440 lines
15 KiB
Ruby
440 lines
15 KiB
Ruby
|
module Cipher
|
||
|
#
|
||
|
# = Brief
|
||
|
#
|
||
|
# The Cipher::DES class allows for encryption and decryption of plain
|
||
|
# text using the "Data Encryption Standard". This version is the modified
|
||
|
# version which is part of the VNC authentication scheme.
|
||
|
#
|
||
|
# Usage is pretty straight forward:
|
||
|
#
|
||
|
# des = Cipher::DES.new 'mysecretkey', :encrypt
|
||
|
# str = des.update 'plain text'
|
||
|
# str << des.update 'more plain text'
|
||
|
# str << final
|
||
|
#
|
||
|
# Or just use the shortcut class methods:
|
||
|
#
|
||
|
# str = Cipher::DES.encrypt 'mysecretkey', 'plain text'
|
||
|
#
|
||
|
# = About
|
||
|
#
|
||
|
# This code was ported from the file "d3des.c", for portability reasons.
|
||
|
# It is not expected to be quick, but is only being used currently for the
|
||
|
# VNC authentication handshake. If you wanted to cipher a lot of text, you
|
||
|
# should probably compile the original C as an extension.
|
||
|
#
|
||
|
# I've included the following copyright info from the C source verbatim:
|
||
|
#
|
||
|
# This is D3DES (V5.09) by Richard Outerbridge with the double and
|
||
|
# triple-length support removed for use in VNC. Also the bytebit[] array
|
||
|
# has been reversed so that the most significant bit in each byte of the
|
||
|
# key is ignored, not the least significant.
|
||
|
#
|
||
|
# These changes are:
|
||
|
# Copyright (C) 1999 AT&T Laboratories Cambridge. All Rights Reserved.
|
||
|
#
|
||
|
# This software is distributed in the hope that it will be useful,
|
||
|
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||
|
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
|
||
|
#
|
||
|
# D3DES (V5.09)
|
||
|
#
|
||
|
# A portable, public domain, version of the Data Encryption Standard.
|
||
|
#
|
||
|
# Written with Symantec's THINK (Lightspeed) C by Richard Outerbridge.
|
||
|
# Thanks to: Dan Hoey for his excellent Initial and Inverse permutation
|
||
|
# code; Jim Gillogly & Phil Karn for the DES key schedule code; Dennis
|
||
|
# Ferguson, Eric Young and Dana How for comparing notes; and Ray Lau,
|
||
|
# for humouring me on.
|
||
|
#
|
||
|
# Copyright (c) 1988,1989,1990,1991,1992 by Richard Outerbridge.
|
||
|
# (GEnie : OUTER; CIS : [71755,204]) Graven Imagery, 1992.
|
||
|
#
|
||
|
class DES
|
||
|
BLOCK_SIZE = 8
|
||
|
|
||
|
attr_reader :key, :mode
|
||
|
|
||
|
# Create a des cipher object. +key+ should be cipher key to use, and +mode+ should
|
||
|
# be either <tt>:encrypt</tt> or <tt>:decrypt</tt>.
|
||
|
#
|
||
|
# It will expand +key+ to be 8 bytes by padding with null bytes. If it is longer than
|
||
|
# 8 bytes, the additional data is discarded.
|
||
|
def initialize key, mode
|
||
|
unless [:encrypt, :decrypt].include? mode
|
||
|
raise ArgumentError, 'invalid mode argument - %s' % mode
|
||
|
end
|
||
|
@mode = mode
|
||
|
|
||
|
# ensure key is 8 bytes. pad with nulls as needed
|
||
|
key = key[0, BLOCK_SIZE]
|
||
|
key << 0.chr * (BLOCK_SIZE - key.length)
|
||
|
@key = key
|
||
|
|
||
|
# now expand the key schedule
|
||
|
@keys = self.class.send :prepare_key_stage2, self.class.send(:prepare_key_stage1, key, mode)
|
||
|
|
||
|
# this internal buffer is used because we must process data in chunks of 8 bytes
|
||
|
@buf = ''
|
||
|
end
|
||
|
|
||
|
# This updates the cipher with +data+, returning any available ciphered output. The +data+ is
|
||
|
# processed in blocks of 8 bytes, so any residual is added to an internal buffer.
|
||
|
def update data
|
||
|
result = ''
|
||
|
data = @buf + data unless @buf.empty?
