aj = [[0,1,2],[2,0,1],[1,2,0]]
n = 100
m = 10
while (n > 0)
  hm = m/2
  (1..(m-6)/4).each { |a| a3 = a**3
    ((a+1)..(((m2=m-a)-3)/3)).each { |b| b3 = b**3
      # a+b+c+d == m; a+d == b+c (mod 6) => c == m/2-b (mod 3)
      c = b+1; c += aj[c%3][(hm-b)%3]
      upper_c = ((m3=m2-b)-1)/2
      while (c <= upper_c)
        d = m3-c
        if ((s = a3 + d**3) == b3 + c**3)
          p [s, [a,d], [b,c]]
          exit if ((n -= 1) <= 0)
        end
        c += 3
      end
    }
  }
  m += 2
end


def sumcube e
  e[0]**3+e[1]**3
end

def taxi_nums n
  b = yield ; found = 0
  while found < n
    a = yield
    #puts "#{a.inspect} => #{sumcube a}"
    if a[0] == b[0]
      a,b = b,a if a[1][0] > b[1][0]
      puts "#{a[1].inspect} , #{b[1].inspect} => #{a[0]}"
      found += 1
    end
    b = a
  end
end

queue = [[9,[1,2]]]

taxi_nums(30){
  r = queue.shift
  a = r[1][0]
  b = r[1][1]
  c = [a,b+1]
  queue << [sumcube(c),c]
  if a+2 == b
    c = [a+1,b]
    queue << [sumcube(c),c]
  end

  queue.sort!{|a,b|
    a[0] <=> b[0]
  }
  r
}