sol_20.aes

@compiler >= 4.2.0
include "List.aes"
contract Day20 =
  datatype tile = Path | Inner(int, int) | Outer(int, int)
  record prob = { start : int * int, end : int * int, maze : map(int * int, tile) }

  entrypoint solve_1() =
    let prob = prob()
    bfs([(prob.start, 0)], prob.end, prob.maze, {})

  function bfs(((x, y), d) :: xs, target, maze, visited) =
    if(target == (x, y)) d
    else
      let visited = visited{ [(x, y)] = () }
      switch(maze[(x, y)])
        Path => bfs'(x, y, d, xs, target, maze, visited)
        Inner(x1, y1) =>
          if(Map.member((x1, y1), visited))
            bfs'(x, y, d, xs, target, maze, visited)
          else
            bfs(xs ++ [((x1, y1), d + 1)], target, maze, visited)
        Outer(x1, y1) =>
          if(Map.member((x1, y1), visited))
            bfs'(x, y, d, xs, target, maze, visited)
          else
            bfs(xs ++ [((x1, y1), d + 1)], target, maze, visited)

  function bfs'(x, y, d, xs, target, maze, visited) =
    let qs = if(!Map.member((x + 1, y), visited) &&
                 Map.member((x + 1, y), maze)) [((x + 1, y), d + 1)] else []
    let qs = if(!Map.member((x - 1, y), visited) &&
                 Map.member((x - 1, y), maze)) ((x - 1, y), d + 1) :: qs else qs
    let qs = if(!Map.member((x, y + 1), visited) &&
                 Map.member((x, y + 1), maze)) ((x, y + 1), d + 1) :: qs else qs
    let qs = if(!Map.member((x, y - 1), visited) &&
                 Map.member((x, y - 1), maze)) ((x, y - 1), d + 1) :: qs else qs
    bfs(xs ++ qs, target, maze, visited)

  entrypoint solve_2() =
    let prob = prob()
    bfs2([((0, prob.start), 0)], (0, prob.end), prob.maze, {})

  function bfs2(((l, (x, y)), d) :: xs, target, maze, visited) =
    let p = (l, (x, y))
    if(target == p) d
    else
      let visited = visited{ [p] = () }
      switch(maze[(x, y)])
        Path => bfs2'(l, x, y, d, xs, target, maze, visited)
        Inner(x1, y1) =>
          if(l > 24 || Map.member((l + 1, (x1, y1)), visited))
            bfs2'(l, x, y, d, xs, target, maze, visited)
          else
            bfs2(xs ++ [((l + 1, (x1, y1)), d + 1)], target, maze, visited)
        Outer(x1, y1) =>
          if(l == 0 || Map.member((l - 1, (x1, y1)), visited))
            bfs2'(l, x, y, d, xs, target, maze, visited)
          else
            bfs2(xs ++ [((l - 1, (x1, y1)), d + 1)], target, maze, visited)

  function bfs2'(l, x, y, d, xs, target, maze, visited) =
    let qs = if(!Map.member((l, (x + 1, y)), visited) &&
                 Map.member((x + 1, y), maze)) [((l, (x + 1, y)), d + 1)] else []
    let qs = if(!Map.member((l, (x - 1, y)), visited) &&
                 Map.member((x - 1, y), maze)) ((l, (x - 1, y)), d + 1) :: qs else qs
    let qs = if(!Map.member((l, (x, y + 1)), visited) &&
                 Map.member((x, y + 1), maze)) ((l, (x, y + 1)), d + 1) :: qs else qs
    let qs = if(!Map.member((l, (x, y - 1)), visited) &&
                 Map.member((x, y - 1), maze)) ((l, (x, y - 1)), d + 1) :: qs else qs
    bfs2(xs ++ qs, target, maze, visited)

  function prob0() =
    { start = (9,2), end = (13,16),
      maze = {[(17,9)] = Path, [(11,3)] = Path, [(13,15)] = Path, [(16,3)] = Path,
              [(13,16)] = Path, [(4,10)] = Path, [(16,15)] = Path, [(17,11)] = Path,
              [(6,10)] = Inner(2,13), [(17,5)] = Path, [(9,2)] = Path, [(3,13)] = Path,
              [(10,3)] = Path, [(17,6)] = Path, [(11,13)] = Path, [(2,8)] = Outer(9,6),
              [(9,4)] = Path, [(17,15)] = Path, [(9,6)] = Inner(2,8), [(13,14)] = Path,
              [(17,10)] = Path, [(12,13)] = Path, [(17,14)] = Path, [(17,8)] = Path,
              [(14,15)] = Path, [(15,15)] = Path, [(9,3)] = Path, [(12,3)] = Path,
              [(17,12)] = Path, [(11,12)] = Inner(2,15), [(13,13)] = Path,
              [(5,10)] = Path, [(3,8)] = Path, [(17,13)] = Path, [(3,15)] = Path,
              [(17,7)] = Path, [(4,9)] = Path, [(2,13)] = Outer(6,10), [(9,5)] = Path,
              [(13,3)] = Path, [(17,4)] = Path, [(17,3)] = Path, [(4,8)] = Path,
              [(2,15)] = Outer(11,12), [(3,14)] = Path, [(15,3)] = Path, [(14,3)] = Path } }

  function prob() =
    { start = (2,83), end = (122,71),
      maze =
       {[(49,108)] = Path, [(59,17)] = Path, [(3,3)] = Path, [(15,35)] = Path,
        [(105,49)] = Path, [(89,17)] = Path, [(39,33)] = Path, [(85,19)] =
        Path, [(95,107)] = Path, [(24,3)] = Path, [(113,89)] = Path, [(15,13)]
        = Path, [(51,28)] = Path, [(117,93)] = Path, [(14,87)] = Path, [(8,27)]
        = Path, [(27,89)] = Path, [(9,77)] = Path, [(65,13)] = Path, [(113,37)]
        = Path, [(9,45)] = Path, [(93,15)] = Path, [(17,17)] = Path, [(121,6)]
        = Path, [(6,9)] = Path, [(9,31)] = Path, [(7,6)] = Path, [(113,99)] =
        Path, [(101,85)] = Path, [(113,50)] = Path, [(49,109)] = Path,
        [(120,101)] = Path, [(59,102)] = Path, [(41,112)] = Path, [(112,45)] =
        Path, [(4,103)] = Path, [(21,91)] = Path, [(119,67)] = Path, [(75,97)]
        = Path, [(33,95)] = Path, [(115,37)] = Path, [(25,82)] = Path,
        [(15,73)] = Path, [(98,101)] = Path, [(61,93)] = Path, [(118,15)] =
        Path, [(5,113)] = Path, [(58,13)] = Path, [(49,31)] = Path, [(89,123)]
        = Path, [(78,33)] = Path, [(77,97)] = Path, [(115,89)] = Path,
        [(57,29)] = Path, [(23,21)] = Path, [(73,7)] = Path, [(12,25)] = Path,
        [(110,15)] = Path, [(117,109)] = Path, [(81,112)] = Path, [(4,51)] =
        Path, [(114,61)] = Path, [(85,23)] = Path, [(11,91)] = Path, [(49,119)]
        = Path, [(81,4)] = Path, [(67,32)] = Path, [(5,39)] = Path, [(26,41)] =
        Path, [(33,91)] = Path, [(5,85)] = Path, [(85,4)] = Path, [(14,101)] =
        Path, [(103,78)] = Path, [(5,44)] = Path, [(48,5)] = Path, [(58,99)] =
        Path, [(98,65)] = Path, [(49,113)] = Path, [(93,121)] = Path, [(23,69)]
        = Path, [(14,41)] = Path, [(25,93)] = Path, [(82,3)] = Path, [(22,17)]
        = Path, [(12,53)] = Path, [(80,113)] = Path, [(121,123)] = Path,
        [(24,63)] = Path, [(117,67)] = Path, [(121,72)] = Path, [(107,5)] =
        Path, [(92,99)] = Path, [(9,9)] = Path, [(13,55)] = Path, [(33,69)] =
        Path, [(9,7)] = Path, [(91,63)] = Path, [(118,123)] = Path, [(93,77)] =
        Path, [(65,108)] = Path, [(113,83)] = Path, [(39,117)] = Path,
        [(99,57)] = Path, [(33,22)] = Path, [(111,5)] = Path, [(99,5)] = Path,
        [(115,60)] = Path, [(107,65)] = Path, [(82,31)] = Path, [(99,15)] =
        Path, [(115,81)] = Path, [(110,9)] = Path, [(89,112)] = Path, [(19,49)]
        = Path, [(59,109)] = Path, [(89,21)] = Path, [(17,112)] = Path,
        [(85,109)] = Path, [(18,21)] = Path, [(61,101)] = Path, [(26,97)] =
        Path, [(22,47)] = Path, [(25,122)] = Path, [(109,108)] = Path,
        [(113,25)] = Path, [(15,119)] = Path, [(88,93)] = Path, [(92,61)] =
        Path, [(57,9)] = Path, [(55,93)] = Path, [(13,91)] = Path, [(25,86)] =
        Path, [(17,67)] = Path, [(39,7)] = Path, [(80,3)] = Path, [(85,120)] =
        Path, [(40,13)] = Path, [(81,97)] = Path, [(29,101)] = Path, [(97,107)]
        = Path, [(67,31)] = Path, [(51,122)] = Path, [(117,54)] = Path,
        [(37,110)] = Path, [(99,62)] = Path, [(115,93)] = Path, [(6,77)] =
        Path, [(91,7)] = Path, [(43,20)] = Path, [(33,89)] = Path, [(13,74)] =
        Path, [(66,21)] = Path, [(118,51)] = Path, [(21,89)] = Path, [(19,9)] =
        Path, [(99,33)] = Path, [(10,91)] = Path, [(15,79)] = Path, [(27,120)]
        = Path, [(119,63)] = Path, [(109,90)] = Path, [(108,97)] = Path,
        [(94,19)] = Path, [(101,122)] = Path, [(3,95)] = Path, [(109,119)] =
        Path, [(114,87)] = Path, [(87,14)] = Path, [(16,11)] = Path, [(29,103)]
        = Path, [(116,107)] = Path, [(66,117)] = Path, [(95,63)] = Path,
        [(75,29)] = Path, [(15,86)] = Path, [(101,5)] = Path, [(72,101)] =
        Path, [(23,92)] = Path, [(19,108)] = Path, [(73,110)] = Path,
        [(111,111)] = Path, [(103,96)] = Path, [(102,117)] = Path, [(117,65)] =
        Path, [(84,113)] = Path, [(111,94)] = Path, [(121,102)] = Path,
        [(21,99)] = Path, [(121,45)] = Path, [(5,61)] = Path, [(39,32)] = Path,
        [(115,23)] = Path, [(32,9)] = Path, [(109,7)] = Path, [(43,111)] =
        Path, [(20,3)] = Path, [(27,61)] = Path, [(7,102)] = Path, [(4,81)] =
        Path, [(28,111)] = Path, [(45,25)] = Path, [(10,77)] = Path, [(92,17)]
        = Path, [(55,97)] = Path, [(85,26)] = Path, [(93,47)] = Path,
        [(113,96)] = Path, [(121,105)] = Path, [(91,52)] = Path, [(97,86)] =
        Path, [(53,31)] = Path, [(10,85)] = Path, [(95,122)] = Path, [(117,99)]
        = Path, [(76,99)] = Path, [(15,5)] = Path, [(103,43)] = Path, [(5,63)]
        = Path, [(5,93)] = Path, [(9,60)] = Path, [(67,29)] = Path, [(85,117)]
        = Path, [(76,115)] = Path, [(11,40)] = Path, [(5,122)] = Path,
        [(101,59)] = Path, [(59,16)] = Path, [(61,122)] = Path, [(105,3)] =
        Path, [(5,98)] = Path, [(31,117)] = Path, [(87,10)] = Path, [(2,45)] =
        Outer(83,92), [(31,50)] = Path, [(57,113)] = Path, [(92,103)] = Path,
        [(25,27)] = Path, [(52,95)] = Path, [(101,95)] = Path, [(87,114)] =
        Path, [(19,105)] = Path, [(11,75)] = Path, [(10,47)] = Path, [(108,73)]
        = Path, [(98,105)] = Path, [(59,123)] = Path, [(117,89)] = Path,
        [(93,95)] = Path, [(107,104)] = Path, [(39,28)] = Path, [(117,107)] =
        Path, [(77,22)] = Path, [(49,25)] = Path, [(103,11)] = Path, [(113,43)]
        = Path, [(41,97)] = Path, [(29,63)] = Path, [(69,105)] = Path, [(5,31)]
        = Path, [(28,67)] = Path, [(23,31)] = Path, [(95,118)] = Path,
        [(91,103)] = Path, [(95,114)] = Path, [(39,22)] = Path, [(67,14)] =
        Path, [(73,123)] = Path, [(87,99)] = Path, [(118,33)] = Path, [(35,94)]
        = Path, [(90,11)] = Path, [(7,76)] = Path, [(12,5)] = Path, [(103,74)]
        = Path, [(25,7)] = Path, [(113,57)] = Path, [(13,80)] = Path,
        [(38,111)] = Path, [(72,9)] = Path, [(112,91)] = Path, [(98,19)] =
        Path, [(19,111)] = Path, [(91,108)] = Path, [(104,101)] = Path,
        [(5,24)] = Path, [(53,25)] = Path, [(28,17)] = Path, [(83,123)] = Path,
        [(18,91)] = Path, [(51,113)] = Path, [(27,83)] = Path, [(15,9)] = Path,
        [(89,101)] = Path, [(51,95)] = Path, [(95,51)] = Path, [(20,55)] =
        Path, [(66,9)] = Path, [(63,119)] = Path, [(89,99)] = Path, [(45,121)]
        = Path, [(110,5)] = Path, [(38,15)] = Path, [(56,33)] = Path,
        [(119,73)] = Path, [(32,31)] = Path, [(120,65)] = Path, [(47,93)] =
        Path, [(21,109)] = Path, [(35,7)] = Path, [(98,37)] = Path, [(100,65)]
        = Path, [(44,23)] = Path, [(61,11)] = Path, [(104,43)] = Path,
        [(15,106)] = Path, [(68,107)] = Path, [(17,9)] = Path, [(103,87)] =
        Path, [(13,12)] = Path, [(52,11)] = Path, [(103,68)] = Path, [(7,107)]
        = Path, [(8,11)] = Path, [(93,27)] = Path, [(32,95)] = Path, [(71,19)]
        = Path, [(95,69)] = Path, [(107,31)] = Path, [(109,106)] = Path,
        [(113,94)] = Path, [(107,64)] = Path, [(41,31)] = Path, [(113,120)] =
        Path, [(10,7)] = Path, [(101,113)] = Path, [(113,116)] = Path,
        [(106,37)] = Path, [(8,91)] = Path, [(9,95)] = Path, [(31,119)] = Path,
        [(63,20)] = Path, [(11,69)] = Path, [(90,85)] = Inner(51,124),
        [(117,3)] = Path, [(110,87)] = Path, [(45,5)] = Path, [(69,116)] =
        Path, [(101,121)] = Path, [(21,77)] = Path, [(113,23)] = Path,
        [(23,38)] = Path, [(102,59)] = Path, [(69,6)] = Path, [(77,27)] = Path,
        [(121,77)] = Path, [(37,9)] = Path, [(47,22)] = Path, [(109,103)] =
        Path, [(41,98)] = Path, [(120,11)] = Path, [(79,25)] = Path, [(21,85)]
        = Path, [(11,11)] = Path, [(91,80)] = Path, [(83,103)] = Path,
        [(115,10)] = Path, [(87,109)] = Path, [(111,10)] = Path, [(55,121)] =
        Path, [(45,3)] = Path, [(23,70)] = Path, [(96,103)] = Path, [(37,27)] =
        Path, [(63,99)] = Path, [(11,84)] = Path, [(65,97)] = Path, [(48,13)] =
        Path, [(40,115)] = Path, [(108,11)] = Path, [(80,103)] = Path,
        [(115,95)] = Path, [(118,37)] = Path, [(30,81)] = Path, [(79,103)] =
        Path, [(29,90)] = Path, [(46,115)] = Path, [(56,3)] = Path, [(99,14)] =
        Path, [(113,91)] = Path, [(37,7)] = Path, [(101,26)] = Path,
        [(106,119)] = Path, [(59,101)] = Path, [(93,37)] = Path, [(6,3)] =
        Path, [(73,5)] = Path, [(21,44)] = Path, [(114,97)] = Path, [(28,27)] =
        Path, [(96,37)] = Path, [(33,81)] = Path, [(57,104)] = Path, [(7,115)]
        = Path, [(87,119)] = Path, [(75,111)] = Path, [(20,63)] = Path,
        [(121,83)] = Path, [(29,61)] = Path, [(64,3)] = Path, [(117,17)] =
        Path, [(29,33)] = Path, [(10,29)] = Path, [(121,39)] = Path, [(19,69)]
        = Path, [(41,10)] = Path, [(107,75)] = Path, [(121,27)] = Path,
        [(31,94)] = Path, [(61,96)] = Path, [(77,7)] = Path, [(19,30)] = Path,
        [(106,71)] = Path, [(31,14)] = Path, [(31,95)] = Path, [(2,77)] =
        Outer(90,59), [(57,5)] = Path, [(76,33)] = Path, [(118,63)] = Path,
        [(45,16)] = Path, [(91,17)] = Path, [(34,5)] = Path, [(9,24)] = Path,
        [(16,39)] = Path, [(103,97)] = Path, [(25,33)] = Path, [(8,29)] = Path,
        [(69,8)] = Path, [(84,121)] = Path, [(58,119)] = Path, [(23,59)] =
        Path, [(75,113)] = Path, [(85,3)] = Path, [(8,87)] = Path, [(9,61)] =
        Path, [(5,7)] = Path, [(3,102)] = Path, [(108,15)] = Path, [(49,3)] =
        Path, [(31,103)] = Path, [(27,73)] = Path, [(21,42)] = Path, [(3,94)] =
        Path, [(47,7)] = Path, [(12,67)] = Path, [(53,96)] = Path, [(69,20)] =
        Path, [(19,103)] = Path, [(39,107)] = Path, [(19,74)] = Path, [(75,96)]
        = Path, [(101,31)] = Path, [(47,113)] = Path, [(89,121)] = Path,
        [(99,4)] = Path, [(121,85)] = Path, [(25,5)] = Path, [(17,64)] = Path,
        [(22,19)] = Path, [(31,109)] = Path, [(39,30)] = Path, [(83,32)] =
        Path, [(55,11)] = Path, [(24,57)] = Path, [(40,121)] = Path, [(23,87)]
        = Path, [(14,71)] = Path, [(47,29)] = Path, [(105,94)] = Path,
        [(59,111)] = Path, [(96,51)] = Path, [(25,34)] = Path, [(90,9)] = Path,
        [(31,83)] = Path, [(47,101)] = Path, [(18,3)] = Path, [(17,87)] = Path,
        [(69,98)] = Path, [(31,7)] = Path, [(21,80)] = Path, [(119,5)] = Path,
        [(87,105)] = Path, [(25,91)] = Path, [(119,81)] = Path, [(91,79)] =
        Path, [(51,8)] = Path, [(63,102)] = Path, [(112,49)] = Path, [(92,9)] =
        Path, [(97,101)] = Path, [(121,80)] = Path, [(72,115)] = Path,
        [(49,105)] = Path, [(31,70)] = Path, [(91,77)] = Path, [(113,122)] =
        Path, [(116,15)] = Path, [(94,85)] = Path, [(93,60)] = Path, [(79,11)]
        = Path, [(54,33)] = Path, [(117,86)] = Path, [(7,63)] = Path,
        [(49,117)] = Path, [(107,68)] = Path, [(73,10)] = Path, [(74,105)] =
        Path, [(17,54)] = Path, [(13,6)] = Path, [(33,107)] = Path, [(19,44)] =
        Path, [(12,75)] = Path, [(63,19)] = Path, [(24,75)] = Path, [(55,12)] =
        Path, [(71,5)] = Path, [(49,22)] = Path, [(91,61)] = Path, [(61,116)] =
        Path, [(103,3)] = Path, [(61,10)] = Path, [(41,9)] = Path, [(33,68)] =
        Path, [(103,52)] = Path, [(12,55)] = Path, [(79,21)] = Path, [(121,40)]
        = Path, [(63,17)] = Path, [(56,25)] = Path, [(14,93)] = Path,
