Problem:
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Areas on the Cross-Section Diagram

Your task is to simulate a flood damage.

For a given cross-section diagram, reports areas of flooded sections.

Assume that rain is falling endlessly in the region and the water overflowing from the region is falling in the sea at the both sides.
For example, for the above cross-section diagram, the rain will create floods which have areas of 4, 2, 1, 19 and 9 respectively.

Input

A string, which represents slopes and flatlands by '/', '\' and '_' respectively, is given in a line. For example, the region of the above example is given by a string "\\///\_/\/\\\\/_/\\///__\\\_\\/_\/_/\".

output

Report the areas of floods in the following format:

$A$

$k$ $L_1$ $L_2$ ... $L_k$

In the first line, print the total area $A$ of created floods.

In the second line, print the number of floods $k$ and areas $L_i (i = 1, 2, ..., k)$ for each flood from the left side of the cross-section diagram. Print a space character before $L_i$.

Constraints

$1 \leq$ length of the string $\leq 20,000$

Sample Input 1

\\//

Sample Output 1

4
1 4

Sample Input 2

\\///\_/\/\\\\/_/\\///__\\\_\\/_\/_/\

Sample Output 2

35
5 4 2 1 19 9

Solution in Ruby (judge verdict: Time Limit Exceeded)

diagram = gets.chomp.chars

upper_skip = ->{
  loop do
    a = diagram[0]
    break if a == "\\"
    diagram.shift
  end
}

downer_skip = ->(target_depth) {
  depth = 0
  index = 0
  until depth == target_depth
    depth -= 1 if diagram.shift == "\\"
    index += 1
  end
  index
}

highest = ->{
  max_index = height = 0
  max_height = -Float::INFINITY 
  0.upto(diagram.size - 1) do |j|
    case diagram[j]
    when "\\"
      height -= 1
    when "/"
      height += 1
      max_height, max_index = height, j if max_height < height
      return [0, j] if height.zero?
    end
  end
  [max_height, max_index]
}

calc = ->(from, to) {
  depth = area = 0
  from.upto(to) do
    case diagram.shift
    when "\\"
      area += depth + 1/2r
      depth += 1
    when "_"
      area += depth
    when "/"
      depth -= 1
      area += depth + 1/2r
    end
  end
  area.to_i
}

pools = []
loop do
  upper_skip.()
  height, index = highest.()
  if height.zero?
    pools << calc.(0, index)
  elsif height == -Float::INFINITY
    break
  else
    first_index = downer_skip.(height)
    pools << calc.(first_index, index)
  end
  break if diagram.size.zero?
end
puts pools.inject(&:+)
puts pools.size.to_s + " " + pools.join(" ")