Problem:
Score : 300 points

Problem Statement

There are N cubes stacked vertically on a desk.

You are given a string S of length N. The color of the i-th cube from the bottom is red if the i-th character in S is 0, and blue if that character is 1.

You can perform the following operation any number of times: choose a red cube and a blue cube that are adjacent, and remove them. Here, the cubes that were stacked on the removed cubes will fall down onto the object below them.

At most how many cubes can be removed?

Constraints

1 \leq N \leq 10^5

|S| = N

Each character in S is 0 or 1.

Input

Input is given from Standard Input in the following format:

S

Output

Print the maximum number of cubes that can be removed.

Sample Input 1

0011

Sample Output 1

4

All four cubes can be removed, by performing the operation as follows:

Remove the second and third cubes from the bottom. Then, the fourth cube drops onto the first cube.

Remove the first and second cubes from the bottom.

Sample Input 2

11011010001011

Sample Output 2

12

Sample Input 3

0

Sample Output 3

0

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

# util functions

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

# input
inputs = []
lc = 0
while l = $stdin.gets do
  if true
    inputs << l.chomp.split(" ").map(&:to_s)
  else
    inputs << l.chomp.split(" ").map(&:to_i)
  end
  lc += 1
end

# input check
if $debugFlag
  p "--- INPUT (begin) ---"
  inputs.each do |l_i|
    p l_i
  end
  p "--- INPUT (end) ---"
  print "\n"
end

# body
$ss = inputs[0][0]
if $debugFlag
  p $ss
end

$hash = {}
def recurse( str )
  p str if $debugFlag
  return $hash[str] if $hash[str] != nil
  return [0, ""] if str == ""
  return [2, ""] if str == "01" or str == "10"
  case str
  when "101" then
    return [2, "1"]
  when "010" then
    return [2, "0"]    
  when "110" then
    return [2, "1"]    
  when "011" then
    return [2, "1"]    
  when "100" then
    return [2, "0"]        
  when "001" then
    return [2, "0"]        
  end
  return [0, str] if str.index("0") == nil or str.index("1") == nil

  i = str.index("10")
  if i == 0
    lres  = [0, ""]
    rres  = recurse( str[i+2..-1] )
  elsif i != nil
    lres  = recurse( str[0..i-1] )
    rres  = recurse( str[i+2..-1] )
  else
    i = str.index("01")
    if i == 0
      lres  = [0, ""]
      rres  = recurse( str[i+2..-1] )
    else
      lres  = recurse( str[0..i-1] )
      rres  = recurse( str[i+2..-1] )
    end
  end
    
  # lres  = recurse( str[0..str.length/2-1] )
  # rres  = recurse( str[str.length/2..-1] )

  if $debugFlag
    print "lres: "
    p lres
    print "rres: "
    p rres    
  end

  num   = lres[0] + rres[0] + 2
  cres  = recurse( lres[1] + rres[1] )
  num  += cres[0]
  redstr = cres[1]
  res = [num, redstr]
  $hash[str] = res
  return res
end

puts recurse( $ss )[0]

# while $ss.size >= 3 or $ss == "01" or $ss == "10"
#   if $debugFlag
#     print "ss: "
#     p $ss
#   end
  
#   if $ss == "01" or $ss == "10"
#     cnt += 2
#     break
#   end

#   ($ss.size - 2).times do |i|
#     case $ss[i..i+2]
#     when "101" then
#       $ss[i..i+2] = "1"; cnt += 2
#     when "010" then
#       $ss[i..i+2] = "0"; cnt += 2
#     when "110" then
#       $ss[i..i+2] = "1"; cnt += 2
#     when "011" then
#       $ss[i..i+2] = "1"; cnt += 2
#     when "100" then
#       $ss[i..i+2] = "0"; cnt += 2
#     when "001" then
#       $ss[i..i+2] = "0"; cnt += 2
#     end
#   end
# end
# puts cnt