        [(103,19)] = Path, [(28,123)] = Path, [(65,3)] = Path, [(25,115)] =
        Path, [(19,77)] = Path, [(111,71)] = Path, [(7,75)] = Path, [(91,24)] =
        Path, [(33,106)] = Path, [(81,121)] = Path, [(18,45)] = Path,
        [(105,55)] = Path, [(113,114)] = Path, [(93,104)] = Path, [(114,33)] =
        Path, [(20,87)] = Path, [(96,57)] = Path, [(111,67)] = Path, [(93,76)]
        = Path, [(81,23)] = Path, [(83,3)] = Path, [(119,87)] = Path, [(25,79)]
        = Path, [(5,108)] = Path, [(89,108)] = Path, [(102,91)] = Path,
        [(39,27)] = Path, [(11,55)] = Path, [(9,69)] = Path, [(35,5)] = Path,
        [(21,119)] = Path, [(105,47)] = Path, [(101,109)] = Path, [(4,61)] =
        Path, [(9,22)] = Path, [(55,34)] = Inner(61,124), [(17,61)] = Path,
        [(107,92)] = Path, [(23,47)] = Path, [(11,123)] = Path, [(77,95)] =
        Path, [(31,82)] = Path, [(31,33)] = Path, [(113,93)] = Path, [(69,29)]
        = Path, [(103,99)] = Path, [(85,118)] = Path, [(107,71)] = Path,
        [(22,119)] = Path, [(110,91)] = Path, [(120,117)] = Path, [(93,71)] =
        Path, [(117,113)] = Path, [(41,27)] = Path, [(103,63)] = Path,
        [(29,25)] = Path, [(110,117)] = Path, [(7,43)] = Path, [(105,52)] =
        Path, [(20,33)] = Path, [(29,94)] = Path, [(102,61)] = Path, [(67,120)]
        = Path, [(121,14)] = Path, [(29,73)] = Path, [(116,63)] = Path,
        [(63,11)] = Path, [(11,89)] = Path, [(17,33)] = Path, [(83,92)] =
        Inner(2,45), [(120,99)] = Path, [(103,65)] = Path, [(17,37)] = Path,
        [(14,61)] = Path, [(91,118)] = Path, [(103,59)] = Path, [(21,110)] =
        Path, [(105,45)] = Path, [(98,87)] = Path, [(40,97)] = Path, [(99,35)]
        = Path, [(115,33)] = Path, [(12,71)] = Path, [(119,91)] = Path,
        [(15,23)] = Path, [(41,119)] = Path, [(21,60)] = Path, [(67,24)] =
        Path, [(65,93)] = Path, [(27,39)] = Path, [(101,99)] = Path, [(100,99)]
        = Path, [(38,115)] = Path, [(67,7)] = Path, [(51,101)] = Path,
        [(11,71)] = Path, [(27,7)] = Path, [(16,19)] = Path, [(105,99)] = Path,
        [(47,12)] = Path, [(48,17)] = Path, [(106,31)] = Path, [(106,123)] =
        Path, [(29,95)] = Path, [(19,55)] = Path, [(117,19)] = Path,
        [(109,110)] = Path, [(11,3)] = Path, [(111,9)] = Path, [(5,36)] = Path,
        [(109,13)] = Path, [(95,23)] = Path, [(38,95)] = Path, [(104,105)] =
        Path, [(93,103)] = Path, [(9,113)] = Path, [(89,9)] = Path, [(3,59)] =
        Path, [(91,34)] = Path, [(33,99)] = Path, [(3,34)] = Path, [(87,6)] =
        Path, [(13,121)] = Path, [(5,106)] = Path, [(120,79)] = Path, [(27,99)]
        = Path, [(119,51)] = Path, [(99,84)] = Path, [(32,111)] = Path,
        [(25,121)] = Path, [(109,54)] = Path, [(51,109)] = Path, [(5,71)] =
        Path, [(60,97)] = Path, [(85,105)] = Path, [(53,113)] = Path, [(43,25)]
        = Path, [(43,21)] = Path, [(109,83)] = Path, [(96,109)] = Path,
        [(54,9)] = Path, [(55,117)] = Path, [(56,109)] = Path, [(11,15)] =
        Path, [(114,123)] = Path, [(103,4)] = Path, [(100,89)] = Path,
        [(91,22)] = Path, [(68,105)] = Path, [(33,52)] = Path, [(11,67)] =
        Path, [(33,33)] = Path, [(65,7)] = Path, [(111,74)] = Path, [(115,20)]
        = Path, [(39,102)] = Path, [(97,73)] = Path, [(81,9)] = Path, [(27,81)]
        = Path, [(31,38)] = Path, [(22,53)] = Path, [(53,93)] = Path, [(13,15)]
        = Path, [(89,31)] = Path, [(104,89)] = Path, [(57,32)] = Path,
        [(77,117)] = Path, [(31,13)] = Path, [(117,32)] = Path, [(36,95)] =
        Path, [(8,9)] = Path, [(69,18)] = Path, [(34,71)] = Inner(122,61),
        [(36,15)] = Path, [(7,45)] = Path, [(92,115)] = Path, [(103,56)] =
        Path, [(21,90)] = Path, [(57,95)] = Path, [(63,107)] = Path, [(33,71)]
        = Path, [(39,97)] = Path, [(48,107)] = Path, [(17,75)] = Path,
        [(93,88)] = Path, [(29,121)] = Path, [(79,3)] = Path, [(95,53)] = Path,
        [(75,27)] = Path, [(71,30)] = Path, [(100,87)] = Path, [(25,15)] =
        Path, [(111,11)] = Path, [(98,73)] = Path, [(101,93)] = Path,
        [(109,41)] = Path, [(115,25)] = Path, [(117,31)] = Path, [(34,75)] =
        Inner(43,2), [(96,13)] = Path, [(17,84)] = Path, [(81,31)] = Path,
        [(5,107)] = Path, [(43,15)] = Path, [(3,23)] = Path, [(55,98)] = Path,
        [(22,73)] = Path, [(102,13)] = Path, [(103,28)] = Path, [(5,96)] =
        Path, [(54,111)] = Path, [(101,11)] = Path, [(49,7)] = Path, [(51,24)]
        = Path, [(107,25)] = Path, [(21,78)] = Path, [(109,45)] = Path,
        [(113,80)] = Path, [(59,31)] = Path, [(99,87)] = Path, [(3,109)] =
        Path, [(87,16)] = Path, [(3,119)] = Path, [(93,100)] = Path, [(43,107)]
        = Path, [(9,74)] = Path, [(79,28)] = Path, [(81,119)] = Path, [(61,25)]
        = Path, [(121,75)] = Path, [(105,15)] = Path, [(112,97)] = Path,
        [(93,69)] = Path, [(29,105)] = Path, [(9,15)] = Path, [(116,111)] =
        Path, [(116,105)] = Path, [(71,26)] = Path, [(59,3)] = Path, [(13,49)]
        = Path, [(23,71)] = Path, [(61,18)] = Path, [(101,45)] = Path,
        [(119,111)] = Path, [(41,26)] = Path, [(72,15)] = Path, [(83,25)] =
        Path, [(100,55)] = Path, [(65,5)] = Path, [(109,117)] = Path,
        [(105,19)] = Path, [(115,68)] = Path, [(28,107)] = Path, [(42,117)] =
        Path, [(53,111)] = Path, [(10,55)] = Path, [(4,15)] = Path, [(93,67)] =
        Path, [(7,57)] = Path, [(29,46)] = Path, [(71,34)] = Inner(47,2),
        [(117,21)] = Path, [(28,41)] = Path, [(94,27)] = Path, [(3,112)] =
        Path, [(8,43)] = Path, [(94,53)] = Path, [(13,45)] = Path, [(117,79)] =
        Path, [(113,59)] = Path, [(68,11)] = Path, [(42,115)] = Path,
        [(111,89)] = Path, [(31,4)] = Path, [(41,15)] = Path, [(17,79)] = Path,
        [(18,119)] = Path, [(87,24)] = Path, [(113,49)] = Path, [(47,25)] =
        Path, [(25,4)] = Path, [(97,59)] = Path, [(68,7)] = Path, [(35,13)] =
        Path, [(5,77)] = Path, [(105,23)] = Path, [(83,111)] = Path, [(99,76)]
        = Path, [(61,104)] = Path, [(13,114)] = Path, [(61,20)] = Path,
        [(109,62)] = Path, [(3,18)] = Path, [(26,27)] = Path, [(27,9)] = Path,
        [(17,90)] = Path, [(75,15)] = Path, [(95,7)] = Path, [(100,27)] = Path,
        [(41,117)] = Path, [(66,27)] = Path, [(29,39)] = Path, [(69,95)] =
        Path, [(48,121)] = Path, [(101,43)] = Path, [(110,13)] = Path,
        [(13,82)] = Path, [(55,5)] = Path, [(80,15)] = Path, [(11,97)] = Path,
        [(122,47)] = Outer(90,57), [(41,115)] = Path, [(37,18)] = Path,
        [(30,101)] = Path, [(57,4)] = Path, [(117,84)] = Path, [(31,46)] =
        Path, [(21,50)] = Path, [(16,3)] = Path, [(15,99)] = Path, [(45,123)] =
        Path, [(55,123)] = Path, [(90,67)] = Inner(2,49), [(96,111)] = Path,
        [(97,32)] = Path, [(41,92)] = Inner(2,79), [(55,113)] = Path, [(97,22)]
        = Path, [(91,88)] = Path, [(113,38)] = Path, [(27,63)] = Path,
        [(89,93)] = Path, [(94,49)] = Path, [(17,105)] = Path, [(17,26)] =
        Path, [(117,92)] = Path, [(109,46)] = Path, [(106,33)] = Path,
        [(49,115)] = Path, [(13,28)] = Path, [(121,73)] = Path, [(11,9)] =
        Path, [(33,44)] = Path, [(41,3)] = Path, [(88,121)] = Path, [(61,17)] =
        Path, [(55,104)] = Path, [(83,21)] = Path, [(115,117)] = Path,
        [(15,77)] = Path, [(19,4)] = Path, [(27,44)] = Path, [(97,15)] = Path,
        [(99,119)] = Path, [(52,33)] = Path, [(111,51)] = Path, [(31,106)] =
        Path, [(45,23)] = Path, [(59,105)] = Path, [(2,59)] = Outer(90,45),
        [(47,27)] = Path, [(92,49)] = Path, [(33,41)] = Path, [(104,99)] =
        Path, [(46,27)] = Path, [(87,113)] = Path, [(113,31)] = Path,
        [(109,27)] = Path, [(40,25)] = Path, [(61,112)] = Path, [(121,110)] =
        Path, [(26,29)] = Path, [(73,118)] = Path, [(93,80)] = Path, [(17,27)]
        = Path, [(103,107)] = Path, [(76,107)] = Path, [(57,25)] = Path,
        [(25,47)] = Path, [(25,12)] = Path, [(13,22)] = Path, [(43,112)] =
        Path, [(101,63)] = Path, [(4,13)] = Path, [(29,79)] = Path, [(35,27)] =
        Path, [(13,16)] = Path, [(33,120)] = Path, [(84,97)] = Path, [(111,77)]
        = Path, [(101,36)] = Path, [(102,55)] = Path, [(3,45)] = Path,
        [(109,107)] = Path, [(121,114)] = Path, [(37,104)] = Path, [(95,56)] =
        Path, [(29,118)] = Path, [(17,51)] = Path, [(20,101)] = Path, [(3,12)]
        = Path, [(77,115)] = Path, [(94,63)] = Path, [(19,121)] = Path,
        [(105,71)] = Path, [(21,97)] = Path, [(99,122)] = Path, [(81,19)] =
        Path, [(118,95)] = Path, [(79,20)] = Path, [(121,99)] = Path,
        [(59,113)] = Path, [(106,13)] = Path, [(27,24)] = Path, [(19,123)] =
        Path, [(68,29)] = Path, [(97,122)] = Path, [(93,22)] = Path, [(25,103)]
        = Path, [(3,101)] = Path, [(16,97)] = Path, [(19,83)] = Path,
        [(88,115)] = Path, [(67,5)] = Path, [(71,13)] = Path, [(100,13)] =
        Path, [(99,111)] = Path, [(111,65)] = Path, [(97,49)] = Path, [(43,26)]
        = Path, [(121,67)] = Path, [(13,50)] = Path, [(97,26)] = Path,
        [(87,117)] = Path, [(26,23)] = Path, [(75,13)] = Path, [(119,57)] =
        Path, [(84,25)] = Path, [(43,108)] = Path, [(99,55)] = Path, [(111,13)]
        = Path, [(121,41)] = Path, [(25,62)] = Path, [(15,113)] = Path,
        [(89,5)] = Path, [(19,86)] = Path, [(97,89)] = Path, [(23,13)] = Path,
        [(43,102)] = Path, [(41,5)] = Path, [(8,25)] = Path, [(31,123)] = Path,
        [(106,113)] = Path, [(25,51)] = Path, [(99,105)] = Path, [(28,93)] =
        Path, [(93,31)] = Path, [(117,9)] = Path, [(81,113)] = Path, [(91,36)]
        = Path, [(37,25)] = Path, [(111,113)] = Path, [(3,20)] = Path,
        [(98,95)] = Path, [(49,28)] = Path, [(51,107)] = Path, [(41,94)] =
        Path, [(15,104)] = Path, [(3,61)] = Path, [(92,47)] = Path, [(95,85)] =
        Path, [(14,73)] = Path, [(11,8)] = Path, [(23,19)] = Path, [(79,118)] =
        Path, [(122,81)] = Outer(90,39), [(97,96)] = Path, [(90,95)] = Path,
        [(27,57)] = Path, [(61,28)] = Path, [(15,38)] = Path, [(15,68)] = Path,
        [(27,43)] = Path, [(95,95)] = Path, [(84,103)] = Path, [(45,112)] =
        Path, [(112,53)] = Path, [(75,17)] = Path, [(96,67)] = Path, [(5,104)]
        = Path, [(15,21)] = Path, [(117,76)] = Path, [(16,15)] = Path,
        [(25,56)] = Path, [(5,121)] = Path, [(25,75)] = Path, [(3,96)] = Path,
        [(97,115)] = Path, [(41,33)] = Path, [(17,11)] = Path, [(35,95)] =
        Path, [(103,40)] = Path, [(113,81)] = Path, [(21,31)] = Path,
        [(121,61)] = Path, [(17,29)] = Path, [(103,103)] = Path, [(37,12)] =
        Path, [(17,49)] = Path, [(118,101)] = Path, [(94,81)] = Path,
        [(103,44)] = Path, [(97,11)] = Path, [(27,123)] = Path, [(9,93)] =
        Path, [(118,5)] = Path, [(43,6)] = Path, [(66,95)] = Path, [(30,115)] =
        Path, [(25,54)] = Path, [(121,57)] = Path, [(29,29)] = Path, [(87,17)]
        = Path, [(10,111)] = Path, [(117,119)] = Path, [(66,121)] = Path,
        [(11,33)] = Path, [(16,53)] = Path, [(115,112)] = Path, [(9,17)] =
        Path, [(11,23)] = Path, [(110,99)] = Path, [(48,25)] = Path, [(21,83)]
        = Path, [(26,33)] = Path, [(29,51)] = Path, [(5,53)] = Path, [(2,79)] =
        Outer(41,92), [(8,41)] = Path, [(119,28)] = Path, [(120,41)] = Path,
        [(23,9)] = Path, [(119,29)] = Path, [(113,101)] = Path, [(115,78)] =
        Path, [(101,40)] = Path, [(39,119)] = Path, [(93,109)] = Path,
        [(112,41)] = Path, [(49,97)] = Path, [(73,24)] = Path, [(111,80)] =
        Path, [(10,89)] = Path, [(111,83)] = Path, [(21,53)] = Path, [(32,73)]
        = Path, [(79,116)] = Path, [(117,82)] = Path, [(95,89)] = Path,
        [(89,3)] = Path, [(121,7)] = Path, [(107,79)] = Path, [(25,11)] = Path,
        [(33,82)] = Path, [(43,116)] = Path, [(103,113)] = Path, [(13,66)] =
        Path, [(53,92)] = Inner(63,2), [(3,83)] = Path, [(35,120)] = Path,
        [(55,6)] = Path, [(7,119)] = Path, [(112,17)] = Path, [(33,105)] =
        Path, [(13,90)] = Path, [(45,116)] = Path, [(102,51)] = Path,
        [(110,63)] = Path, [(105,61)] = Path, [(113,95)] = Path, [(41,118)] =
        Path, [(87,20)] = Path, [(114,35)] = Path, [(119,48)] = Path, [(33,13)]
        = Path, [(45,101)] = Path, [(105,103)] = Path, [(109,8)] = Path,
        [(116,37)] = Path, [(6,87)] = Path, [(3,88)] = Path, [(57,106)] = Path,
        [(102,115)] = Path, [(118,99)] = Path, [(80,105)] = Path, [(11,46)] =
        Path, [(37,103)] = Path, [(7,25)] = Path, [(118,61)] = Path, [(69,103)]
        = Path, [(41,108)] = Path, [(93,119)] = Path, [(21,30)] = Path,
        [(95,11)] = Path, [(34,105)] = Path, [(7,9)] = Path, [(109,97)] = Path,
        [(32,119)] = Path, [(51,93)] = Path, [(34,9)] = Path, [(17,107)] =
        Path, [(20,11)] = Path, [(7,33)] = Path, [(83,15)] = Path, [(99,110)] =
        Path, [(9,32)] = Path, [(88,19)] = Path, [(23,68)] = Path, [(15,117)] =
        Path, [(32,5)] = Path, [(32,97)] = Path, [(27,121)] = Path, [(118,109)]
        = Path, [(8,69)] = Path, [(73,117)] = Path, [(9,18)] = Path, [(6,45)] =
        Path, [(25,104)] = Path, [(12,57)] = Path, [(39,99)] = Path, [(89,4)] =
        Path, [(33,63)] = Path, [(27,90)] = Path, [(56,111)] = Path, [(105,67)]
        = Path, [(109,68)] = Path, [(107,52)] = Path, [(103,38)] = Path,
        [(5,100)] = Path, [(33,61)] = Path, [(119,64)] = Path, [(65,110)] =
        Path, [(76,101)] = Path, [(15,75)] = Path, [(108,75)] = Path,
        [(93,113)] = Path, [(26,49)] = Path, [(95,58)] = Path, [(55,122)] =
        Path, [(109,31)] = Path, [(86,115)] = Path, [(3,85)] = Path, [(117,6)]
        = Path, [(117,4)] = Path, [(67,119)] = Path, [(51,30)] = Path,
        [(104,67)] = Path, [(106,59)] = Path, [(63,14)] = Path, [(109,26)] =
        Path, [(21,61)] = Path, [(85,2)] = Outer(43,34), [(96,17)] = Path,
        [(15,57)] = Path, [(26,11)] = Path, [(115,67)] = Path, [(77,13)] =
        Path, [(20,69)] = Path, [(101,123)] = Path, [(5,79)] = Path, [(107,27)]
        = Path, [(98,99)] = Path, [(96,101)] = Path, [(85,16)] = Path,
        [(41,105)] = Path, [(97,55)] = Path, [(82,113)] = Path, [(43,118)] =
        Path, [(83,106)] = Path, [(39,111)] = Path, [(67,104)] = Path,
        [(27,40)] = Path, [(66,97)] = Path, [(33,121)] = Path, [(63,115)] =
        Path, [(52,121)] = Path, [(121,118)] = Path, [(107,20)] = Path,
        [(70,109)] = Path, [(21,55)] = Path, [(91,20)] = Path, [(32,33)] =
        Path, [(57,20)] = Path, [(57,105)] = Path, [(29,19)] = Path, [(121,56)]
        = Path, [(117,59)] = Path, [(84,109)] = Path, [(95,109)] = Path,
        [(91,96)] = Path, [(76,103)] = Path, [(111,91)] = Path, [(96,33)] =
        Path, [(99,41)] = Path, [(101,120)] = Path, [(112,113)] = Path,
        [(37,29)] = Path, [(30,9)] = Path, [(111,27)] = Path, [(81,33)] = Path,
        [(63,23)] = Path, [(10,83)] = Path, [(43,5)] = Path, [(23,57)] = Path,
        [(4,73)] = Path, [(75,105)] = Path, [(108,31)] = Path, [(96,65)] =
        Path, [(102,123)] = Path, [(118,117)] = Path, [(107,113)] = Path,
        [(97,77)] = Path, [(84,119)] = Path, [(45,117)] = Path, [(19,98)] =
        Path, [(99,44)] = Path, [(118,57)] = Path, [(69,21)] = Path, [(115,72)]
        = Path, [(24,53)] = Path, [(108,83)] = Path, [(13,85)] = Path,
        [(97,76)] = Path, [(3,106)] = Path, [(61,103)] = Path, [(81,109)] =
