,910 --> 01:11:39,030

 

2240
01:11:39,030 --> 01:11:41,590

 

2241
01:11:41,590 --> 01:11:44,070

 

2242
01:11:44,070 --> 01:11:45,910

 

2243
01:11:45,910 --> 01:11:48,470

 

2244
01:11:48,470 --> 01:11:50,149

 

2245
01:11:50,149 --> 01:11:52,229

 

2246
01:11:52,229 --> 01:11:54,630

 

2247
01:11:54,630 --> 01:11:54,640

 

2248
01:11:54,640 --> 01:11:55,430


2249
01:11:55,430 --> 01:11:57,270

 

2250
01:11:57,270 --> 01:11:57,280

 

2251
01:11:57,280 --> 01:11:58,149


2252
01:11:58,149 --> 01:12:00,790

 

2253
01:12:00,790 --> 01:12:01,830

 

2254
01:12:01,830 --> 01:12:01,840

 

2255
01:12:01,840 --> 01:12:04,470


2256
01:12:04,470 --> 01:12:04,480

 

2257
01:12:04,480 --> 01:12:05,510


2258
01:12:05,510 --> 01:12:07,590

 

2259
01:12:07,590 --> 01:12:09,750

 

2260
01:12:09,750 --> 01:12:13,189

 

2261
01:12:13,189 --> 01:12:15,110

 

2262
01:12:15,110 --> 01:12:15,120

 

2263
01:12:15,120 --> 01:12:16,070


2264
01:12:16,070 --> 01:12:18,229

 

2265
01:12:18,229 --> 01:12:19,830

 

2266
01:12:19,830 --> 01:12:21,990

 

2267
01:12:21,990 --> 01:12:23,990

 

2268
01:12:23,990 --> 01:12:24,000

 

2269
01:12:24,000 --> 01:12:25,270


2270
01:12:25,270 --> 01:12:27,590

 

2271
01:12:27,590 --> 01:12:29,830

 

2272
01:12:29,830 --> 01:12:31,590

 

2273
01:12:31,590 --> 01:12:33,030

 

2274
01:12:33,030 --> 01:12:33,040

 

2275
01:12:33,040 --> 01:12:34,310


2276
01:12:34,310 --> 01:12:34,320

 

2277
01:12:34,320 --> 01:12:35,189


2278
01:12:35,189 --> 01:12:37,110

 

2279
01:12:37,110 --> 01:12:39,590

 

2280
01:12:39,590 --> 01:12:41,669

 

2281
01:12:41,669 --> 01:12:43,669

 

2282
01:12:43,669 --> 01:12:45,030

 

2283
01:12:45,030 --> 01:12:47,430

 

2284
01:12:47,430 --> 01:12:48,870

 

2285
01:12:48,870 --> 01:12:51,350

 

2286
01:12:51,350 --> 01:12:52,870

 

2287
01:12:52,870 --> 01:12:54,550

 

2288
01:12:54,550 --> 01:12:56,470

 

2289
01:12:56,470 --> 01:12:58,390

 

2290
01:12:58,390 --> 01:13:00,790

 

2291
01:13:00,790 --> 01:13:03,189

 

2292
01:13:03,189 --> 01:13:06,229

 

2293
01:13:06,229 --> 01:13:09,110

 

2294
01:13:09,110 --> 01:13:11,270

 

2295
01:13:11,270 --> 01:13:14,870

 

2296
01:13:14,870 --> 01:13:16,070

 

2297
01:13:16,070 --> 01:13:17,510

 

2298
01:13:17,510 --> 01:13:18,950

 

2299
01:13:18,950 --> 01:13:20,390

 

2300
01:13:20,390 --> 01:13:23,990

 

2301
01:13:23,990 --> 01:13:24,000

 

2302
01:13:24,000 --> 01:13:27,189


2303
01:13:27,189 --> 01:13:27,199

 

2304
01:13:27,199 --> 01:13:28,229


2305
01:13:28,229 --> 01:13:30,390

 

2306
01:13:30,390 --> 01:13:34,709

 

2307
01:13:34,709 --> 01:13:38,630

 

2308
01:13:38,630 --> 01:13:42,790

 

2309
01:13:42,790 --> 01:13:42,800

 

2310
01:13:42,800 --> 01:13:45,110


2311
01:13:45,110 --> 01:13:49,910

 

2312
01:13:49,910 --> 01:13:52,630

 

2313
01:13:52,630 --> 01:13:54,149

 

2314
01:13:54,149 --> 01:13:56,550

 

2315
01:13:56,550 --> 01:14:01,030

 