        Path, [(91,120)] = Path, [(56,29)] = Path, [(17,62)] = Path, [(3,90)] =
        Path, [(113,104)] = Path, [(116,31)] = Path, [(81,27)] = Path,
        [(63,97)] = Path, [(121,28)] = Path, [(63,111)] = Path, [(35,115)] =
        Path, [(78,95)] = Path, [(115,121)] = Path, [(60,19)] = Path,
        [(103,45)] = Path, [(75,25)] = Path, [(113,84)] = Path, [(15,7)] =
        Path, [(95,75)] = Path, [(29,111)] = Path, [(29,62)] = Path, [(7,48)] =
        Path, [(72,107)] = Path, [(89,29)] = Path, [(14,79)] = Path, [(83,94)]
        = Path, [(85,10)] = Path, [(67,110)] = Path, [(55,119)] = Path,
        [(97,84)] = Path, [(93,54)] = Path, [(67,95)] = Path, [(32,25)] = Path,
        [(70,97)] = Path, [(7,117)] = Path, [(119,75)] = Path, [(21,73)] =
        Path, [(12,91)] = Path, [(107,91)] = Path, [(29,55)] = Path, [(27,118)]
        = Path, [(15,95)] = Path, [(70,95)] = Path, [(105,86)] = Path,
        [(70,117)] = Path, [(99,21)] = Path, [(17,5)] = Path, [(23,17)] = Path,
        [(81,17)] = Path, [(94,109)] = Path, [(69,123)] = Path, [(25,49)] =
        Path, [(113,87)] = Path, [(93,17)] = Path, [(86,103)] = Path, [(13,11)]
        = Path, [(110,59)] = Path, [(99,69)] = Path, [(110,103)] = Path,
        [(65,10)] = Path, [(45,7)] = Path, [(14,105)] = Path, [(63,110)] =
        Path, [(59,15)] = Path, [(101,24)] = Path, [(26,79)] = Path, [(15,53)]
        = Path, [(79,115)] = Path, [(87,107)] = Path, [(33,34)] = Path,
        [(49,101)] = Path, [(3,28)] = Path, [(45,115)] = Path, [(99,3)] = Path,
        [(33,5)] = Path, [(25,69)] = Path, [(80,97)] = Path, [(16,31)] = Path,
        [(111,61)] = Path, [(78,27)] = Path, [(5,119)] = Path, [(44,33)] =
        Path, [(117,56)] = Path, [(111,115)] = Path, [(3,44)] = Path, [(11,27)]
        = Path, [(85,101)] = Path, [(67,99)] = Path, [(19,58)] = Path,
        [(101,69)] = Path, [(39,113)] = Path, [(65,95)] = Path, [(77,5)] =
        Path, [(83,97)] = Path, [(109,71)] = Path, [(24,29)] = Path, [(27,23)]
        = Path, [(38,105)] = Path, [(69,17)] = Path, [(9,87)] = Path, [(69,24)]
        = Path, [(49,26)] = Path, [(14,123)] = Path, [(21,65)] = Path, [(93,8)]
        = Path, [(30,49)] = Path, [(107,120)] = Path, [(23,82)] = Path,
        [(113,11)] = Path, [(43,97)] = Path, [(61,111)] = Path, [(65,104)] =
        Path, [(33,78)] = Path, [(77,17)] = Path, [(113,115)] = Path, [(119,3)]
        = Path, [(15,59)] = Path, [(95,117)] = Path, [(105,111)] = Path,
        [(91,70)] = Path, [(22,87)] = Path, [(13,70)] = Path, [(95,9)] = Path,
        [(97,51)] = Path, [(25,45)] = Path, [(23,111)] = Path, [(27,38)] =
        Path, [(93,89)] = Path, [(11,83)] = Path, [(87,110)] = Path, [(115,15)]
        = Path, [(3,116)] = Path, [(105,89)] = Path, [(31,116)] = Path,
        [(21,105)] = Path, [(76,15)] = Path, [(27,59)] = Path, [(103,18)] =
        Path, [(39,3)] = Path, [(20,95)] = Path, [(91,45)] = Path, [(13,60)] =
        Path, [(26,9)] = Path, [(9,119)] = Path, [(91,105)] = Path, [(117,49)]
        = Path, [(13,104)] = Path, [(86,119)] = Path, [(61,107)] = Path,
        [(111,41)] = Path, [(45,103)] = Path, [(67,18)] = Path, [(19,65)] =
        Path, [(29,54)] = Path, [(116,89)] = Path, [(13,86)] = Path, [(27,117)]
        = Path, [(115,5)] = Path, [(17,52)] = Path, [(93,5)] = Path, [(19,100)]
        = Path, [(43,113)] = Path, [(9,122)] = Path, [(108,23)] = Path,
        [(37,120)] = Path, [(99,68)] = Path, [(95,103)] = Path, [(24,25)] =
        Path, [(105,63)] = Path, [(92,105)] = Path, [(39,121)] = Path, [(81,5)]
        = Path, [(87,25)] = Path, [(111,32)] = Path, [(62,119)] = Path,
        [(97,91)] = Path, [(101,6)] = Path, [(23,79)] = Path, [(121,51)] =
        Path, [(39,19)] = Path, [(115,61)] = Path, [(91,13)] = Path, [(9,78)] =
        Path, [(25,83)] = Path, [(121,22)] = Path, [(65,102)] = Path, [(86,97)]
        = Path, [(30,51)] = Path, [(121,49)] = Path, [(11,119)] = Path,
        [(59,7)] = Path, [(97,10)] = Path, [(37,109)] = Path, [(103,9)] = Path,
        [(93,12)] = Path, [(21,63)] = Path, [(6,65)] = Path, [(39,103)] = Path,
        [(18,87)] = Path, [(117,61)] = Path, [(77,23)] = Path, [(54,97)] =
        Path, [(33,77)] = Path, [(43,12)] = Path, [(109,20)] = Path, [(69,115)]
        = Path, [(97,111)] = Path, [(5,91)] = Path, [(73,105)] = Path,
        [(23,64)] = Path, [(99,50)] = Path, [(107,41)] = Path, [(75,23)] =
        Path, [(72,7)] = Path, [(90,93)] = Path, [(121,17)] = Path, [(11,107)]
        = Path, [(17,35)] = Path, [(26,95)] = Path, [(95,37)] = Path, [(91,53)]
        = Path, [(54,105)] = Path, [(75,115)] = Path, [(113,3)] = Path,
        [(27,69)] = Path, [(23,11)] = Path, [(121,54)] = Path, [(8,119)] =
        Path, [(82,109)] = Path, [(12,15)] = Path, [(34,49)] = Inner(55,124),
        [(5,13)] = Path, [(69,7)] = Path, [(121,91)] = Path, [(67,101)] = Path,
        [(101,107)] = Path, [(37,97)] = Path, [(61,123)] = Path, [(78,3)] =
        Path, [(85,122)] = Path, [(108,17)] = Path, [(107,13)] = Path,
        [(49,110)] = Path, [(107,123)] = Path, [(73,113)] = Path, [(99,118)] =
        Path, [(23,89)] = Path, [(39,123)] = Path, [(65,27)] = Path, [(51,98)]
        = Path, [(40,21)] = Path, [(107,10)] = Path, [(15,33)] = Path,
        [(29,45)] = Path, [(41,14)] = Path, [(25,29)] = Path, [(7,83)] = Path,
        [(65,11)] = Path, [(105,51)] = Path, [(18,101)] = Path, [(11,105)] =
        Path, [(27,88)] = Path, [(81,24)] = Path, [(65,15)] = Path, [(99,120)]
        = Path, [(3,47)] = Path, [(41,8)] = Path, [(32,3)] = Path, [(54,101)] =
        Path, [(93,14)] = Path, [(21,74)] = Path, [(71,96)] = Path, [(102,7)] =
        Path, [(111,117)] = Path, [(32,101)] = Path, [(58,123)] = Path,
        [(107,105)] = Path, [(19,102)] = Path, [(67,34)] = Inner(85,124),
        [(52,19)] = Path, [(23,22)] = Path, [(48,21)] = Path, [(3,105)] = Path,
        [(121,46)] = Path, [(118,91)] = Path, [(113,8)] = Path, [(35,101)] =
        Path, [(71,119)] = Path, [(9,89)] = Path, [(112,59)] = Path, [(93,99)]
        = Path, [(5,6)] = Path, [(119,109)] = Path, [(101,77)] = Path,
        [(41,107)] = Path, [(109,15)] = Path, [(18,41)] = Path, [(77,9)] =
        Path, [(85,93)] = Path, [(116,17)] = Path, [(27,47)] = Path, [(97,74)]
        = Path, [(13,116)] = Path, [(57,16)] = Path, [(91,39)] = Path, [(6,15)]
        = Path, [(121,12)] = Path, [(46,123)] = Path, [(73,13)] = Path,
        [(107,51)] = Path, [(31,57)] = Path, [(5,15)] = Path, [(19,73)] = Path,
        [(57,96)] = Path, [(69,119)] = Path, [(21,29)] = Path, [(77,32)] =
        Path, [(71,2)] = Outer(81,34), [(101,67)] = Path, [(65,117)] = Path,
        [(69,107)] = Path, [(53,106)] = Path, [(8,33)] = Path, [(115,39)] =
        Path, [(39,114)] = Path, [(15,66)] = Path, [(93,11)] = Path, [(117,85)]
        = Path, [(7,73)] = Path, [(93,105)] = Path, [(49,107)] = Path,
        [(118,75)] = Path, [(10,33)] = Path, [(22,115)] = Path, [(19,116)] =
        Path, [(12,117)] = Path, [(14,121)] = Path, [(117,98)] = Path,
        [(45,105)] = Path, [(97,48)] = Path, [(19,51)] = Path, [(121,59)] =
        Path, [(7,106)] = Path, [(95,17)] = Path, [(30,87)] = Path, [(71,95)] =
        Path, [(12,39)] = Path, [(31,9)] = Path, [(62,19)] = Path, [(24,79)] =
        Path, [(98,21)] = Path, [(57,107)] = Path, [(36,31)] = Path, [(75,3)] =
        Path, [(13,54)] = Path, [(53,103)] = Path, [(115,92)] = Path, [(99,85)]
        = Path, [(121,89)] = Path, [(92,67)] = Path, [(15,62)] = Path,
        [(121,60)] = Path, [(37,23)] = Path, [(23,114)] = Path, [(71,14)] =
        Path, [(85,32)] = Path, [(21,39)] = Path, [(19,6)] = Path, [(22,11)] =
        Path, [(91,97)] = Path, [(75,28)] = Path, [(10,73)] = Path, [(99,75)] =
        Path, [(94,107)] = Path, [(31,80)] = Path, [(94,73)] = Path, [(12,111)]
        = Path, [(17,113)] = Path, [(13,119)] = Path, [(79,5)] = Path,
        [(77,14)] = Path, [(103,95)] = Path, [(115,100)] = Path, [(107,72)] =
        Path, [(5,75)] = Path, [(38,31)] = Path, [(120,25)] = Path, [(39,21)] =
        Path, [(103,115)] = Path, [(62,27)] = Path, [(56,21)] = Path, [(5,123)]
        = Path, [(57,101)] = Path, [(87,103)] = Path, [(109,85)] = Path,
        [(106,83)] = Path, [(33,123)] = Path, [(98,115)] = Path, [(69,28)] =
        Path, [(85,111)] = Path, [(33,58)] = Path, [(69,122)] = Path, [(95,96)]
        = Path, [(65,124)] = Outer(34,77), [(15,76)] = Path, [(87,28)] = Path,
        [(93,101)] = Path, [(26,87)] = Path, [(108,63)] = Path, [(43,115)] =
        Path, [(3,63)] = Path, [(19,88)] = Path, [(113,14)] = Path, [(99,77)] =
        Path, [(3,80)] = Path, [(111,52)] = Path, [(119,9)] = Path, [(13,43)] =
        Path, [(101,87)] = Path, [(67,19)] = Path, [(4,69)] = Path, [(21,48)] =
        Path, [(27,3)] = Path, [(73,15)] = Path, [(23,29)] = Path, [(119,6)] =
        Path, [(3,51)] = Path, [(117,51)] = Path, [(58,117)] = Path, [(3,100)]
        = Path, [(15,60)] = Path, [(105,65)] = Path, [(15,108)] = Path,
        [(119,39)] = Path, [(54,103)] = Path, [(120,29)] = Path, [(81,93)] =
        Path, [(75,7)] = Path, [(17,119)] = Path, [(75,119)] = Path, [(28,61)]
        = Path, [(116,119)] = Path, [(115,113)] = Path, [(44,121)] = Path,
        [(95,46)] = Path, [(63,3)] = Path, [(3,42)] = Path, [(47,19)] = Path,
        [(7,67)] = Path, [(82,99)] = Path, [(68,33)] = Path, [(13,20)] = Path,
        [(97,110)] = Path, [(5,55)] = Path, [(108,77)] = Path, [(27,15)] =
        Path, [(5,90)] = Path, [(122,51)] = Outer(59,92), [(45,97)] = Path,
        [(108,115)] = Path, [(103,79)] = Path, [(118,69)] = Path, [(29,21)] =
        Path, [(39,8)] = Path, [(53,105)] = Path, [(9,103)] = Path, [(8,39)] =
        Path, [(102,85)] = Path, [(3,13)] = Path, [(3,99)] = Path, [(51,31)] =
        Path, [(21,57)] = Path, [(67,23)] = Path, [(57,119)] = Path, [(5,19)] =
        Path, [(102,77)] = Path, [(16,77)] = Path, [(55,15)] = Path, [(79,4)] =
        Path, [(85,22)] = Path, [(27,55)] = Path, [(41,93)] = Path, [(103,76)]
        = Path, [(106,19)] = Path, [(91,114)] = Path, [(101,55)] = Path,
        [(92,11)] = Path, [(43,117)] = Path, [(101,33)] = Path, [(20,119)] =
        Path, [(47,115)] = Path, [(66,25)] = Path, [(47,32)] = Path, [(119,32)]
        = Path, [(19,97)] = Path, [(107,9)] = Path, [(20,111)] = Path, [(10,3)]
        = Path, [(93,123)] = Path, [(113,117)] = Path, [(47,11)] = Path,
        [(11,36)] = Path, [(107,33)] = Path, [(92,73)] = Path, [(95,60)] =
        Path, [(15,91)] = Path, [(7,77)] = Path, [(15,31)] = Path, [(30,107)] =
        Path, [(28,71)] = Path, [(9,105)] = Path, [(101,25)] = Path, [(33,66)]
        = Path, [(91,102)] = Path, [(93,35)] = Path, [(65,113)] = Path,
        [(30,73)] = Path, [(105,8)] = Path, [(5,47)] = Path, [(48,9)] = Path,
        [(30,23)] = Path, [(15,55)] = Path, [(25,116)] = Path, [(13,113)] =
        Path, [(21,24)] = Path, [(101,104)] = Path, [(9,114)] = Path,
        [(115,120)] = Path, [(51,115)] = Path, [(21,7)] = Path, [(75,117)] =
        Path, [(25,59)] = Path, [(107,11)] = Path, [(5,60)] = Path, [(85,121)]
        = Path, [(12,17)] = Path, [(20,83)] = Path, [(79,93)] = Path, [(46,11)]
        = Path, [(115,53)] = Path, [(99,89)] = Path, [(12,43)] = Path,
        [(52,119)] = Path, [(87,13)] = Path, [(17,46)] = Path, [(4,65)] = Path,
        [(34,97)] = Path, [(115,106)] = Path, [(14,67)] = Path, [(95,16)] =
        Path, [(83,27)] = Path, [(36,5)] = Path, [(113,72)] = Path, [(94,7)] =
        Path, [(23,53)] = Path, [(30,121)] = Path, [(50,119)] = Path, [(23,93)]
        = Path, [(8,85)] = Path, [(32,123)] = Path, [(113,77)] = Path,
        [(49,103)] = Path, [(99,121)] = Path, [(21,21)] = Path, [(107,43)] =
        Path, [(73,19)] = Path, [(31,52)] = Path, [(33,65)] = Path, [(34,57)] =
        Inner(122,73), [(19,27)] = Path, [(38,33)] = Path, [(13,118)] = Path,
        [(95,119)] = Path, [(107,19)] = Path, [(73,115)] = Path, [(81,25)] =
        Path, [(97,109)] = Path, [(89,30)] = Path, [(38,123)] = Path,
        [(19,117)] = Path, [(11,95)] = Path, [(77,111)] = Path, [(77,10)] =
        Path, [(121,96)] = Path, [(50,93)] = Path, [(7,4)] = Path, [(109,93)] =
        Path, [(81,120)] = Path, [(5,76)] = Path, [(9,25)] = Path, [(24,33)] =
        Path, [(87,104)] = Path, [(31,55)] = Path, [(55,118)] = Path,
        [(37,119)] = Path, [(80,27)] = Path, [(113,67)] = Path, [(115,9)] =
        Path, [(93,32)] = Path, [(77,102)] = Path, [(110,79)] = Path,
        [(109,77)] = Path, [(98,69)] = Path, [(95,76)] = Path, [(95,116)] =
        Path, [(77,20)] = Path, [(67,92)] = Inner(57,2), [(79,107)] = Path,
        [(33,31)] = Path, [(84,123)] = Path, [(92,87)] = Path, [(77,19)] =
        Path, [(35,11)] = Path, [(25,37)] = Path, [(91,27)] = Path, [(13,77)] =
        Path, [(11,25)] = Path, [(7,12)] = Path, [(89,23)] = Path, [(27,95)] =
        Path, [(9,12)] = Path, [(111,105)] = Path, [(93,122)] = Path, [(99,83)]
        = Path, [(3,5)] = Path, [(107,85)] = Path, [(33,45)] = Path, [(117,83)]
        = Path, [(13,19)] = Path, [(103,123)] = Path, [(30,7)] = Path,
        [(97,90)] = Path, [(81,29)] = Path, [(60,93)] = Path, [(15,18)] = Path,
        [(99,97)] = Path, [(61,6)] = Path, [(20,27)] = Path, [(117,10)] = Path,
        [(17,94)] = Path, [(117,48)] = Path, [(91,37)] = Path, [(83,102)] =
        Path, [(21,54)] = Path, [(105,34)] = Path, [(9,75)] = Path, [(7,113)] =
        Path, [(87,27)] = Path, [(103,84)] = Path, [(117,36)] = Path, [(9,57)]
        = Path, [(81,106)] = Path, [(19,34)] = Path, [(15,22)] = Path,
        [(19,21)] = Path, [(30,75)] = Path, [(3,32)] = Path, [(81,22)] = Path,
        [(42,21)] = Path, [(25,53)] = Path, [(47,23)] = Path, [(109,91)] =
        Path, [(95,115)] = Path, [(9,94)] = Path, [(76,25)] = Path, [(92,63)] =
        Path, [(22,81)] = Path, [(121,36)] = Path, [(60,23)] = Path, [(63,18)]
        = Path, [(81,102)] = Path, [(26,71)] = Path, [(87,21)] = Path,
        [(11,47)] = Path, [(113,21)] = Path, [(27,77)] = Path, [(58,23)] =
        Path, [(20,65)] = Path, [(108,25)] = Path, [(47,98)] = Path, [(48,101)]
        = Path, [(119,114)] = Path, [(99,47)] = Path, [(115,97)] = Path,
        [(74,3)] = Path, [(5,50)] = Path, [(113,17)] = Path, [(93,44)] = Path,
        [(67,21)] = Path, [(112,87)] = Path, [(103,67)] = Path, [(3,55)] =
        Path, [(18,39)] = Path, [(71,33)] = Path, [(21,47)] = Path, [(35,98)] =
        Path, [(117,37)] = Path, [(61,124)] = Outer(55,34), [(97,12)] = Path,
        [(21,19)] = Path, [(33,57)] = Path, [(33,93)] = Path, [(18,27)] = Path,
        [(11,13)] = Path, [(43,11)] = Path, [(85,8)] = Path, [(122,83)] =
        Outer(90,81), [(3,35)] = Path, [(23,115)] = Path, [(27,113)] = Path,
        [(91,57)] = Path, [(112,37)] = Path, [(103,83)] = Path, [(27,16)] =
        Path, [(83,13)] = Path, [(36,105)] = Path, [(35,93)] = Path, [(12,33)]
        = Path, [(21,14)] = Path, [(15,14)] = Path, [(64,31)] = Path, [(6,119)]
        = Path, [(68,3)] = Path, [(103,27)] = Path, [(5,89)] = Path, [(23,120)]
        = Path, [(27,85)] = Path, [(58,115)] = Path, [(61,5)] = Path, [(21,41)]
        = Path, [(54,13)] = Path, [(81,11)] = Path, [(116,103)] = Path,
        [(119,97)] = Path, [(97,104)] = Path, [(115,77)] = Path, [(63,93)] =
        Path, [(4,33)] = Path, [(62,29)] = Path, [(119,117)] = Path, [(90,29)]
        = Path, [(107,42)] = Path, [(65,18)] = Path, [(20,17)] = Path,
        [(11,74)] = Path, [(7,91)] = Path, [(113,33)] = Path, [(95,111)] =
        Path, [(102,23)] = Path, [(11,28)] = Path, [(17,63)] = Path, [(119,58)]
        = Path, [(4,63)] = Path, [(37,95)] = Path, [(9,79)] = Path, [(99,81)] =
        Path, [(50,31)] = Path, [(91,89)] = Path, [(13,84)] = Path, [(99,72)] =
        Path, [(15,54)] = Path, [(114,89)] = Path, [(37,24)] = Path, [(119,95)]
        = Path, [(45,107)] = Path, [(61,33)] = Path, [(5,115)] = Path,
        [(107,81)] = Path, [(45,99)] = Path, [(31,75)] = Path, [(83,7)] = Path,
        [(31,5)] = Path, [(17,73)] = Path, [(51,23)] = Path, [(91,67)] = Path,
        [(3,58)] = Path, [(36,123)] = Path, [(117,114)] = Path, [(33,110)] =
        Path, [(27,91)] = Path, [(94,123)] = Path, [(5,87)] = Path, [(119,69)]
        = Path, [(34,45)] = Inner(75,124), [(37,118)] = Path, [(11,49)] = Path,
        [(79,96)] = Path, [(5,68)] = Path, [(29,87)] = Path, [(122,71)] = Path,
        [(120,67)] = Path, [(93,46)] = Path, [(117,121)] = Path, [(7,5)] =
        Path, [(80,29)] = Path, [(43,106)] = Path, [(78,105)] = Path, [(69,23)]
        = Path, [(114,91)] = Path, [(23,48)] = Path, [(35,29)] = Path,
        [(57,31)] = Path, [(93,21)] = Path, [(107,46)] = Path, [(40,19)] =
        Path, [(33,38)] = Path, [(12,97)] = Path, [(23,15)] = Path, [(51,112)]
        = Path, [(117,115)] = Path, [(101,39)] = Path, [(93,91)] = Path,
        [(101,34)] = Path, [(7,96)] = Path, [(98,13)] = Path, [(7,101)] = Path,
        [(11,61)] = Path, [(13,99)] = Path, [(45,4)] = Path, [(17,57)] = Path,
        [(103,85)] = Path, [(29,83)] = Path, [(14,31)] = Path, [(105,24)] =
        Path, [(96,63)] = Path, [(5,84)] = Path, [(12,21)] = Path, [(35,111)] =
        Path, [(36,13)] = Path, [(16,71)] = Path, [(71,107)] = Path,
        [(103,101)] = Path, [(107,74)] = Path, [(93,115)] = Path, [(110,67)] =
        Path, [(15,122)] = Path, [(117,35)] = Path, [(73,17)] = Path,
        [(103,108)] = Path, [(77,113)] = Path, [(115,47)] = Path, [(68,23)] =
        Path, [(24,41)] = Path, [(21,49)] = Path, [(119,52)] = Path, [(31,49)]
        = Path, [(115,54)] = Path, [(13,27)] = Path, [(96,3)] = Path, [(115,7)]
        = Path, [(85,18)] = Path, [(97,62)] = Path, [(29,53)] = Path, [(73,21)]
        = Path, [(5,65)] = Path, [(16,87)] = Path, [(108,21)] = Path, [(73,95)]
        = Path, [(17,71)] = Path, [(100,49)] = Path, [(13,81)] = Path, [(51,3)]
        = Path, [(95,41)] = Path, [(108,103)] = Path, [(91,94)] = Path,
        [(28,109)] = Path, [(48,105)] = Path, [(111,39)] = Path, [(93,3)] =
        Path, [(52,117)] = Path, [(117,68)] = Path, [(9,13)] = Path, [(47,2)] =
        Outer(71,34), [(62,121)] = Path, [(52,21)] = Path, [(5,17)] = Path,
        [(107,87)] = Path, [(91,82)] = Path, [(43,119)] = Path, [(77,21)] =
        Path, [(117,15)] = Path, [(21,108)] = Path, [(17,16)] = Path,
        [(114,21)] = Path, [(92,111)] = Path, [(67,93)] = Path, [(6,51)] =
        Path, [(25,81)] = Path, [(121,95)] = Path, [(61,3)] = Path, [(58,7)] =
        Path, [(95,33)] = Path, [(24,51)] = Path, [(45,13)] = Path, [(105,109)]
        = Path, [(75,123)] = Path, [(29,65)] = Path, [(78,101)] = Path,
        [(11,62)] = Path, [(93,117)] = Path, [(109,56)] = Path, [(99,79)] =
        Path, [(85,31)] = Path, [(19,113)] = Path, [(71,123)] = Path,
        [(12,105)] = Path, [(95,13)] = Path, [(115,50)] = Path, [(55,4)] =
        Path, [(97,21)] = Path, [(79,31)] = Path, [(61,117)] = Path, [(71,3)] =
        Path, [(15,34)] = Path, [(117,94)] = Path, [(11,117)] = Path, [(77,8)]
        = Path, [(7,65)] = Path, [(51,15)] = Path, [(39,98)] = Path, [(15,39)]
        = Path, [(119,71)] = Path, [(25,57)] = Path, [(7,55)] = Path, [(25,6)]
        = Path, [(115,107)] = Path, [(109,112)] = Path, [(90,17)] = Path,
        [(10,63)] = Path, [(100,67)] = Path, [(9,73)] = Path, [(67,17)] = Path,
        [(97,6)] = Path, [(11,77)] = Path, [(80,93)] = Path, [(19,19)] = Path,
        [(13,39)] = Path, [(27,11)] = Path, [(103,81)] = Path, [(119,89)] =
        Path, [(13,17)] = Path, [(103,54)] = Path, [(73,107)] = Path, [(47,20)]
        = Path, [(114,53)] = Path, [(107,93)] = Path, [(22,35)] = Path,
        [(97,79)] = Path, [(13,37)] = Path, [(68,121)] = Path, [(90,3)] = Path,
        [(32,51)] = Path, [(51,100)] = Path, [(31,84)] = Path, [(3,89)] = Path,
        [(25,95)] = Path, [(82,19)] = Path, [(57,21)] = Path, [(3,79)] = Path,
        [(95,3)] = Path, [(44,107)] = Path, [(51,25)] = Path, [(54,123)] =
        Path, [(116,21)] = Path, [(51,104)] = Path, [(47,24)] = Path, [(17,77)]
        = Path, [(38,27)] = Path, [(14,49)] = Path, [(45,14)] = Path,
        [(112,77)] = Path, [(103,37)] = Path, [(32,17)] = Path, [(15,47)] =
        Path, [(89,95)] = Path, [(7,27)] = Path, [(17,15)] = Path, [(85,99)] =
        Path, [(105,57)] = Path, [(31,25)] = Path, [(20,97)] = Path, [(17,31)]
        = Path, [(15,101)] = Path, [(75,26)] = Path, [(52,17)] = Path, [(93,7)]
        = Path, [(35,4)] = Path, [(103,75)] = Path, [(105,35)] = Path,
        [(107,77)] = Path, [(90,23)] = Path, [(93,53)] = Path, [(23,35)] =
        Path, [(103,5)] = Path, [(69,31)] = Path, [(15,105)] = Path, [(29,74)]
        = Path, [(25,97)] = Path, [(113,97)] = Path, [(3,114)] = Path,
        [(60,95)] = Path, [(30,63)] = Path, [(109,121)] = Path, [(33,14)] =
        Path, [(101,100)] = Path, [(40,9)] = Path, [(29,99)] = Path, [(25,16)]
        = Path, [(105,85)] = Path, [(121,119)] = Path, [(25,55)] = Path,
        [(103,39)] = Path, [(71,97)] = Path, [(51,19)] = Path, [(71,111)] =
        Path, [(67,103)] = Path, [(29,69)] = Path, [(80,111)] = Path, [(11,50)]
        = Path, [(49,23)] = Path, [(22,71)] = Path, [(19,54)] = Path, [(93,45)]
        = Path, [(45,31)] = Path, [(50,29)] = Path, [(35,102)] = Path,
        [(31,100)] = Path, [(111,76)] = Path, [(44,115)] = Path, [(5,117)] =
        Path, [(53,117)] = Path, [(119,121)] = Path, [(119,25)] = Path,
        [(21,38)] = Path, [(109,81)] = Path, [(82,23)] = Path, [(60,33)] =
        Path, [(63,4)] = Path, [(107,7)] = Path, [(23,121)] = Path, [(13,106)]
        = Path, [(91,47)] = Path, [(102,81)] = Path, [(108,27)] = Path,
        [(119,72)] = Path, [(91,23)] = Path, [(11,35)] = Path, [(28,51)] =
        Path, [(46,95)] = Path, [(121,43)] = Path, [(115,49)] = Path, [(85,6)]
        = Path, [(116,33)] = Path, [(105,41)] = Path, [(108,123)] = Path,
        [(101,47)] = Path, [(29,47)] = Path, [(95,38)] = Path, [(25,89)] =
        Path, [(99,31)] = Path, [(120,9)] = Path, [(28,49)] = Path, [(79,119)]
        = Path, [(67,4)] = Path, [(7,68)] = Path, [(7,94)] = Path, [(24,107)] =
        Path, [(59,120)] = Path, [(42,101)] = Path, [(101,21)] = Path, [(9,43)]
        = Path, [(50,111)] = Path, [(15,4)] = Path, [(54,3)] = Path, [(8,79)] =
        Path, [(29,32)] = Path, [(29,113)] = Path, [(63,15)] = Path, [(97,41)]
        = Path, [(91,66)] = Path, [(53,3)] = Path, [(13,97)] = Path,
        [(111,110)] = Path, [(12,9)] = Path, [(48,123)] = Path, [(57,22)] =
        Path, [(99,8)] = Path, [(101,73)] = Path, [(59,122)] = Path, [(50,99)]
        = Path, [(120,89)] = Path, [(33,19)] = Path, [(41,103)] = Path,
        [(62,97)] = Path, [(7,7)] = Path, [(11,106)] = Path, [(30,27)] = Path,
        [(93,63)] = Path, [(5,26)] = Path, [(71,29)] = Path, [(9,37)] = Path,
        [(113,13)] = Path, [(99,59)] = Path, [(29,112)] = Path, [(69,15)] =
        Path, [(7,38)] = Path, [(19,39)] = Path, [(71,120)] = Path, [(101,65)]
        = Path, [(91,85)] = Path, [(6,11)] = Path, [(109,25)] = Path,
        [(104,35)] = Path, [(101,8)] = Path, [(22,67)] = Path, [(98,107)] =
        Path, [(103,35)] = Path, [(72,97)] = Path, [(102,83)] = Path, [(42,5)]
        = Path, [(111,95)] = Path, [(51,4)] = Path, [(41,7)] = Path, [(4,57)] =
        Path, [(81,103)] = Path, [(115,57)] = Path, [(94,115)] = Path, [(3,43)]
        = Path, [(31,11)] = Path, [(33,11)] = Path, [(11,98)] = Path, [(67,27)]
        = Path, [(79,19)] = Path, [(31,85)] = Path, [(109,111)] = Path,
        [(28,55)] = Path, [(114,109)] = Path, [(53,109)] = Path, [(55,105)] =
        Path, [(31,59)] = Path, [(53,102)] = Path, [(115,29)] = Path, [(25,63)]
        = Path, [(16,25)] = Path, [(91,100)] = Path, [(7,21)] = Path, [(39,5)]
        = Path, [(101,57)] = Path, [(23,55)] = Path, [(95,55)] = Path,
        [(27,98)] = Path, [(23,101)] = Path, [(103,60)] = Path, [(107,96)] =
        Path, [(59,98)] = Path, [(96,25)] = Path, [(11,58)] = Path, [(22,69)] =
        Path, [(107,29)] = Path, [(31,61)] = Path, [(62,109)] = Path,
        [(110,109)] = Path, [(33,9)] = Path, [(3,4)] = Path, [(7,35)] = Path,
        [(99,95)] = Path, [(92,95)] = Path, [(3,123)] = Path, [(115,73)] =
        Path, [(47,5)] = Path, [(8,45)] = Path, [(102,43)] = Path, [(58,15)] =
        Path, [(75,93)] = Path, [(107,53)] = Path, [(83,115)] = Path, [(97,85)]
        = Path, [(17,47)] = Path, [(29,9)] = Path, [(32,27)] = Path, [(61,7)] =
        Path, [(53,94)] = Path, [(99,43)] = Path, [(16,117)] = Path, [(3,48)] =
        Path, [(121,93)] = Path, [(72,111)] = Path, [(28,105)] = Path,
        [(77,25)] = Path, [(26,119)] = Path, [(93,97)] = Path, [(14,83)] =
        Path, [(111,79)] = Path, [(19,60)] = Path, [(34,77)] = Inner(65,124),
        [(117,111)] = Path, [(65,111)] = Path, [(53,9)] = Path, [(93,85)] =
        Path, [(119,46)] = Path, [(107,115)] = Path, [(101,70)] = Path,
        [(16,119)] = Path, [(28,23)] = Path, [(59,33)] = Path, [(23,23)] =
        Path, [(11,63)] = Path, [(25,13)] = Path, [(115,87)] = Path, [(63,109)]
        = Path, [(108,3)] = Path, [(15,11)] = Path, [(91,123)] = Path,
        [(65,98)] = Path, [(120,69)] = Path, [(36,33)] = Path, [(21,111)] =
        Path, [(93,51)] = Path, [(25,107)] = Path, [(35,24)] = Path, [(47,96)]
        = Path, [(17,109)] = Path, [(108,37)] = Path, [(59,30)] = Path,
        [(4,49)] = Path, [(48,11)] = Path, [(83,107)] = Path, [(2,83)] = Path,
        [(53,115)] = Path, [(15,97)] = Path, [(63,113)] = Path, [(3,72)] =
        Path, [(103,53)] = Path, [(95,35)] = Path, [(4,7)] = Path, [(40,117)] =
        Path, [(119,13)] = Path, [(110,95)] = Path, [(111,103)] = Path,
        [(6,43)] = Path, [(119,93)] = Path, [(74,99)] = Path, [(115,63)] =
        Path, [(27,97)] = Path, [(119,115)] = Path, [(20,109)] = Path,
        [(25,90)] = Path, [(51,103)] = Path, [(108,61)] = Path, [(96,21)] =
        Path, [(45,119)] = Path, [(53,97)] = Path, [(71,101)] = Path, [(2,71)]
        = Outer(34,85), [(97,16)] = Path, [(23,37)] = Path, [(35,10)] = Path,
        [(97,116)] = Path, [(100,45)] = Path, [(89,8)] = Path, [(117,69)] =
        Path, [(113,40)] = Path, [(47,95)] = Path, [(35,15)] = Path, [(40,11)]
        = Path, [(121,21)] = Path, [(51,29)] = Path, [(57,24)] = Path,
        [(73,114)] = Path, [(77,16)] = Path, [(42,15)] = Path, [(27,101)] =
        Path, [(42,113)] = Path, [(50,13)] = Path, [(11,81)] = Path, [(95,24)]
        = Path, [(106,85)] = Path, [(111,16)] = Path, [(51,121)] = Path,
        [(39,109)] = Path, [(119,118)] = Path, [(49,94)] = Path, [(11,45)] =
        Path, [(3,81)] = Path, [(119,23)] = Path, [(53,28)] = Path, [(5,81)] =
        Path, [(109,42)] = Path, [(9,28)] = Path, [(21,20)] = Path, [(109,52)]
        = Path, [(120,57)] = Path, [(9,109)] = Path, [(111,87)] = Path,
        [(114,15)] = Path, [(89,97)] = Path, [(29,110)] = Path, [(32,45)] =
        Path, [(51,7)] = Path, [(67,109)] = Path, [(105,74)] = Path, [(23,63)]
        = Path, [(97,81)] = Path, [(54,109)] = Path, [(74,109)] = Path,
        [(24,69)] = Path, [(115,30)] = Path, [(5,52)] = Path, [(55,9)] = Path,
        [(100,119)] = Path, [(43,121)] = Path, [(119,92)] = Path, [(115,85)] =
        Path, [(119,65)] = Path, [(55,31)] = Path, [(28,53)] = Path, [(77,93)]
        = Path, [(9,6)] = Path, [(113,119)] = Path, [(81,8)] = Path, [(6,31)] =
        Path, [(24,11)] = Path, [(25,108)] = Path, [(105,108)] = Path,
        [(104,25)] = Path, [(83,119)] = Path, [(93,26)] = Path, [(51,26)] =
        Path, [(63,7)] = Path, [(103,29)] = Path, [(19,119)] = Path,
        [(115,115)] = Path, [(3,98)] = Path, [(99,100)] = Path, [(3,17)] =
        Path, [(66,15)] = Path, [(52,5)] = Path, [(82,15)] = Path, [(122,41)] =
        Outer(73,92), [(109,33)] = Path, [(41,109)] = Path, [(13,14)] = Path,
        [(101,10)] = Path, [(9,111)] = Path, [(45,11)] = Path, [(91,106)] =
        Path, [(5,22)] = Path, [(86,117)] = Path, [(42,123)] = Path,
        [(119,119)] = Path, [(19,14)] = Path, [(10,21)] = Path, [(9,46)] =
        Path, [(29,4)] = Path, [(115,119)] = Path, [(9,55)] = Path, [(78,29)] =
        Path, [(7,41)] = Path, [(57,7)] = Path, [(11,26)] = Path, [(13,112)] =
        Path, [(23,123)] = Path, [(93,40)] = Path, [(101,61)] = Path,
        [(25,111)] = Path, [(97,47)] = Path, [(31,19)] = Path, [(85,104)] =
        Path, [(70,123)] = Path, [(19,68)] = Path, [(106,75)] = Path,
        [(39,104)] = Path, [(3,75)] = Path, [(117,62)] = Path, [(49,9)] = Path,
        [(109,123)] = Path, [(6,23)] = Path, [(99,9)] = Path, [(95,123)] =
        Path, [(3,73)] = Path, [(90,101)] = Path, [(104,115)] = Path, [(67,28)]
        = Path, [(52,15)] = Path, [(4,85)] = Path, [(85,28)] = Path, [(54,107)]
        = Path, [(118,115)] = Path, [(89,120)] = Path, [(103,33)] = Path,
        [(95,81)] = Path, [(44,93)] = Path, [(71,113)] = Path, [(109,55)] =
        Path, [(80,21)] = Path, [(113,100)] = Path, [(30,79)] = Path, [(15,19)]
        = Path, [(89,19)] = Path, [(97,95)] = Path, [(95,90)] = Path, [(97,87)]
        = Path, [(31,115)] = Path, [(90,117)] = Path, [(121,19)] = Path,
        [(17,24)] = Path, [(49,21)] = Path, [(23,103)] = Path, [(86,11)] =
        Path, [(21,104)] = Path, [(44,29)] = Path, [(33,23)] = Path, [(13,83)]
        = Path, [(103,7)] = Path, [(107,119)] = Path, [(9,63)] = Path,
        [(37,31)] = Path, [(109,66)] = Path, [(11,85)] = Path, [(95,87)] =
        Path, [(114,95)] = Path, [(91,40)] = Path, [(107,17)] = Path, [(91,11)]
        = Path, [(17,97)] = Path, [(101,4)] = Path, [(27,103)] = Path,
        [(105,84)] = Path, [(109,88)] = Path, [(107,69)] = Path, [(17,10)] =
        Path, [(43,110)] = Path, [(107,90)] = Path, [(94,33)] = Path,
        [(109,102)] = Path, [(103,17)] = Path, [(103,111)] = Path, [(29,109)] =
        Path, [(95,40)] = Path, [(18,19)] = Path, [(97,23)] = Path, [(40,113)]
        = Path, [(31,15)] = Path, [(83,33)] = Path, [(61,115)] = Path,
        [(71,11)] = Path, [(93,55)] = Path, [(77,119)] = Path, [(19,64)] =
        Path, [(107,80)] = Path, [(29,77)] = Path, [(81,123)] = Path, [(5,111)]
        = Path, [(25,70)] = Path, [(7,59)] = Path, [(5,42)] = Path, [(23,117)]
        = Path, [(93,70)] = Path, [(31,21)] = Path, [(117,47)] = Path, [(7,18)]
        = Path, [(11,93)] = Path, [(3,11)] = Path, [(115,24)] = Path,
        [(100,29)] = Path, [(12,31)] = Path, [(109,29)] = Path, [(105,40)] =
        Path, [(27,45)] = Path, [(69,10)] = Path, [(121,113)] = Path, [(3,117)]
        = Path, [(91,101)] = Path, [(75,19)] = Path, [(103,51)] = Path,
        [(106,57)] = Path, [(107,47)] = Path, [(15,25)] = Path, [(45,27)] =
        Path, [(106,9)] = Path, [(33,39)] = Path, [(21,67)] = Path, [(77,123)]