2316
01:14:01,030 --> 01:14:02,950

 

2317
01:14:02,950 --> 01:14:09,430

 

2318
01:14:09,430 --> 01:14:10,709

 

2319
01:14:10,709 --> 01:14:11,830

 

2320
01:14:11,830 --> 01:14:13,990

 

2321
01:14:13,990 --> 01:14:16,709

 

2322
01:14:16,709 --> 01:14:16,719

 

2323
01:14:16,719 --> 01:14:17,510


2324
01:14:17,510 --> 01:14:19,590

 

2325
01:14:19,590 --> 01:14:19,600

 

2326
01:14:19,600 --> 01:14:21,030


2327
01:14:21,030 --> 01:14:22,470

 

2328
01:14:22,470 --> 01:14:24,310

 

2329
01:14:24,310 --> 01:14:24,320

 

2330
01:14:24,320 --> 01:14:25,189


2331
01:14:25,189 --> 01:14:28,390

 

2332
01:14:28,390 --> 01:14:30,229

 

2333
01:14:30,229 --> 01:14:32,149

 

2334
01:14:32,149 --> 01:14:33,750

 

2335
01:14:33,750 --> 01:14:33,760

 

2336
01:14:33,760 --> 01:14:36,229


2337
01:14:36,229 --> 01:14:37,830

 

2338
01:14:37,830 --> 01:14:40,790

 

2339
01:14:40,790 --> 01:14:43,510

 

2340
01:14:43,510 --> 01:14:46,870

 

2341
01:14:46,870 --> 01:14:49,350

 

2342
01:14:49,350 --> 01:14:52,310

 

2343
01:14:52,310 --> 01:14:54,950

 

2344
01:14:54,950 --> 01:14:57,750

 

2345
01:14:57,750 --> 01:14:57,760

 

2346
01:14:57,760 --> 01:15:00,709


2347
01:15:00,709 --> 01:15:02,390

 

2348
01:15:02,390 --> 01:15:05,350

 

2349
01:15:05,350 --> 01:15:08,630

 

2350
01:15:08,630 --> 01:15:08,640

 

2351
01:15:08,640 --> 01:15:09,510


2352
01:15:09,510 --> 01:15:11,830

 

2353
01:15:11,830 --> 01:15:14,229

 

2354
01:15:14,229 --> 01:15:19,510

 

2355
01:15:19,510 --> 01:15:22,070

 

2356
01:15:22,070 --> 01:15:24,630

 

2357
01:15:24,630 --> 01:15:26,229

 

2358
01:15:26,229 --> 01:15:29,110

 

2359
01:15:29,110 --> 01:15:30,630

 

2360
01:15:30,630 --> 01:15:32,709

 

2361
01:15:32,709 --> 01:15:34,950

 

2362
01:15:34,950 --> 01:15:36,709

 

2363
01:15:36,709 --> 01:15:39,590

 

2364
01:15:39,590 --> 01:15:41,350

 

2365
01:15:41,350 --> 01:15:43,990

 

2366
01:15:43,990 --> 01:15:48,070

 

2367
01:15:48,070 --> 01:15:49,110

 

2368
01:15:49,110 --> 01:15:51,750

 

2369
01:15:51,750 --> 01:15:53,910

 

2370
01:15:53,910 --> 01:15:53,920

 

2371
01:15:53,920 --> 01:15:55,669


2372
01:15:55,669 --> 01:15:57,350

 

2373
01:15:57,350 --> 01:15:59,110

 

2374
01:15:59,110 --> 01:16:02,149

 

2375
01:16:02,149 --> 01:16:03,430

 

2376
01:16:03,430 --> 01:16:03,440

 

2377
01:16:03,440 --> 01:16:04,630


2378
01:16:04,630 --> 01:16:06,630

 

2379
01:16:06,630 --> 01:16:08,470

 

2380
01:16:08,470 --> 01:16:08,480

 

2381
01:16:08,480 --> 01:16:09,750


2382
01:16:09,750 --> 01:16:11,030

 

2383
01:16:11,030 --> 01:16:12,950

 

2384
01:16:12,950 --> 01:16:14,550

 

2385
01:16:14,550 --> 01:16:15,990

 

2386
01:16:15,990 --> 01:16:16,000

 

2387
01:16:16,000 --> 01:16:19,590


2388
01:16:19,590 --> 01:16:19,600

 

2389
01:16:19,600 --> 01:16:20,950


2390
01:16:20,950 --> 01:16:35,830

 

2391
01:16:35,830 --> 01:16:35,840

 

2392
01:16:35,840 --> 01:16:37,920