        = Path, [(27,27)] = Path, [(79,98)] = Path, [(3,27)] = Path, [(98,23)]
        = Path, [(116,65)] = Path, [(9,19)] = Path, [(33,55)] = Path, [(75,9)]
        = Path, [(44,3)] = Path, [(91,115)] = Path, [(35,105)] = Path,
        [(83,29)] = Path, [(9,99)] = Path, [(27,114)] = Path, [(116,39)] =
        Path, [(15,89)] = Path, [(97,39)] = Path, [(29,41)] = Path, [(115,21)]
        = Path, [(15,46)] = Path, [(35,19)] = Path, [(4,93)] = Path, [(3,68)] =
        Path, [(104,75)] = Path, [(89,27)] = Path, [(115,56)] = Path, [(49,15)]
        = Path, [(75,4)] = Path, [(111,55)] = Path, [(55,18)] = Path,
        [(53,101)] = Path, [(35,33)] = Path, [(3,104)] = Path, [(63,106)] =
        Path, [(79,14)] = Path, [(16,49)] = Path, [(3,77)] = Path, [(19,87)] =
        Path, [(113,71)] = Path, [(57,12)] = Path, [(49,8)] = Path, [(46,19)] =
        Path, [(25,67)] = Path, [(31,121)] = Path, [(105,17)] = Path, [(95,84)]
        = Path, [(26,57)] = Path, [(117,73)] = Path, [(103,73)] = Path,
        [(113,107)] = Path, [(79,95)] = Path, [(6,57)] = Path, [(11,5)] = Path,
        [(94,89)] = Path, [(99,32)] = Path, [(79,12)] = Path, [(100,21)] =
        Path, [(35,31)] = Path, [(93,38)] = Path, [(39,93)] = Path, [(115,43)]
        = Path, [(91,15)] = Path, [(89,113)] = Path, [(119,88)] = Path,
        [(97,29)] = Path, [(27,105)] = Path, [(103,89)] = Path, [(33,74)] =
        Path, [(15,85)] = Path, [(7,20)] = Path, [(27,53)] = Path, [(121,13)] =
        Path, [(107,121)] = Path, [(71,25)] = Path, [(93,114)] = Path, [(5,37)]
        = Path, [(101,3)] = Path, [(25,39)] = Path, [(67,105)] = Path,
        [(23,116)] = Path, [(69,14)] = Path, [(69,16)] = Path, [(73,121)] =
        Path, [(117,8)] = Path, [(77,3)] = Path, [(55,16)] = Path, [(33,92)] =
        Path, [(97,57)] = Path, [(61,97)] = Path, [(120,17)] = Path, [(24,109)]
        = Path, [(23,75)] = Path, [(15,45)] = Path, [(119,105)] = Path,
        [(32,89)] = Path, [(95,49)] = Path, [(121,25)] = Path, [(91,87)] =
        Path, [(115,69)] = Path, [(4,29)] = Path, [(119,17)] = Path, [(101,81)]
        = Path, [(15,71)] = Path, [(106,115)] = Path, [(4,123)] = Path,
        [(20,47)] = Path, [(76,97)] = Path, [(55,111)] = Path, [(121,121)] =
        Path, [(5,45)] = Path, [(73,29)] = Path, [(107,39)] = Path, [(39,15)] =
        Path, [(97,83)] = Path, [(97,78)] = Path, [(20,79)] = Path, [(59,5)] =
        Path, [(102,93)] = Path, [(38,9)] = Path, [(64,95)] = Path, [(111,63)]
        = Path, [(29,5)] = Path, [(17,38)] = Path, [(3,30)] = Path, [(107,59)]
        = Path, [(93,64)] = Path, [(13,63)] = Path, [(88,105)] = Path,
        [(93,68)] = Path, [(121,71)] = Path, [(11,39)] = Path, [(70,113)] =
        Path, [(27,14)] = Path, [(27,42)] = Path, [(101,119)] = Path, [(45,9)]
        = Path, [(76,93)] = Path, [(86,99)] = Path, [(101,23)] = Path,
        [(3,115)] = Path, [(27,104)] = Path, [(27,65)] = Path, [(95,31)] =
        Path, [(87,102)] = Path, [(103,70)] = Path, [(88,9)] = Path, [(104,31)]
        = Path, [(13,57)] = Path, [(101,32)] = Path, [(70,23)] = Path,
        [(45,93)] = Path, [(69,30)] = Path, [(117,110)] = Path, [(114,71)] =
        Path, [(102,41)] = Path, [(5,51)] = Path, [(115,51)] = Path, [(92,13)]
        = Path, [(13,111)] = Path, [(91,73)] = Path, [(36,19)] = Path,
        [(8,111)] = Path, [(88,111)] = Path, [(93,90)] = Path, [(21,6)] = Path,
        [(9,97)] = Path, [(27,4)] = Path, [(31,47)] = Path, [(117,75)] = Path,
        [(121,35)] = Path, [(19,79)] = Path, [(63,12)] = Path, [(31,79)] =
        Path, [(47,102)] = Path, [(119,11)] = Path, [(46,31)] = Path, [(92,69)]
        = Path, [(25,25)] = Path, [(13,40)] = Path, [(95,88)] = Path, [(11,73)]
        = Path, [(7,81)] = Path, [(80,121)] = Path, [(7,85)] = Path, [(18,105)]
        = Path, [(93,84)] = Path, [(93,65)] = Path, [(107,109)] = Path,
        [(116,81)] = Path, [(101,74)] = Path, [(17,44)] = Path, [(111,7)] =
        Path, [(13,5)] = Path, [(74,15)] = Path, [(109,94)] = Path, [(102,57)]
        = Path, [(64,9)] = Path, [(51,5)] = Path, [(99,113)] = Path, [(99,12)]
        = Path, [(29,97)] = Path, [(115,79)] = Path, [(91,60)] = Path,
        [(75,21)] = Path, [(62,23)] = Path, [(102,63)] = Path, [(79,17)] =
        Path, [(15,115)] = Path, [(95,92)] = Path, [(33,21)] = Path, [(104,91)]
        = Path, [(104,107)] = Path, [(119,107)] = Path, [(95,70)] = Path,
        [(33,117)] = Path, [(75,6)] = Path, [(3,7)] = Path, [(14,5)] = Path,
        [(23,95)] = Path, [(32,49)] = Path, [(53,11)] = Path, [(93,79)] = Path,
        [(53,8)] = Path, [(90,39)] = Inner(122,81), [(9,11)] = Path, [(112,65)]
        = Path, [(49,116)] = Path, [(76,117)] = Path, [(77,29)] = Path,
        [(61,27)] = Path, [(91,78)] = Path, [(23,58)] = Path, [(17,41)] = Path,
        [(121,98)] = Path, [(54,29)] = Path, [(105,33)] = Path, [(75,10)] =
        Path, [(109,53)] = Path, [(105,73)] = Path, [(109,19)] = Path,
        [(91,65)] = Path, [(57,115)] = Path, [(18,23)] = Path, [(33,43)] =
        Path, [(73,116)] = Path, [(12,51)] = Path, [(98,75)] = Path, [(111,56)]
        = Path, [(19,23)] = Path, [(39,11)] = Path, [(6,89)] = Path, [(48,33)]
        = Path, [(55,25)] = Path, [(46,97)] = Path, [(95,48)] = Path, [(29,24)]
        = Path, [(29,120)] = Path, [(31,29)] = Path, [(13,41)] = Path, [(3,25)]
        = Path, [(85,14)] = Path, [(105,26)] = Path, [(29,3)] = Path,
        [(106,111)] = Path, [(61,31)] = Path, [(77,31)] = Path, [(24,101)] =
        Path, [(103,93)] = Path, [(2,85)] = Outer(49,34), [(25,32)] = Path,
        [(27,116)] = Path, [(116,29)] = Path, [(19,25)] = Path, [(115,123)] =
        Path, [(3,87)] = Path, [(111,45)] = Path, [(71,117)] = Path, [(79,30)]
        = Path, [(67,117)] = Path, [(29,86)] = Path, [(97,36)] = Path,
        [(83,101)] = Path, [(31,87)] = Path, [(87,121)] = Path, [(68,109)] =
        Path, [(43,8)] = Path, [(80,95)] = Path, [(39,25)] = Path, [(84,23)] =
        Path, [(26,63)] = Path, [(71,7)] = Path, [(93,59)] = Path, [(42,121)] =
        Path, [(26,45)] = Path, [(55,3)] = Path, [(7,118)] = Path, [(33,67)] =
        Path, [(107,37)] = Path, [(23,41)] = Path, [(34,17)] = Path, [(46,93)]
        = Path, [(45,29)] = Path, [(61,113)] = Path, [(81,115)] = Path,
        [(25,35)] = Path, [(110,83)] = Path, [(43,104)] = Path, [(31,92)] =
        Path, [(15,43)] = Path, [(78,113)] = Path, [(9,26)] = Path, [(108,13)]
        = Path, [(31,10)] = Path, [(107,103)] = Path, [(65,99)] = Path,
        [(33,73)] = Path, [(7,17)] = Path, [(17,116)] = Path, [(119,38)] =
        Path, [(118,111)] = Path, [(81,21)] = Path, [(112,89)] = Path, [(44,5)]
        = Path, [(55,20)] = Path, [(23,32)] = Path, [(99,102)] = Path,
        [(95,91)] = Path, [(97,123)] = Path, [(110,119)] = Path, [(93,81)] =
        Path, [(93,33)] = Path, [(92,121)] = Path, [(113,29)] = Path, [(57,11)]
        = Path, [(116,83)] = Path, [(23,67)] = Path, [(117,34)] = Path,
        [(12,123)] = Path, [(73,16)] = Path, [(99,51)] = Path, [(83,19)] =
        Path, [(116,109)] = Path, [(73,101)] = Path, [(91,113)] = Path,
        [(107,60)] = Path, [(113,63)] = Path, [(121,97)] = Path, [(85,96)] =
        Path, [(21,23)] = Path, [(9,98)] = Path, [(17,23)] = Path, [(101,29)] =
        Path, [(32,105)] = Path, [(78,119)] = Path, [(19,37)] = Path,
        [(53,119)] = Path, [(32,57)] = Path, [(105,30)] = Path, [(26,59)] =
        Path, [(36,7)] = Path, [(61,30)] = Path, [(65,9)] = Path, [(117,87)] =
        Path, [(13,89)] = Path, [(89,33)] = Path, [(95,71)] = Path, [(53,10)] =
        Path, [(101,103)] = Path, [(19,29)] = Path, [(13,51)] = Path, [(24,99)]
        = Path, [(97,3)] = Path, [(119,79)] = Path, [(46,103)] = Path,
        [(29,70)] = Path, [(8,19)] = Path, [(103,21)] = Path, [(87,23)] = Path,
        [(113,70)] = Path, [(59,12)] = Path, [(36,29)] = Path, [(66,99)] =
        Path, [(17,123)] = Path, [(31,28)] = Path, [(95,86)] = Path, [(53,121)]
        = Path, [(16,57)] = Path, [(15,109)] = Path, [(55,115)] = Path,
        [(95,19)] = Path, [(9,76)] = Path, [(86,111)] = Path, [(7,121)] = Path,
        [(5,105)] = Path, [(114,29)] = Path, [(23,91)] = Path, [(32,91)] =
        Path, [(97,102)] = Path, [(121,62)] = Path, [(48,99)] = Path, [(31,63)]
        = Path, [(46,119)] = Path, [(33,60)] = Path, [(31,37)] = Path,
        [(120,31)] = Path, [(99,23)] = Path, [(19,26)] = Path, [(37,112)] =
        Path, [(39,12)] = Path, [(117,90)] = Path, [(74,5)] = Path, [(3,67)] =
        Path, [(16,113)] = Path, [(106,35)] = Path, [(13,78)] = Path,
        [(114,45)] = Path, [(16,41)] = Path, [(118,53)] = Path, [(79,97)] =
        Path, [(19,31)] = Path, [(12,13)] = Path, [(115,116)] = Path, [(17,19)]
        = Path, [(34,13)] = Path, [(16,61)] = Path, [(97,9)] = Path, [(97,43)]
        = Path, [(7,89)] = Path, [(110,37)] = Path, [(17,101)] = Path,
        [(13,35)] = Path, [(75,11)] = Path, [(63,25)] = Path, [(7,84)] = Path,
        [(87,29)] = Path, [(23,10)] = Path, [(91,91)] = Path, [(112,9)] = Path,
        [(87,31)] = Path, [(68,115)] = Path, [(55,114)] = Path, [(108,121)] =
        Path, [(90,115)] = Path, [(36,101)] = Path, [(105,43)] = Path,
        [(19,46)] = Path, [(92,35)] = Path, [(53,21)] = Path, [(43,2)] =
        Outer(34,75), [(65,94)] = Path, [(119,22)] = Path, [(70,21)] = Path,
        [(81,117)] = Path, [(46,101)] = Path, [(96,35)] = Path, [(63,27)] =
        Path, [(9,23)] = Path, [(33,119)] = Path, [(6,73)] = Path, [(49,95)] =
        Path, [(58,107)] = Path, [(48,93)] = Path, [(55,99)] = Path, [(83,93)]
        = Path, [(97,56)] = Path, [(10,59)] = Path, [(65,31)] = Path, [(21,40)]
        = Path, [(16,73)] = Path, [(63,104)] = Path, [(63,32)] = Path,
        [(40,33)] = Path, [(102,21)] = Path, [(91,5)] = Path, [(113,113)] =
        Path, [(113,111)] = Path, [(13,23)] = Path, [(45,10)] = Path, [(7,37)]
        = Path, [(117,105)] = Path, [(17,81)] = Path, [(91,90)] = Path,
        [(60,25)] = Path, [(55,107)] = Path, [(40,31)] = Path, [(3,107)] =
        Path, [(81,13)] = Path, [(98,113)] = Path, [(9,29)] = Path, [(25,58)] =
        Path, [(105,91)] = Path, [(56,121)] = Path, [(26,55)] = Path,
        [(26,121)] = Path, [(119,8)] = Path, [(107,55)] = Path, [(106,43)] =
        Path, [(120,73)] = Path, [(4,37)] = Path, [(75,124)] = Outer(34,45),
        [(73,108)] = Path, [(66,101)] = Path, [(99,49)] = Path, [(51,9)] =
        Path, [(21,62)] = Path, [(115,109)] = Path, [(11,109)] = Path,
        [(19,101)] = Path, [(89,12)] = Path, [(109,65)] = Path, [(33,109)] =
        Path, [(32,71)] = Path, [(103,31)] = Path, [(69,27)] = Path, [(83,8)] =
        Path, [(31,53)] = Path, [(59,21)] = Path, [(71,115)] = Path, [(22,27)]
        = Path, [(13,7)] = Path, [(97,65)] = Path, [(99,63)] = Path, [(103,41)]
        = Path, [(107,45)] = Path, [(75,33)] = Path, [(96,59)] = Path, [(9,50)]
        = Path, [(23,78)] = Path, [(101,7)] = Path, [(4,23)] = Path, [(32,109)]
        = Path, [(35,107)] = Path, [(92,77)] = Path, [(7,105)] = Path,
        [(81,116)] = Path, [(6,7)] = Path, [(91,111)] = Path, [(84,29)] = Path,
        [(97,118)] = Path, [(91,43)] = Path, [(101,111)] = Path, [(65,33)] =
        Path, [(71,21)] = Path, [(43,101)] = Path, [(15,69)] = Path, [(117,77)]
        = Path, [(21,37)] = Path, [(24,23)] = Path, [(63,105)] = Path,
        [(37,94)] = Path, [(18,73)] = Path, [(98,7)] = Path, [(61,121)] = Path,
        [(75,99)] = Path, [(15,100)] = Path, [(120,91)] = Path, [(37,115)] =
        Path, [(47,31)] = Path, [(113,7)] = Path, [(69,117)] = Path, [(54,115)]
        = Path, [(91,99)] = Path, [(111,31)] = Path, [(101,98)] = Path,
        [(19,17)] = Path, [(57,121)] = Path, [(117,81)] = Path, [(5,27)] =
        Path, [(91,51)] = Path, [(97,93)] = Path, [(13,96)] = Path, [(87,101)]
        = Path, [(3,19)] = Path, [(97,108)] = Path, [(62,103)] = Path,
        [(48,109)] = Path, [(111,118)] = Path, [(15,12)] = Path, [(101,35)] =
        Path, [(64,33)] = Path, [(73,93)] = Path, [(104,11)] = Path, [(5,11)] =
        Path, [(19,15)] = Path, [(24,5)] = Path, [(4,87)] = Path, [(77,109)] =
        Path, [(56,11)] = Path, [(15,121)] = Path, [(39,31)] = Path, [(29,10)]
        = Path, [(37,19)] = Path, [(119,83)] = Path, [(33,86)] = Path,
        [(61,95)] = Path, [(92,23)] = Path, [(17,70)] = Path, [(23,107)] =
        Path, [(92,37)] = Path, [(101,106)] = Path, [(117,70)] = Path,
        [(90,21)] = Path, [(67,15)] = Path, [(3,65)] = Path, [(41,123)] = Path,
        [(116,73)] = Path, [(9,107)] = Path, [(87,26)] = Path, [(101,17)] =
        Path, [(111,97)] = Path, [(27,93)] = Path, [(13,33)] = Path, [(81,14)]
        = Path, [(105,21)] = Path, [(19,33)] = Path, [(111,15)] = Path,
        [(5,97)] = Path, [(29,115)] = Path, [(115,26)] = Path, [(11,59)] =
        Path, [(111,104)] = Path, [(3,122)] = Path, [(28,63)] = Path, [(97,13)]
        = Path, [(69,99)] = Path, [(119,106)] = Path, [(118,23)] = Path,
        [(17,59)] = Path, [(111,4)] = Path, [(99,36)] = Path, [(95,99)] = Path,
        [(37,15)] = Path, [(111,101)] = Path, [(97,42)] = Path, [(111,34)] =
        Path, [(55,95)] = Path, [(37,33)] = Path, [(83,12)] = Path, [(53,29)] =
        Path, [(57,15)] = Path, [(117,23)] = Path, [(93,23)] = Path, [(24,67)]
        = Path, [(104,111)] = Path, [(12,65)] = Path, [(86,33)] = Path,
        [(107,98)] = Path, [(98,91)] = Path, [(118,85)] = Path, [(20,103)] =
        Path, [(51,21)] = Path, [(43,31)] = Path, [(57,117)] = Path,
        [(119,102)] = Path, [(80,123)] = Path, [(93,39)] = Path, [(95,21)] =
        Path, [(17,43)] = Path, [(17,91)] = Path, [(15,15)] = Path, [(79,33)] =
        Path, [(34,103)] = Path, [(109,75)] = Path, [(89,115)] = Path,
        [(98,45)] = Path, [(19,114)] = Path, [(39,95)] = Path, [(25,113)] =
        Path, [(119,113)] = Path, [(27,109)] = Path, [(21,79)] = Path, [(6,69)]
        = Path, [(16,7)] = Path, [(113,112)] = Path, [(57,111)] = Path,
        [(17,68)] = Path, [(51,17)] = Path, [(102,97)] = Path, [(19,10)] =
        Path, [(78,111)] = Path, [(110,123)] = Path, [(99,91)] = Path,
        [(95,12)] = Path, [(18,51)] = Path, [(115,6)] = Path, [(10,51)] = Path,
        [(11,92)] = Path, [(47,122)] = Path, [(84,99)] = Path, [(63,103)] =
        Path, [(9,20)] = Path, [(21,101)] = Path, [(57,23)] = Path, [(115,111)]
        = Path, [(59,92)] = Inner(122,51), [(102,121)] = Path, [(113,105)] =
        Path, [(69,113)] = Path, [(9,21)] = Path, [(19,41)] = Path, [(104,59)]
        = Path, [(98,61)] = Path, [(13,21)] = Path, [(25,3)] = Path, [(86,123)]
        = Path, [(13,44)] = Path, [(18,81)] = Path, [(119,35)] = Path,
        [(21,75)] = Path, [(31,88)] = Path, [(119,12)] = Path, [(86,7)] = Path,
        [(109,69)] = Path, [(80,31)] = Path, [(111,81)] = Path, [(5,101)] =
        Path, [(40,123)] = Path, [(120,87)] = Path, [(95,27)] = Path,
        [(27,111)] = Path, [(23,104)] = Path, [(8,63)] = Path, [(47,109)] =
        Path, [(119,27)] = Path, [(95,28)] = Path, [(104,123)] = Path,
        [(67,11)] = Path, [(41,101)] = Path, [(21,13)] = Path, [(14,97)] =
        Path, [(75,30)] = Path, [(55,13)] = Path, [(111,38)] = Path, [(91,81)]
        = Path, [(60,103)] = Path, [(69,97)] = Path, [(84,111)] = Path,
        [(34,19)] = Path, [(79,101)] = Path, [(45,111)] = Path, [(100,57)] =
        Path, [(25,105)] = Path, [(88,23)] = Path, [(27,25)] = Path, [(25,21)]
        = Path, [(93,43)] = Path, [(7,69)] = Path, [(14,13)] = Path, [(48,113)]
        = Path, [(100,39)] = Path, [(81,107)] = Path, [(37,4)] = Path, [(20,5)]
        = Path, [(107,56)] = Path, [(73,32)] = Path, [(51,102)] = Path,
        [(115,4)] = Path, [(118,73)] = Path, [(25,19)] = Path, [(105,119)] =
        Path, [(109,30)] = Path, [(63,101)] = Path, [(93,30)] = Path, [(93,58)]
        = Path, [(89,122)] = Path, [(115,75)] = Path, [(3,21)] = Path,
        [(12,37)] = Path, [(45,113)] = Path, [(103,91)] = Path, [(109,47)] =
        Path, [(101,75)] = Path, [(23,62)] = Path, [(91,72)] = Path, [(43,109)]
        = Path, [(41,113)] = Path, [(22,61)] = Path, [(24,97)] = Path,
        [(68,123)] = Path, [(17,78)] = Path, [(6,19)] = Path, [(65,30)] = Path,
        [(31,43)] = Path, [(20,71)] = Path, [(115,3)] = Path, [(105,44)] =
        Path, [(105,106)] = Path, [(101,117)] = Path, [(47,99)] = Path,
        [(17,93)] = Path, [(105,87)] = Path, [(93,96)] = Path, [(120,5)] =
        Path, [(41,121)] = Path, [(9,3)] = Path, [(44,17)] = Path, [(9,49)] =
        Path, [(18,7)] = Path, [(105,6)] = Path, [(103,71)] = Path, [(118,121)]
        = Path, [(24,47)] = Path, [(55,17)] = Path, [(9,27)] = Path, [(21,33)]
        = Path, [(108,67)] = Path, [(5,54)] = Path, [(85,25)] = Path, [(5,64)]
        = Path, [(73,20)] = Path, [(7,93)] = Path, [(12,3)] = Path, [(15,74)] =
        Path, [(25,117)] = Path, [(27,5)] = Path, [(97,14)] = Path, [(19,85)] =
        Path, [(113,103)] = Path, [(71,93)] = Path, [(5,88)] = Path, [(64,93)]
        = Path, [(5,83)] = Path, [(117,112)] = Path, [(45,26)] = Path,
        [(121,87)] = Path, [(33,79)] = Path, [(23,90)] = Path, [(51,99)] =
        Path, [(75,5)] = Path, [(75,101)] = Path, [(35,6)] = Path, [(50,109)] =
        Path, [(111,93)] = Path, [(15,37)] = Path, [(108,51)] = Path, [(13,29)]
        = Path, [(95,26)] = Path, [(9,116)] = Path, [(112,57)] = Path,
        [(99,37)] = Path, [(53,110)] = Path, [(81,3)] = Path, [(3,92)] = Path,
        [(73,8)] = Path, [(37,121)] = Path, [(112,85)] = Path, [(47,17)] =
        Path, [(21,34)] = Path, [(59,117)] = Path, [(5,35)] = Path, [(32,67)] =
        Path, [(105,29)] = Path, [(98,89)] = Path, [(7,99)] = Path, [(6,105)] =
        Path, [(17,85)] = Path, [(61,15)] = Path, [(27,115)] = Path, [(82,21)]
        = Path, [(111,6)] = Path, [(26,77)] = Path, [(93,49)] = Path,
        [(96,117)] = Path, [(23,33)] = Path, [(112,15)] = Path, [(8,113)] =
        Path, [(105,27)] = Path, [(93,120)] = Path, [(47,111)] = Path,
        [(107,35)] = Path, [(13,101)] = Path, [(57,109)] = Path, [(50,21)] =
        Path, [(64,13)] = Path, [(71,9)] = Path, [(45,6)] = Path, [(57,27)] =
        Path, [(69,109)] = Path, [(83,26)] = Path, [(79,6)] = Path, [(34,29)] =
        Path, [(114,105)] = Path, [(63,6)] = Path, [(75,107)] = Path,
        [(111,99)] = Path, [(5,57)] = Path, [(41,13)] = Path, [(95,44)] = Path,
        [(111,85)] = Path, [(105,93)] = Path, [(113,121)] = Path, [(59,19)] =
        Path, [(113,55)] = Path, [(91,109)] = Path, [(111,36)] = Path,
        [(102,5)] = Path, [(97,27)] = Path, [(103,14)] = Path, [(50,3)] = Path,
        [(28,21)] = Path, [(21,27)] = Path, [(117,39)] = Path, [(83,31)] =
        Path, [(111,57)] = Path, [(106,81)] = Path, [(66,33)] = Path,
        [(65,109)] = Path, [(113,15)] = Path, [(63,117)] = Path, [(97,75)] =
        Path, [(111,29)] = Path, [(105,68)] = Path, [(34,7)] = Path, [(54,31)]
        = Path, [(88,17)] = Path, [(71,104)] = Path, [(17,99)] = Path,
        [(49,20)] = Path, [(45,33)] = Path, [(97,7)] = Path, [(111,21)] = Path,
        [(93,34)] = Path, [(95,77)] = Path, [(28,79)] = Path, [(7,31)] = Path,
        [(113,75)] = Path, [(27,75)] = Path, [(100,43)] = Path, [(83,109)] =
        Path, [(55,30)] = Path, [(13,59)] = Path, [(119,21)] = Path, [(116,79)]
        = Path, [(20,73)] = Path, [(111,20)] = Path, [(29,59)] = Path,
        [(95,121)] = Path, [(24,37)] = Path, [(51,118)] = Path, [(29,15)] =
        Path, [(26,81)] = Path, [(5,25)] = Path, [(103,112)] = Path, [(12,29)]
        = Path, [(53,22)] = Path, [(99,24)] = Path, [(15,107)] = Path,
        [(108,43)] = Path, [(86,29)] = Path, [(55,94)] = Path, [(110,19)] =
        Path, [(28,9)] = Path, [(122,61)] = Outer(34,71), [(111,35)] = Path,
        [(50,113)] = Path, [(27,13)] = Path, [(102,11)] = Path, [(117,122)] =
        Path, [(4,25)] = Path, [(107,8)] = Path, [(121,26)] = Path, [(28,87)] =
        Path, [(61,29)] = Path, [(22,123)] = Path, [(21,103)] = Path, [(73,9)]
        = Path, [(74,93)] = Path, [(37,113)] = Path, [(24,119)] = Path,
        [(87,33)] = Path, [(113,56)] = Path, [(99,29)] = Path, [(41,24)] =
        Path, [(119,123)] = Path, [(57,97)] = Path, [(21,69)] = Path,
        [(113,109)] = Path, [(83,116)] = Path, [(103,49)] = Path, [(100,103)] =
        Path, [(54,19)] = Path, [(17,12)] = Path, [(34,27)] = Path, [(58,19)] =
        Path, [(16,95)] = Path, [(75,109)] = Path, [(77,103)] = Path,
        [(105,42)] = Path, [(113,26)] = Path, [(112,115)] = Path, [(90,81)] =
        Inner(122,83), [(56,107)] = Path, [(19,53)] = Path, [(107,95)] = Path,
        [(44,105)] = Path, [(90,45)] = Inner(2,59), [(3,71)] = Path, [(77,11)]
        = Path, [(65,21)] = Path, [(120,83)] = Path, [(19,99)] = Path,
        [(13,67)] = Path, [(99,11)] = Path, [(110,43)] = Path, [(3,38)] = Path,
        [(18,11)] = Path, [(114,119)] = Path, [(97,69)] = Path, [(15,10)] =
        Path, [(47,16)] = Path, [(25,20)] = Path, [(43,27)] = Path, [(95,101)]
        = Path, [(113,42)] = Path, [(98,85)] = Path, [(99,123)] = Path,
        [(93,6)] = Path, [(31,69)] = Path, [(33,17)] = Path, [(88,13)] = Path,
        [(11,53)] = Path, [(62,115)] = Path, [(66,93)] = Path, [(17,122)] =
        Path, [(41,21)] = Path, [(69,104)] = Path, [(11,121)] = Path, [(29,84)]
        = Path, [(105,36)] = Path, [(47,110)] = Path, [(23,105)] = Path,
        [(95,32)] = Path, [(109,73)] = Path, [(121,79)] = Path, [(25,40)] =
        Path, [(104,53)] = Path, [(37,98)] = Path, [(90,111)] = Path, [(5,49)]
        = Path, [(7,23)] = Path, [(24,91)] = Path, [(95,5)] = Path, [(6,33)] =
        Path, [(61,9)] = Path, [(13,53)] = Path, [(3,40)] = Path, [(55,100)] =
        Path, [(120,123)] = Path, [(31,41)] = Path, [(121,23)] = Path,
        [(105,7)] = Path, [(23,65)] = Path, [(97,31)] = Path, [(20,93)] = Path,
        [(84,105)] = Path, [(15,61)] = Path, [(5,69)] = Path, [(41,25)] = Path,
        [(57,2)] = Outer(67,92), [(30,41)] = Path, [(43,32)] = Path, [(79,109)]
        = Path, [(60,123)] = Path, [(99,98)] = Path, [(53,17)] = Path,
        [(47,21)] = Path, [(64,123)] = Path, [(27,29)] = Path, [(77,18)] =
        Path, [(91,107)] = Path, [(43,23)] = Path, [(55,7)] = Path, [(91,29)] =
        Path, [(55,22)] = Path, [(10,97)] = Path, [(85,27)] = Path, [(105,97)]
        = Path, [(79,104)] = Path, [(5,67)] = Path, [(74,113)] = Path,
        [(34,119)] = Path, [(39,105)] = Path, [(71,112)] = Path, [(27,17)] =
        Path, [(6,63)] = Path, [(30,3)] = Path, [(107,38)] = Path, [(75,121)] =
        Path, [(20,15)] = Path, [(88,27)] = Path, [(11,29)] = Path, [(99,65)] =
        Path, [(120,75)] = Path, [(101,15)] = Path, [(85,5)] = Path, [(104,77)]
        = Path, [(37,17)] = Path, [(104,103)] = Path, [(82,121)] = Path,
        [(104,17)] = Path, [(73,104)] = Path, [(22,23)] = Path, [(17,89)] =
        Path, [(93,93)] = Path, [(43,19)] = Path, [(105,53)] = Path, [(55,108)]
        = Path, [(112,103)] = Path, [(18,95)] = Path, [(91,44)] = Path,
        [(44,109)] = Path, [(121,117)] = Path, [(113,5)] = Path, [(11,65)] =
        Path, [(109,36)] = Path, [(119,7)] = Path, [(5,95)] = Path, [(19,115)]
        = Path, [(19,3)] = Path, [(41,99)] = Path, [(73,3)] = Path, [(16,101)]
        = Path, [(73,25)] = Path, [(18,61)] = Path, [(17,22)] = Path, [(63,2)]
        = Outer(53,92), [(17,21)] = Path, [(95,29)] = Path, [(97,113)] = Path,
        [(5,3)] = Path, [(23,5)] = Path, [(121,69)] = Path, [(35,8)] = Path,
        [(107,89)] = Path, [(10,69)] = Path, [(9,70)] = Path, [(121,37)] =
        Path, [(39,100)] = Path, [(105,13)] = Path, [(31,44)] = Path, [(31,76)]
        = Path, [(21,95)] = Path, [(3,41)] = Path, [(31,77)] = Path, [(17,111)]
        = Path, [(10,71)] = Path, [(6,59)] = Path, [(33,84)] = Path, [(53,27)]
        = Path, [(19,95)] = Path, [(45,15)] = Path, [(109,59)] = Path,
        [(42,13)] = Path, [(31,111)] = Path, [(121,65)] = Path, [(121,15)] =
        Path, [(38,21)] = Path, [(119,53)] = Path, [(31,97)] = Path, [(11,12)]
        = Path, [(10,81)] = Path, [(9,41)] = Path, [(99,18)] = Path, [(34,111)]
        = Path, [(13,105)] = Path, [(107,111)] = Path, [(19,11)] = Path,
        [(101,105)] = Path, [(37,99)] = Path, [(97,53)] = Path, [(67,115)] =
        Path, [(116,61)] = Path, [(27,68)] = Path, [(5,99)] = Path, [(11,32)] =
        Path, [(8,55)] = Path, [(98,67)] = Path, [(31,45)] = Path, [(43,28)] =
        Path, [(58,93)] = Path, [(13,48)] = Path, [(85,12)] = Path, [(11,31)] =
        Path, [(18,77)] = Path, [(75,12)] = Path, [(59,112)] = Path, [(13,25)]
        = Path, [(9,64)] = Path, [(49,13)] = Path, [(25,31)] = Path, [(61,24)]
        = Path, [(43,93)] = Path, [(51,11)] = Path, [(8,15)] = Path, [(27,49)]
        = Path, [(108,91)] = Path, [(47,117)] = Path, [(117,117)] = Path,
        [(107,50)] = Path, [(41,29)] = Path, [(28,119)] = Path, [(95,97)] =
        Path, [(35,99)] = Path, [(91,71)] = Path, [(75,16)] = Path, [(107,3)] =
        Path, [(99,67)] = Path, [(85,29)] = Path, [(37,105)] = Path, [(15,114)]
        = Path, [(5,16)] = Path, [(3,29)] = Path, [(53,6)] = Path, [(80,17)] =
        Path, [(108,59)] = Path, [(103,117)] = Path, [(39,124)] = Outer(51,92),
        [(7,53)] = Path, [(33,54)] = Path, [(39,115)] = Path, [(17,74)] = Path,
        [(73,11)] = Path, [(94,39)] = Path, [(119,77)] = Path, [(77,24)] =
        Path, [(113,45)] = Path, [(40,5)] = Path, [(91,38)] = Path, [(11,79)] =
        Path, [(105,117)] = Path, [(68,21)] = Path, [(55,32)] = Path, [(27,52)]
        = Path, [(111,3)] = Path, [(81,108)] = Path, [(78,23)] = Path,
        [(101,116)] = Path, [(105,9)] = Path, [(11,78)] = Path, [(63,9)] =
        Path, [(13,31)] = Path, [(81,95)] = Path, [(76,5)] = Path, [(111,19)] =
        Path, [(115,99)] = Path, [(11,102)] = Path, [(77,101)] = Path,
        [(10,113)] = Path, [(53,114)] = Path, [(106,79)] = Path, [(87,123)] =
        Path, [(79,18)] = Path, [(109,95)] = Path, [(37,123)] = Path,
        [(73,122)] = Path, [(34,85)] = Inner(2,71), [(65,123)] = Path,
        [(113,27)] = Path, [(73,27)] = Path, [(91,75)] = Path, [(17,88)] =
        Path, [(26,47)] = Path, [(49,4)] = Path, [(65,115)] = Path, [(33,51)] =
        Path, [(112,71)] = Path, [(9,53)] = Path, [(91,30)] = Path, [(71,32)] =
        Path, [(51,13)] = Path, [(25,96)] = Path, [(61,108)] = Path,
        [(107,102)] = Path, [(116,5)] = Path, [(118,83)] = Path, [(99,80)] =
        Path, [(106,45)] = Path, [(45,19)] = Path, [(85,11)] = Path, [(23,56)]
        = Path, [(22,5)] = Path, [(43,99)] = Path, [(73,112)] = Path, [(57,94)]
        = Path, [(99,71)] = Path, [(5,58)] = Path, [(118,49)] = Path,
        [(111,75)] = Path, [(65,118)] = Path, [(31,24)] = Path, [(76,21)] =
        Path, [(111,73)] = Path, [(101,41)] = Path, [(45,95)] = Path,
        [(117,60)] = Path, [(97,63)] = Path, [(49,29)] = Path, [(71,16)] =
        Path, [(121,5)] = Path, [(19,93)] = Path, [(35,16)] = Path, [(81,99)] =
        Path, [(93,24)] = Path, [(17,40)] = Path, [(49,5)] = Path, [(105,75)] =
        Path, [(17,60)] = Path, [(32,77)] = Path, [(22,43)] = Path, [(35,3)] =
        Path, [(120,43)] = Path, [(15,36)] = Path, [(107,18)] = Path, [(28,47)]
        = Path, [(19,109)] = Path, [(11,100)] = Path, [(15,90)] = Path,
        [(3,57)] = Path, [(54,27)] = Path, [(79,24)] = Path, [(109,89)] = Path,
        [(10,109)] = Path, [(27,51)] = Path, [(59,9)] = Path, [(3,70)] = Path,
        [(29,106)] = Path, [(23,27)] = Path, [(25,65)] = Path, [(17,42)] =
        Path, [(79,108)] = Path, [(9,47)] = Path, [(65,22)] = Path, [(95,47)] =
        Path, [(114,69)] = Path, [(95,83)] = Path, [(42,25)] = Path, [(81,15)]
        = Path, [(18,97)] = Path, [(7,111)] = Path, [(10,15)] = Path, [(47,30)]
        = Path, [(39,18)] = Path, [(101,97)] = Path, [(7,122)] = Path,
        [(93,13)] = Path, [(10,9)] = Path, [(120,109)] = Path, [(65,6)] = Path,
        [(121,29)] = Path, [(44,15)] = Path, [(95,78)] = Path, [(105,107)] =
        Path, [(86,101)] = Path, [(23,97)] = Path, [(105,96)] = Path, [(14,53)]
        = Path, [(109,37)] = Path, [(79,113)] = Path, [(5,103)] = Path,
        [(29,117)] = Path, [(19,35)] = Path, [(19,59)] = Path, [(119,96)] =
        Path, [(61,32)] = Path, [(53,13)] = Path, [(13,65)] = Path, [(110,113)]
        = Path, [(26,5)] = Path, [(53,95)] = Path, [(29,23)] = Path, [(119,41)]
        = Path, [(26,123)] = Path, [(65,119)] = Path, [(47,33)] = Path,
        [(71,99)] = Path, [(23,88)] = Path, [(7,40)] = Path, [(17,39)] = Path,
        [(21,100)] = Path, [(35,112)] = Path, [(93,78)] = Path, [(109,9)] =
        Path, [(21,113)] = Path, [(6,61)] = Path, [(86,19)] = Path, [(29,57)] =
        Path, [(10,105)] = Path, [(83,114)] = Path, [(37,107)] = Path,
        [(105,122)] = Path, [(103,64)] = Path, [(19,67)] = Path, [(11,43)] =
        Path, [(47,123)] = Path, [(43,17)] = Path, [(71,15)] = Path, [(51,124)]
        = Outer(90,85), [(6,71)] = Path, [(113,47)] = Path, [(33,37)] = Path,
        [(93,29)] = Path, [(59,28)] = Path, [(7,103)] = Path, [(61,26)] = Path,
        [(103,25)] = Path, [(11,41)] = Path, [(115,31)] = Path, [(11,113)] =
        Path, [(19,63)] = Path, [(10,123)] = Path, [(73,111)] = Path,
        [(75,120)] = Path, [(83,11)] = Path, [(19,38)] = Path, [(104,33)] =
        Path, [(11,19)] = Path, [(59,27)] = Path, [(43,105)] = Path,
        [(120,113)] = Path, [(85,113)] = Path, [(30,61)] = Path, [(61,8)] =
        Path, [(99,107)] = Path, [(39,20)] = Path, [(109,87)] = Path, [(33,85)]
        = Path, [(7,95)] = Path, [(51,106)] = Path, [(24,7)] = Path, [(109,11)]
        = Path, [(19,28)] = Path, [(104,95)] = Path, [(32,19)] = Path,
        [(103,15)] = Path, [(10,115)] = Path, [(87,7)] = Path, [(61,114)] =
        Path, [(43,34)] = Inner(85,2), [(42,99)] = Path, [(103,50)] = Path,
        [(74,95)] = Path, [(15,88)] = Path, [(59,29)] = Path, [(63,33)] = Path,
        [(74,111)] = Path, [(30,33)] = Path, [(116,75)] = Path, [(93,83)] =
        Path, [(114,3)] = Path, [(103,100)] = Path, [(16,27)] = Path,
        [(107,97)] = Path, [(24,95)] = Path, [(70,111)] = Path, [(33,122)] =
        Path, [(99,101)] = Path, [(19,122)] = Path, [(91,56)] = Path, [(13,13)]
        = Path, [(93,9)] = Path, [(29,34)] = Path, [(35,22)] = Path,
        [(117,120)] = Path, [(31,66)] = Path, [(58,97)] = Path, [(29,56)] =
        Path, [(25,87)] = Path, [(27,33)] = Path, [(120,105)] = Path,
        [(95,113)] = Path, [(7,51)] = Path, [(22,85)] = Path, [(91,33)] = Path,
        [(82,29)] = Path, [(25,92)] = Path, [(90,59)] = Inner(2,77), [(94,99)]
        = Path, [(27,41)] = Path, [(13,47)] = Path, [(75,94)] = Path,
        [(76,119)] = Path, [(7,61)] = Path, [(23,112)] = Path, [(35,17)] =
        Path, [(19,107)] = Path, [(13,75)] = Path, [(47,8)] = Path, [(7,49)] =
        Path, [(35,97)] = Path, [(57,17)] = Path, [(17,96)] = Path, [(98,57)] =
        Path, [(47,13)] = Path, [(11,103)] = Path, [(79,27)] = Path, [(68,95)]
        = Path, [(23,85)] = Path, [(106,27)] = Path, [(85,108)] = Path,
        [(71,31)] = Path, [(97,35)] = Path, [(30,117)] = Path, [(85,9)] = Path,
        [(97,117)] = Path, [(63,29)] = Path, [(3,9)] = Path, [(107,61)] = Path,
        [(100,83)] = Path, [(91,9)] = Path, [(17,121)] = Path, [(81,32)] =
        Path, [(13,79)] = Path, [(19,43)] = Path, [(93,19)] = Path, [(121,52)]
        = Path, [(98,79)] = Path, [(119,20)] = Path, [(49,17)] = Path,
        [(107,21)] = Path, [(71,103)] = Path, [(9,56)] = Path, [(16,123)] =
        Path, [(37,13)] = Path, [(41,18)] = Path, [(121,53)] = Path,
        [(103,119)] = Path, [(86,31)] = Path, [(109,80)] = Path, [(95,65)] =
        Path, [(84,95)] = Path, [(33,49)] = Path, [(109,105)] = Path,
        [(35,106)] = Path, [(47,14)] = Path, [(102,103)] = Path, [(67,13)] =
        Path, [(101,9)] = Path, [(9,100)] = Path, [(61,21)] = Path, [(35,121)]
        = Path, [(33,7)] = Path, [(32,21)] = Path, [(19,5)] = Path, [(117,57)]
        = Path, [(109,34)] = Path, [(13,52)] = Path, [(47,103)] = Path,
        [(19,82)] = Path, [(111,43)] = Path, [(12,81)] = Path, [(103,47)] =
        Path, [(91,62)] = Path, [(33,47)] = Path, [(115,105)] = Path,
        [(21,112)] = Path, [(59,97)] = Path, [(75,108)] = Path, [(52,99)] =
        Path, [(7,29)] = Path, [(14,51)] = Path, [(29,11)] = Path, [(109,3)] =
        Path, [(7,19)] = Path, [(85,17)] = Path, [(91,3)] = Path, [(21,3)] =
        Path, [(105,39)] = Path, [(35,113)] = Path, [(36,21)] = Path, [(28,99)]
        = Path, [(105,31)] = Path, [(71,118)] = Path, [(71,4)] = Path,
        [(81,111)] = Path, [(118,17)] = Path, [(30,19)] = Path, [(49,99)] =
        Path, [(95,79)] = Path, [(91,74)] = Path, [(93,107)] = Path, [(91,21)]
        = Path, [(53,5)] = Path, [(96,95)] = Path, [(100,5)] = Path, [(117,97)]
        = Path, [(105,25)] = Path, [(111,68)] = Path, [(50,117)] = Path,
        [(39,101)] = Path, [(41,11)] = Path, [(65,121)] = Path, [(113,69)] =
        Path, [(97,17)] = Path, [(73,100)] = Path, [(11,86)] = Path, [(59,4)] =
        Path, [(96,53)] = Path, [(59,25)] = Path, [(49,34)] = Inner(2,85),
        [(89,111)] = Path, [(87,19)] = Path, [(94,55)] = Path, [(119,85)] =
        Path, [(11,30)] = Path, [(93,61)] = Path, [(11,122)] = Path, [(2,49)] =
        Outer(90,67), [(13,115)] = Path, [(101,90)] = Path, [(33,97)] = Path,
        [(95,25)] = Path, [(65,100)] = Path, [(31,102)] = Path, [(111,23)] =
        Path, [(40,93)] = Path, [(105,121)] = Path, [(98,81)] = Path, [(61,12)]
        = Path, [(89,28)] = Path, [(97,61)] = Path, [(121,20)] = Path, [(5,46)]
        = Path, [(29,66)] = Path, [(25,73)] = Path, [(105,56)] = Path,
        [(73,92)] = Inner(122,41), [(11,116)] = Path, [(101,53)] = Path,
        [(120,107)] = Path, [(11,110)] = Path, [(115,22)] = Path, [(33,111)] =
        Path, [(65,29)] = Path, [(71,121)] = Path, [(7,92)] = Path, [(15,63)] =
        Path, [(117,14)] = Path, [(62,99)] = Path, [(13,95)] = Path, [(34,23)]
        = Path, [(9,71)] = Path, [(95,39)] = Path, [(11,18)] = Path, [(50,121)]
        = Path, [(31,39)] = Path, [(99,108)] = Path, [(115,83)] = Path,
        [(99,61)] = Path, [(121,107)] = Path, [(63,95)] = Path, [(18,109)] =
        Path, [(114,75)] = Path, [(25,71)] = Path, [(53,15)] = Path, [(89,13)]
        = Path, [(43,29)] = Path, [(103,121)] = Path, [(67,123)] = Path,
        [(58,29)] = Path, [(79,13)] = Path, [(96,93)] = Path, [(32,41)] = Path,
        [(57,8)] = Path, [(73,28)] = Path, [(72,31)] = Path, [(37,93)] = Path,
        [(90,123)] = Path, [(59,23)] = Path, [(51,108)] = Path, [(71,6)] =
        Path, [(60,11)] = Path, [(107,15)] = Path, [(99,10)] = Path, [(47,28)]
        = Path, [(41,100)] = Path, [(19,75)] = Path, [(48,29)] = Path,
        [(73,33)] = Path, [(52,25)] = Path, [(19,62)] = Path, [(67,97)] = Path,
        [(3,103)] = Path, [(113,39)] = Path, [(23,46)] = Path, [(5,43)] = Path,
        [(38,121)] = Path, [(37,96)] = Path, [(104,27)] = Path, [(111,59)] =
        Path, [(114,31)] = Path, [(73,6)] = Path, [(7,79)] = Path, [(93,73)] =
        Path, [(21,56)] = Path, [(19,47)] = Path, [(37,21)] = Path, [(25,77)] =
        Path, [(59,6)] = Path, [(53,107)] = Path, [(101,89)] = Path, [(45,98)]
        = Path, [(121,3)] = Path, [(86,93)] = Path, [(27,10)] = Path, [(28,45)]
        = Path, [(106,107)] = Path, [(63,112)] = Path, [(60,113)] = Path,
        [(63,5)] = Path, [(18,55)] = Path, [(107,117)] = Path, [(24,77)] =
        Path, [(5,9)] = Path, [(89,117)] = Path, [(8,115)] = Path, [(31,23)] =
        Path, [(113,73)] = Path, [(57,3)] = Path, [(61,102)] = Path, [(93,75)]
        = Path, [(23,81)] = Path, [(91,55)] = Path, [(65,105)] = Path, [(28,3)]
        = Path, [(59,103)] = Path, [(57,103)] = Path, [(65,112)] = Path,
        [(77,100)] = Path, [(18,29)] = Path, [(99,73)] = Path, [(87,95)] =
        Path, [(107,83)] = Path, [(91,83)] = Path, [(5,40)] = Path, [(23,49)] =
        Path, [(29,102)] = Path, [(48,15)] = Path, [(9,91)] = Path, [(19,7)] =
        Path, [(13,34)] = Path, [(23,18)] = Path, [(122,73)] = Outer(34,57),
        [(11,34)] = Path, [(71,105)] = Path, [(95,93)] = Path, [(107,108)] =
        Path, [(30,97)] = Path, [(8,37)] = Path, [(85,95)] = Path, [(116,23)] =
        Path, [(112,101)] = Path, [(91,48)] = Path, [(3,111)] = Path, [(17,36)]
        = Path, [(52,9)] = Path, [(26,31)] = Path, [(99,19)] = Path, [(103,32)]
        = Path, [(47,9)] = Path, [(20,89)] = Path, [(79,23)] = Path, [(47,4)] =
        Path, [(8,123)] = Path, [(117,25)] = Path, [(5,23)] = Path, [(121,4)] =
        Path, [(95,15)] = Path, [(113,35)] = Path, [(30,29)] = Path, [(6,103)]
        = Path, [(101,30)] = Path, [(112,117)] = Path, [(9,39)] = Path,
        [(43,13)] = Path, [(7,123)] = Path, [(85,115)] = Path, [(21,12)] =
        Path, [(85,119)] = Path, [(38,119)] = Path, [(109,92)] = Path, [(9,54)]
        = Path, [(17,106)] = Path, [(78,97)] = Path, [(15,65)] = Path,
        [(66,113)] = Path, [(79,111)] = Path, [(115,17)] = Path, [(79,123)] =
        Path, [(81,18)] = Path, [(29,43)] = Path, [(26,75)] = Path, [(39,106)]
        = Path, [(71,17)] = Path, [(115,35)] = Path, [(121,33)] = Path,
        [(27,30)] = Path, [(26,111)] = Path, [(9,33)] = Path, [(13,73)] = Path,
        [(35,21)] = Path, [(101,28)] = Path, [(49,93)] = Path, [(100,73)] =
        Path, [(107,57)] = Path, [(28,35)] = Path, [(23,61)] = Path, [(75,31)]
        = Path, [(105,66)] = Path, [(117,63)] = Path, [(83,113)] = Path,
        [(25,9)] = Path, [(99,16)] = Path, [(105,95)] = Path, [(106,69)] =
        Path, [(90,57)] = Inner(122,47), [(3,8)] = Path, [(105,62)] = Path,
        [(117,95)] = Path, [(94,93)] = Path, [(49,123)] = Path, [(105,123)] =
        Path, [(95,45)] = Path, [(114,99)] = Path, [(31,93)] = Path, [(121,50)]
        = Path, [(10,87)] = Path, [(39,17)] = Path, [(69,94)] = Path,
        [(111,25)] = Path, [(91,25)] = Path, [(100,37)] = Path, [(17,13)] =
        Path, [(39,6)] = Path, [(21,16)] = Path, [(15,16)] = Path, [(5,5)] =
        Path, [(119,43)] = Path, [(21,117)] = Path, [(28,19)] = Path,
        [(63,100)] = Path, [(9,123)] = Path, [(109,23)] = Path, [(121,64)] =
        Path, [(29,27)] = Path, [(121,9)] = Path, [(89,119)] = Path, [(31,101)]
        = Path, [(39,13)] = Path, [(97,97)] = Path, [(25,119)] = Path,
        [(11,38)] = Path, [(119,59)] = Path, [(15,116)] = Path, [(3,15)] =
        Path, [(69,25)] = Path, [(30,15)] = Path, [(23,109)] = Path, [(42,3)] =
        Path, [(107,23)] = Path, [(29,76)] = Path, [(121,109)] = Path,
        [(97,71)] = Path, [(27,66)] = Path, [(102,19)] = Path, [(113,51)] =
        Path, [(17,69)] = Path, [(71,10)] = Path, [(61,13)] = Path, [(47,107)]
        = Path, [(37,3)] = Path, [(100,115)] = Path, [(109,67)] = Path,
        [(89,15)] = Path, [(5,73)] = Path, [(7,11)] = Path, [(29,17)] = Path,
        [(53,123)] = Path, [(21,35)] = Path, [(105,11)] = Path, [(41,106)] =
        Path, [(25,109)] = Path, [(81,94)] = Path, [(88,3)] = Path, [(107,6)] =
        Path, [(121,31)] = Path, [(71,98)] = Path, [(119,103)] = Path,
        [(29,49)] = Path, [(17,86)] = Path, [(71,23)] = Path, [(120,19)] =
        Path, [(73,18)] = Path, [(22,93)] = Path, [(79,29)] = Path, [(17,7)] =
        Path, [(31,60)] = Path, [(92,27)] = Path, [(102,67)] = Path,
        [(112,121)] = Path, [(15,49)] = Path, [(5,29)] = Path, [(109,21)] =
        Path, [(95,68)] = Path, [(119,116)] = Path, [(25,100)] = Path,
        [(119,37)] = Path, [(112,95)] = Path, [(53,99)] = Path, [(9,81)] =
        Path, [(33,83)] = Path, [(32,23)] = Path, [(50,101)] = Path, [(5,114)]
        = Path, [(119,55)] = Path, [(110,57)] = Path, [(65,114)] = Path,
        [(61,4)] = Path, [(73,119)] = Path, [(61,19)] = Path, [(57,28)] = Path,
        [(119,45)] = Path, [(55,14)] = Path, [(93,25)] = Path, [(45,17)] =
        Path, [(109,79)] = Path, [(83,17)] = Path, [(113,123)] = Path, [(3,97)]
        = Path, [(29,12)] = Path, [(115,45)] = Path, [(98,49)] = Path,
        [(23,74)] = Path, [(117,43)] = Path, [(37,102)] = Path, [(92,51)] =
        Path, [(112,69)] = Path, [(104,61)] = Path, [(13,9)] = Path, [(47,105)]
        = Path, [(109,115)] = Path, [(35,119)] = Path, [(115,59)] = Path,
        [(36,99)] = Path, [(105,112)] = Path, [(106,103)] = Path, [(99,94)] =
        Path, [(29,123)] = Path, [(97,106)] = Path, [(118,103)] = Path,
        [(107,99)] = Path, [(25,14)] = Path, [(34,115)] = Path, [(99,27)] =
        Path, [(27,79)] = Path, [(68,97)] = Path, [(76,121)] = Path, [(115,65)]
        = Path, [(117,101)] = Path, [(47,97)] = Path, [(19,118)] = Path,
        [(101,51)] = Path, [(13,61)] = Path, [(53,7)] = Path, [(31,99)] = Path,
        [(95,57)] = Path, [(3,62)] = Path, [(27,87)] = Path, [(38,93)] = Path,
        [(7,78)] = Path, [(57,13)] = Path, [(117,13)] = Path, [(69,5)] = Path,
        [(29,119)] = Path, [(107,101)] = Path, [(47,120)] = Path, [(63,116)] =
        Path, [(29,81)] = Path, [(117,123)] = Path, [(71,109)] = Path,
        [(101,38)] = Path, [(11,21)] = Path, [(115,11)] = Path, [(109,84)] =
        Path, [(108,9)] = Path, [(109,5)] = Path, [(60,99)] = Path, [(77,15)] =
        Path, [(51,33)] = Path, [(31,105)] = Path, [(63,121)] = Path,
        [(113,28)] = Path, [(22,113)] = Path, [(119,99)] = Path, [(29,91)] =
        Path, [(109,17)] = Path, [(83,105)] = Path, [(27,19)] = Path,
        [(109,109)] = Path, [(11,115)] = Path, [(51,105)] = Path, [(3,54)] =
        Path, [(21,15)] = Path, [(14,9)] = Path, [(111,49)] = Path, [(21,82)] =
        Path, [(55,120)] = Path, [(69,11)] = Path, [(116,45)] = Path, [(5,21)]
        = Path, [(77,116)] = Path, [(59,10)] = Path, [(37,108)] = Path,
        [(89,24)] = Path, [(11,51)] = Path, [(114,37)] = Path, [(87,15)] =
        Path, [(15,103)] = Path, [(74,27)] = Path, [(113,53)] = Path,
        [(119,36)] = Path, [(39,29)] = Path, [(9,59)] = Path, [(103,98)] =
        Path, [(87,115)] = Path, [(25,94)] = Path, [(108,57)] = Path,
        [(61,119)] = Path, [(78,115)] = Path, [(97,44)] = Path, [(28,85)] =
        Path, [(23,34)] = Path, [(91,86)] = Path, [(9,85)] = Path, [(32,99)] =
        Path, [(99,13)] = Path, [(91,93)] = Path, [(97,119)] = Path, [(85,103)]
        = Path, [(55,101)] = Path, [(31,31)] = Path, [(71,106)] = Path,
        [(103,13)] = Path, [(104,57)] = Path, [(37,22)] = Path, [(97,112)] =
        Path, [(83,9)] = Path, [(45,21)] = Path, [(86,95)] = Path, [(27,119)] =
        Path, [(115,38)] = Path, [(17,92)] = Path, [(59,115)] = Path, [(33,15)]
        = Path, [(90,99)] = Path, [(5,110)] = Path, [(59,14)] = Path,
        [(107,14)] = Path, [(31,89)] = Path, [(95,4)] = Path, [(13,68)] = Path,
        [(115,8)] = Path, [(63,8)] = Path, [(15,41)] = Path, [(59,93)] = Path,
        [(112,99)] = Path, [(79,9)] = Path, [(23,14)] = Path, [(19,13)] = Path,
        [(73,23)] = Path, [(21,93)] = Path, [(83,24)] = Path, [(41,17)] = Path,
        [(69,121)] = Path, [(41,95)] = Path, [(15,102)] = Path, [(91,117)] =
        Path, [(95,61)] = Path, [(101,101)] = Path, [(119,47)] = Path,
        [(99,103)] = Path, [(27,107)] = Path, [(98,29)] = Path, [(79,105)] =
        Path, [(15,67)] = Path, [(60,105)] = Path, [(96,43)] = Path, [(55,29)]
        = Path, [(94,13)] = Path, [(78,123)] = Path, [(29,13)] = Path,
        [(105,83)] = Path, [(55,33)] = Path, [(112,11)] = Path, [(103,62)] =
        Path, [(85,13)] = Path, [(67,121)] = Path, [(96,89)] = Path, [(25,99)]
        = Path, [(27,37)] = Path, [(113,78)] = Path, [(115,101)] = Path,
        [(93,116)] = Path, [(102,53)] = Path, [(28,39)] = Path, [(121,44)] =
        Path, [(83,121)] = Path, [(104,79)] = Path, [(23,119)] = Path,
        [(5,112)] = Path, [(97,37)] = Path, [(83,23)] = Path, [(121,120)] =
        Path, [(107,73)] = Path, [(25,50)] = Path, [(31,113)] = Path,
        [(25,101)] = Path, [(9,51)] = Path, [(59,121)] = Path, [(63,13)] =
        Path, [(8,109)] = Path, [(21,84)] = Path, [(93,94)] = Path, [(65,101)]
        = Path, [(99,25)] = Path, [(85,124)] = Outer(67,34), [(59,110)] = Path,
        [(77,33)] = Path, [(109,51)] = Path, [(15,17)] = Path, [(56,7)] = Path,
        [(55,109)] = Path, [(113,9)] = Path, [(7,97)] = Path, [(75,103)] =
        Path, [(57,33)] = Path, [(111,47)] = Path, [(85,100)] = Path,
        [(79,100)] = Path, [(6,55)] = Path, [(117,29)] = Path, [(74,121)] =
        Path, [(84,11)] = Path, [(74,9)] = Path, [(9,92)] = Path, [(27,21)] =
        Path, [(35,114)] = Path, [(100,93)] = Path, [(121,103)] = Path,
        [(119,49)] = Path, [(79,7)] = Path, [(91,19)] = Path, [(57,19)] = Path,
        [(111,121)] = Path, [(102,87)] = Path, [(121,66)] = Path, [(44,21)] =
        Path, [(81,105)] = Path, [(96,75)] = Path, [(42,17)] = Path, [(4,3)] =
        Path, [(109,44)] = Path, [(7,52)] = Path, [(47,10)] = Path, [(25,43)] =
        Path, [(15,123)] = Path, [(6,41)] = Path, [(21,5)] = Path, [(87,11)] =
        Path, [(9,67)] = Path, [(69,13)] = Path, [(83,99)] = Path, [(9,68)] =
        Path, [(55,27)] = Path, [(13,69)] = Path, [(29,31)] = Path, [(88,11)] =
        Path, [(105,110)] = Path, [(99,17)] = Path, [(53,19)] = Path,
        [(87,106)] = Path, [(41,104)] = Path, [(9,90)] = Path, [(119,76)] =
        Path, [(34,101)] = Path, [(110,77)] = Path, [(65,116)] = Path,
        [(15,111)] = Path, [(17,115)] = Path, [(43,123)] = Path, [(42,33)] =
        Path, [(104,15)] = Path, [(17,103)] = Path, [(21,59)] = Path,
        [(14,111)] = Path, [(47,15)] = Path, [(5,14)] = Path, [(81,10)] = Path,
        [(36,119)] = Path, [(81,34)] = Inner(71,2), [(61,109)] = Path,
        [(33,115)] = Path, [(62,113)] = Path, [(112,83)] = Path, [(68,117)] =
        Path, [(121,104)] = Path, [(103,77)] = Path, [(21,32)] = Path,
        [(87,97)] = Path, [(43,103)] = Path, [(37,117)] = Path, [(109,61)] =
        Path, [(11,111)] = Path, [(111,53)] = Path, [(5,94)] = Path, [(5,33)] =
        Path, [(107,4)] = Path, [(77,105)] = Path, [(67,22)] = Path, [(87,9)] =
        Path, [(21,11)] = Path, [(3,49)] = Path, [(70,3)] = Path, [(7,87)] =
        Path, [(18,33)] = Path, [(77,110)] = Path, [(82,17)] = Path, [(59,116)]
        = Path, [(3,69)] = Path, [(43,3)] = Path, [(53,18)] = Path, [(89,109)]
        = Path, [(113,19)] = Path, [(95,64)] = Path, [(79,15)] = Path,
        [(26,107)] = Path, [(11,99)] = Path, [(59,22)] = Path, [(97,40)] =
        Path, [(101,91)] = Path, [(97,72)] = Path, [(115,18)] = Path,
        [(44,113)] = Path, [(51,97)] = Path, [(25,17)] = Path, [(71,94)] =
        Path, [(7,109)] = Path, [(27,67)] = Path, [(87,93)] = Path, [(26,101)]
        = Path, [(9,35)] = Path, [(97,25)] = Path, [(81,110)] = Path,
        [(69,111)] = Path, [(105,12)] = Path, [(57,112)] = Path, [(7,47)] =
        Path, [(28,91)] = Path, [(22,117)] = Path, [(75,20)] = Path, [(63,21)]
        = Path, [(19,91)] = Path, [(121,11)] = Path, [(29,89)] = Path,
        [(28,69)] = Path, [(95,105)] = Path, [(117,53)] = Path, [(35,9)] =
        Path, [(113,88)] = Path, [(113,65)] = Path, [(112,119)] = Path,
        [(19,81)] = Path, [(24,13)] = Path, [(21,121)] = Path, [(81,16)] =
        Path, [(109,43)] = Path, [(117,45)] = Path, [(106,95)] = Path,
        [(25,74)] = Path, [(103,55)] = Path, [(15,44)] = Path, [(35,103)] =
        Path, [(111,109)] = Path, [(33,101)] = Path, [(31,35)] = Path,
        [(72,13)] = Path, [(97,33)] = Path, [(35,23)] = Path, [(35,109)] =
        Path, [(7,36)] = Path, [(13,62)] = Path, [(49,27)] = Path, [(9,106)] =
        Path, [(59,114)] = Path, [(115,55)] = Path, [(29,7)] = Path, [(91,121)]
        = Path, [(69,26)] = Path, [(103,80)] = Path, [(15,20)] = Path,
        [(105,46)] = Path, [(11,17)] = Path, [(13,107)] = Path, [(57,118)] =
        Path, [(81,114)] = Path, [(73,103)] = Path, [(103,10)] = Path,
        [(59,11)] = Path, [(51,117)] = Path, [(119,19)] = Path, [(9,83)] =
        Path, [(115,71)] = Path, [(114,27)] = Path, [(101,49)] = Path,
        [(114,5)] = Path, [(109,39)] = Path, [(71,27)] = Path, [(65,17)] =
        Path, [(85,33)] = Path, [(121,78)] = Path, [(88,107)] = Path, [(34,11)]
        = Path, [(117,41)] = Path, [(61,99)] = Path, [(109,101)] = Path,
        [(23,25)] = Path, [(63,24)] = Path, [(23,43)] = Path, [(33,75)] = Path,
        [(114,57)] = Path, [(23,7)] = Path, [(119,31)] = Path, [(83,95)] =
        Path, [(118,65)] = Path, [(17,53)] = Path, [(33,35)] = Path, [(89,107)]
        = Path, [(11,44)] = Path, [(25,38)] = Path, [(23,77)] = Path,
        [(16,105)] = Path, [(74,23)] = Path, [(91,95)] = Path, [(114,47)] =
        Path, [(36,9)] = Path, [(47,18)] = Path, [(11,120)] = Path, [(33,103)]
        = Path, [(11,24)] = Path, [(23,86)] = Path, [(11,96)] = Path, [(15,29)]
        = Path, [(101,83)] = Path, [(18,71)] = Path, [(73,31)] = Path,
        [(99,117)] = Path, [(100,77)] = Path, [(25,123)] = Path, [(96,107)] =
        Path, [(9,5)] = Path, [(63,108)] = Path, [(13,108)] = Path, [(83,98)] =
        Path, [(76,123)] = Path, [(8,3)] = Path, [(15,27)] = Path, [(105,37)] =
        Path, [(41,122)] = Path, [(51,27)] = Path, [(101,14)] = Path,
        [(55,103)] = Path, [(31,17)] = Path, [(117,44)] = Path, [(18,117)] =
        Path, [(30,93)] = Path, [(102,111)] = Path, [(11,37)] = Path, [(30,65)]
        = Path, [(33,48)] = Path, [(110,75)] = Path, [(53,112)] = Path,
        [(17,56)] = Path, [(121,115)] = Path, [(97,99)] = Path, [(51,16)] =
        Path, [(83,117)] = Path, [(85,7)] = Path, [(105,116)] = Path,
        [(115,19)] = Path, [(19,57)] = Path, [(23,118)] = Path, [(117,42)] =
        Path, [(51,119)] = Path, [(32,115)] = Path, [(33,59)] = Path,
        [(48,119)] = Path, [(31,112)] = Path, [(119,44)] = Path, [(103,69)] =
        Path, [(40,29)] = Path, [(55,19)] = Path, [(101,27)] = Path, [(51,114)]
        = Path, [(11,101)] = Path, [(81,6)] = Path, [(3,113)] = Path, [(43,95)]
        = Path, [(103,109)] = Path, [(18,123)] = Path, [(117,103)] = Path,
        [(87,5)] = Path, [(115,41)] = Path, [(83,4)] = Path, [(121,111)] =
        Path, [(102,119)] = Path, [(91,35)] = Path, [(89,103)] = Path,
        [(29,58)] = Path, [(9,65)] = Path, [(11,7)] = Path, [(107,49)] = Path,
        [(37,30)] = Path, [(73,99)] = Path, [(63,123)] = Path, [(90,33)] =
        Path, [(110,65)] = Path, [(31,51)] = Path, [(101,79)] = Path, [(25,64)]
        = Path, [(81,101)] = Path, [(117,91)] = Path, [(55,23)] = Path,
        [(111,37)] = Path, [(23,113)] = Path, [(115,84)] = Path, [(120,55)] =
        Path, [(76,31)] = Path, [(35,123)] = Path, [(37,101)] = Path, [(38,11)]
        = Path, [(5,41)] = Path, [(11,87)] = Path, [(15,93)] = Path, [(92,5)] =
        Path, [(25,98)] = Path, [(102,105)] = Path, [(105,115)] = Path,
        [(15,42)] = Path, [(24,83)] = Path, [(92,45)] = Path, [(75,22)] = Path,
        [(33,53)] = Path, [(37,11)] = Path, [(46,117)] = Path, [(13,123)] =
        Path, [(93,87)] = Path, [(111,69)] = Path, [(15,83)] = Path, [(91,119)]
        = Path, [(19,71)] = Path, [(41,23)] = Path, [(16,93)] = Path, [(7,13)]
        = Path, [(80,109)] = Path, [(3,78)] = Path, [(31,3)] = Path, [(99,109)]
        = Path, [(102,65)] = Path, [(74,13)] = Path, [(111,48)] = Path,
        [(93,57)] = Path, [(14,117)] = Path, [(5,78)] = Path, [(31,65)] = Path,
        [(39,4)] = Path, [(67,20)] = Path, [(39,9)] = Path, [(35,25)] = Path,
        [(15,51)] = Path, [(13,109)] = Path, [(6,27)] = Path, [(107,22)] =
        Path, [(101,19)] = Path, [(99,45)] = Path, [(101,46)] = Path,
        [(103,23)] = Path, [(13,3)] = Path, [(91,49)] = Path, [(101,71)] =
        Path, [(87,111)] = Path, [(24,113)] = Path, [(85,107)] = Path,
        [(35,116)] = Path, [(29,93)] = Path, [(91,54)] = Path, [(3,37)] = Path,
        [(21,107)] = Path, [(27,35)] = Path, [(32,55)] = Path, [(55,124)] =
        Outer(34,49), [(25,44)] = Path, [(11,57)] = Path, [(31,68)] = Path,
        [(105,101)] = Path, [(109,63)] = Path, [(68,101)] = Path, [(113,60)] =
        Path, [(119,101)] = Path, [(94,51)] = Path, [(65,120)] = Path,
        [(99,96)] = Path, [(119,15)] = Path, [(114,13)] = Path, [(25,118)] =
        Path, [(62,13)] = Path, [(15,87)] = Path, [(23,51)] = Path, [(13,103)]
        = Path, [(100,69)] = Path, [(53,23)] = Path, [(65,20)] = Path,
        [(114,85)] = Path, [(27,76)] = Path, [(69,19)] = Path, [(100,41)] =
        Path, [(8,103)] = Path, [(25,23)] = Path, [(83,5)] = Path, [(77,107)] =
        Path, [(27,8)] = Path, [(21,87)] = Path, [(31,67)] = Path, [(78,9)] =
        Path, [(21,46)] = Path, [(29,42)] = Path, [(57,123)] = Path, [(38,117)]
        = Path, [(47,3)] = Path, [(36,117)] = Path, [(101,96)] = Path,
        [(77,99)] = Path, [(74,117)] = Path, [(89,11)] = Path, [(81,118)] =
        Path, [(85,15)] = Path, [(61,120)] = Path, [(120,81)] = Path,
        [(120,39)] = Path, [(41,22)] = Path, [(55,116)] = Path, [(27,31)] =
        Path, [(13,71)] = Path, [(85,123)] = Path, [(49,111)] = Path,
        [(21,123)] = Path, [(43,7)] = Path, [(3,74)] = Path, [(10,119)] = Path,
        [(21,71)] = Path, [(4,77)] = Path, [(39,23)] = Path, [(105,69)] = Path,
        [(97,24)] = Path, [(95,104)] = Path, [(33,112)] = Path, [(27,82)] =
        Path, [(17,3)] = Path, [(113,66)] = Path, [(117,55)] = Path, [(3,108)]
        = Path, [(95,67)] = Path, [(113,24)] = Path, [(23,73)] = Path, [(7,15)]
        = Path, [(7,32)] = Path, [(13,117)] = Path, [(48,103)] = Path,
        [(91,31)] = Path, [(111,17)] = Path, [(95,10)] = Path, [(114,77)] =
        Path, [(93,4)] = Path, [(19,89)] = Path, [(115,76)] = Path, [(41,111)]
        = Path, [(85,21)] = Path, [(105,59)] = Path, [(81,7)] = Path,
        [(56,101)] = Path, [(49,33)] = Path, [(119,70)] = Path, [(73,106)] =
        Path, [(121,94)] = Path, [(31,40)] = Path, [(4,113)] = Path, [(23,83)]
        = Path, [(111,107)] = Path, [(66,123)] = Path, [(69,33)] = Path,
        [(117,11)] = Path, [(25,85)] = Path, [(5,109)] = Path, [(107,63)] =
        Path, [(116,47)] = Path, [(37,111)] = Path, [(19,120)] = Path,
        [(27,84)] = Path, [(67,33)] = Path, [(100,113)] = Path, [(85,97)] =
        Path, [(106,23)] = Path, [(107,116)] = Path, [(40,27)] = Path, [(8,47)]
        = Path, [(110,107)] = Path, [(43,33)] = Path, [(99,93)] = Path,
        [(3,53)] = Path, [(21,122)] = Path, [(59,99)] = Path, [(67,9)] = Path,
        [(101,13)] = Path, [(65,103)] = Path, [(29,75)] = Path, [(9,115)] =
        Path, [(3,39)] = Path, [(89,105)] = Path, [(17,65)] = Path, [(17,95)] =
        Path, [(33,3)] = Path, [(65,23)] = Path, [(47,104)] = Path, [(104,37)]
        = Path, [(53,33)] = Path, [(29,18)] = Path, [(13,93)] = Path, [(97,94)]
        = Path, [(7,14)] = Path, [(113,20)] = Path, [(111,33)] = Path,
        [(68,13)] = Path, [(96,49)] = Path, [(114,113)] = Path, [(67,12)] =
        Path, [(27,71)] = Path, [(110,29)] = Path, [(13,87)] = Path, [(95,59)]
        = Path, [(4,53)] = Path, [(96,83)] = Path, [(114,9)] = Path, [(117,7)]
        = Path, [(69,101)] = Path, [(111,8)] = Path, [(88,101)] = Path,
        [(32,87)] = Path, [(33,30)] = Path, [(121,101)] = Path, [(32,79)] =
        Path, [(19,48)] = Path, [(29,71)] = Path, [(27,72)] = Path, [(100,17)]
        = Path, [(108,39)] = Path, [(36,111)] = Path, [(101,115)] = Path,
        [(3,91)] = Path, [(17,83)] = Path, [(113,64)] = Path, [(15,81)] = Path,
        [(117,5)] = Path, [(43,9)] = Path, [(109,113)] = Path, [(91,14)] =
        Path, [(45,109)] = Path, [(73,97)] = Path, [(99,53)] = Path, [(23,45)]
        = Path, [(115,52)] = Path, [(57,99)] = Path, [(83,112)] = Path,
        [(108,107)] = Path, [(25,41)] = Path, [(17,117)] = Path, [(119,86)] =
        Path, [(39,16)] = Path, [(108,87)] = Path, [(37,100)] = Path,
        [(77,121)] = Path, [(74,123)] = Path, [(32,35)] = Path, [(33,113)] =
        Path, [(103,61)] = Path, [(87,3)] = Path, [(109,49)] = Path, [(103,57)]
        = Path, [(97,5)] = Path, [(3,16)] = Path, [(91,122)] = Path, [(51,123)]
        = Path, [(113,41)] = Path, [(121,10)] = Path, [(31,90)] = Path,
        [(3,33)] = Path, [(42,97)] = Path, [(104,47)] = Path, [(23,39)] = Path,
        [(11,88)] = Path, [(119,30)] = Path, [(69,9)] = Path, [(111,44)] =
        Path, [(4,71)] = Path, [(73,102)] = Path, [(7,39)] = Path, [(101,12)] =
        Path, [(9,117)] = Path, [(105,77)] = Path, [(12,59)] = Path, [(15,82)]
        = Path, [(3,118)] = Path, [(65,106)] = Path, [(102,17)] = Path,
        [(115,44)] = Path, [(117,20)] = Path, [(4,41)] = Path, [(109,99)] =
        Path, [(31,71)] = Path, [(39,108)] = Path, [(33,87)] = Path, [(29,35)]
        = Path, [(114,49)] = Path, [(14,45)] = Path, [(51,111)] = Path,
        [(79,121)] = Path, [(107,67)] = Path, [(116,51)] = Path, [(25,106)] =
        Path, [(31,16)] = Path, [(95,73)] = Path, [(113,36)] = Path, [(121,47)]
        = Path, [(121,84)] = Path, [(69,108)] = Path, [(119,33)] = Path,
        [(30,37)] = Path, [(21,17)] = Path, [(17,100)] = Path, [(88,15)] =
        Path, [(99,115)] = Path, [(31,107)] = Path, [(22,9)] = Path, [(105,10)]
        = Path, [(21,115)] = Path, [(88,5)] = Path, [(79,10)] = Path, [(91,59)]
        = Path, [(66,109)] = Path, [(30,21)] = Path, [(61,23)] = Path,
        [(33,29)] = Path, [(100,109)] = Path, [(79,8)] = Path, [(9,121)] =
        Path, [(100,79)] = Path, [(97,105)] = Path, [(89,25)] = Path, [(21,51)]
        = Path, [(109,72)] = Path, [(105,81)] = Path, [(99,39)] = Path,
        [(97,19)] = Path, [(6,99)] = Path, [(7,82)] = Path, [(60,15)] = Path,
        [(45,94)] = Path, [(107,30)] = Path, [(85,116)] = Path, [(110,23)] =
        Path, [(33,25)] = Path, [(21,120)] = Path, [(29,67)] = Path, [(30,43)]
        = Path, [(8,81)] = Path, [(55,21)] = Path, [(51,92)] = Inner(39,124),
        [(5,116)] = Path, [(107,107)] = Path, [(6,123)] = Path, [(113,61)] =
        Path, [(121,63)] = Path, [(101,37)] = Path, [(67,3)] = Path, [(97,45)]
        = Path, [(70,27)] = Path, [(117,33)] = Path, [(117,24)] = Path,
        [(17,45)] = Path, [(98,53)] = Path, [(29,107)] = Path, [(37,5)] = Path,
        [(111,123)] = Path, [(105,88)] = Path, [(70,119)] = Path, [(32,63)] =
        Path, [(113,106)] = Path, [(93,111)] = Path, [(70,19)] = Path,
        [(115,114)] = Path, [(66,103)] = Path, [(13,98)] = Path, [(65,19)] =
        Path, [(113,85)] = Path, [(120,37)] = Path, [(21,25)] = Path, [(19,45)]
        = Path, [(79,117)] = Path, [(59,107)] = Path, [(33,62)] = Path,
        [(95,43)] = Path, [(63,31)] = Path, [(113,98)] = Path, [(120,33)] =
        Path, [(115,91)] = Path, [(50,7)] = Path, [(60,3)] = Path, [(115,27)] =
        Path, [(103,105)] = Path, [(91,41)] = Path, [(21,43)] = Path, [(31,81)]
        = Path, [(96,81)] = Path, [(3,93)] = Path, [(83,6)] = Path, [(121,92)]
        = Path, [(79,99)] = Path, [(29,8)] = Path, [(5,59)] = Path, [(113,86)]
        = Path, [(95,72)] = Path, [(59,119)] = Path, [(35,28)] = Path,
        [(93,41)] = Path, [(105,48)] = Path, [(121,81)] = Path, [(65,25)] =
        Path, [(109,57)] = Path, [(115,13)] = Path, [(50,97)] = Path,
        [(65,107)] = Path, [(15,30)] = Path, [(82,105)] = Path, [(98,33)] =
        Path, [(17,55)] = Path, [(37,20)] = Path, [(117,46)] = Path, [(31,91)]
        = Path, [(67,25)] = Path, [(75,95)] = Path, [(7,71)] = Path, [(25,61)]
        = Path, [(17,25)] = Path, [(106,21)] = Path, [(3,121)] = Path,
        [(59,13)] = Path, [(30,111)] = Path, [(97,121)] = Path, [(59,32)] =
        Path, [(88,123)] = Path, [(35,117)] = Path, [(9,34)] = Path, [(26,19)]
        = Path, [(99,46)] = Path, [(7,3)] = Path, [(92,19)] = Path, [(57,93)] =
        Path, [(99,7)] = Path, [(69,93)] = Path, [(111,28)] = Path, [(15,3)] =
        Path, [(97,67)] = Path, [(105,105)] = Path, [(51,116)] = Path,
        [(105,113)] = Path, [(21,81)] = Path, [(112,79)] = Path, [(10,61)] =
        Path, [(24,103)] = Path, [(117,27)] = Path, [(23,99)] = Path,
        [(108,49)] = Path, [(17,104)] = Path, [(47,119)] = Path, [(31,27)] =
        Path, [(120,77)] = Path, [(90,97)] = Path, [(83,10)] = Path, [(35,110)]
        = Path, [(3,86)] = Path, [(23,3)] = Path, [(98,117)] = Path,
        [(107,118)] = Path, [(74,33)] = Path, [(29,85)] = Path, [(31,73)] =
        Path, [(47,121)] = Path, [(59,95)] = Path, [(105,5)] = Path, [(33,27)]
        = Path, [(90,103)] = Path, [(3,31)] = Path, [(109,35)] = Path,
        [(97,52)] = Path, [(21,45)] = Path, [(89,7)] = Path, [(105,79)] = Path,
        [(115,42)] = Path, [(56,93)] = Path, [(40,105)] = Path, [(4,83)] =
        Path, [(9,101)] = Path, [(61,105)] = Path, [(49,121)] = Path, [(69,3)]
        = Path, [(84,31)] = Path, [(67,111)] = Path, [(95,6)] = Path, [(21,9)]
        = Path, [(23,24)] = Path, [(14,3)] = Path, [(119,61)] = Path, [(91,69)]
        = Path, [(73,109)] = Path, [(67,107)] = Path, [(67,8)] = Path,
        [(49,11)] = Path, [(111,119)] = Path, [(121,55)] = Path, [(121,100)] =
        Path, [(65,28)] = Path, [(90,7)] = Path, [(41,19)] = Path, [(23,36)] =
        Path, [(118,3)] = Path, [(18,5)] = Path, [(104,3)] = Path, [(102,29)] =
        Path, [(117,71)] = Path, [(112,25)] = Path, [(113,79)] = Path,
        [(117,26)] = Path, [(42,23)] = Path, [(99,99)] = Path, [(29,37)] =
        Path, [(104,83)] = Path, [(96,123)] = Path, [(111,60)] = Path,
        [(99,60)] = Path, [(33,36)] = Path, [(115,103)] = Path, [(19,32)] =
        Path, [(49,19)] = Path, [(33,118)] = Path, [(19,61)] = Path, [(44,95)]
        = Path, [(97,103)] = Path, [(67,113)] = Path, [(32,39)] = Path } }