|
||
|
num_blocks, residual = data.length.divmod BLOCK_SIZE
|
||
|
num_blocks.times do |i|
|
||
|
block = data[i * BLOCK_SIZE, BLOCK_SIZE].unpack('N2')
|
||
|
result << self.class.send(:desfunc, block, @keys).pack('N2')
|
||
|
end
|
||
|
@buf = residual == 0 ? '' : data[-residual..-1]
|
||
|
result
|
||
|
end
|
||
|
|
||
|
# This flushes the internal buffer by padding it out with null bytes, and doing a final
|
||
|
# DES round. Note that this means the ciphered text is always padded out to a multiple of
|
||
|
# 8 bytes.
|
||
|
def final
|
||
|
if @buf.empty?
|
||
|
''
|
||
|
else
|
||
|
update 0.chr * (BLOCK_SIZE - @buf.length)
|
||
|
end
|
||
|
end
|
||
|
|
||
|
# A shortcut method to create a cipher object using +key+, and fully encrypt +data+
|
||
|
def self.encrypt key, data
|
||
|
des = new key, :encrypt
|
||
|
des.update(data) << des.final
|
||
|
end
|
||
|
|
||
|
# A shortcut method to create a cipher object using +key+, and fully decrypt +data+
|
||
|
def self.decrypt key, data
|
||
|
des = new key, :decrypt
|
||
|
des.update(data) << des.final
|
||
|
end
|
||
|
|
||
|
class << self #:nodoc: all
|
||
|
BYTEBIT = [
|
||
|
01, 02, 04, 010, 020, 040, 0100, 0200
|
||
|
]
|
||
|
|
||
|
BIGBYTE = [
|
||
|
0x800000, 0x400000, 0x200000, 0x100000,
|
||
|
0x080000, 0x040000, 0x020000, 0x010000,
|
||
|
0x008000, 0x004000, 0x002000, 0x001000,
|
||
|
0x000800, 0x000400, 0x000200, 0x000100,
|
||
|
0x000080, 0x000040, 0x000020, 0x000010,
|
||
|
0x000008, 0x000004, 0x000002, 0x000001
|
||
|
]
|
||
|
|
||
|
# Use the key schedule specified in the Standard (ANSI X3.92-1981).
|
||
|
|
||
|
PC1 = [
|
||
|
56, 48, 40, 32, 24, 16, 8, 0, 57, 49, 41, 33, 25, 17,
|
||
|
9, 1, 58, 50, 42, 34, 26, 18, 10, 2, 59, 51, 43, 35,
|
||
|
62, 54, 46, 38, 30, 22, 14, 6, 61, 53, 45, 37, 29, 21,
|
||
|
13, 5, 60, 52, 44, 36, 28, 20, 12, 4, 27, 19, 11, 3
|
||
|
]
|
||
|
|
||
|
TOTROT = [
|
||
|
1, 2, 4, 6, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 28
|
||
|
]
|
||
|
|
||
|
PC2 = [
|
||
|
13, 16, 10, 23, 0, 4, 2, 27, 14, 5, 20, 9,
|
||
|
22, 18, 11, 3, 25, 7, 15, 6, 26, 19, 12, 1,
|
||
|
40, 51, 30, 36, 46, 54, 29, 39, 50, 44, 32, 47,
|
||
|
43, 48, 38, 55, 33, 52, 45, 41, 49, 35, 28, 31
|
||
|
]
|
||
|
|
||
|
private
|
||
|
|
||
|
#
|
||
|
# Prepares +key+ to be used
|
||
|
#
|
||
|
# +key+:: String
|
||
|
# +mode+:: :encrypt or :decrypt
|
||
|
#
|
||
|
# Thanks to James Gillogly & Phil Karn!
|
||
|
#
|
||
|
# corresponds to "deskey"
|
||
|
#
|
||
|
def prepare_key_stage1 key, mode
|
||
|
pcr = [nil] * 56
|
||
|
kn = [nil] * 32
|
||
|
|
||
|
pc1m = (0...56).map do |j|
|
||
|
l = PC1[j]
|
||
|
m = l & 07
|
||
|
(key[l >> 3] & BYTEBIT[m]) != 0 ? 1 : 0;
|
||
|
end
|
||
|
|
||
|
16.times do |i|
|
||
|
m = mode == :encrypt ? i << 1 : (15 - i) << 1
|
||
|
n = m + 1
|
||
|
kn[m] = kn[n] = 0
|
||
|
28.times do |j|
|
||
|
l = (j + TOTROT[i]) % 28
|
||
|
pcr[j] = pc1m[l]
|
||
|
pcr[j + 28] = pc1m[l + 28]
|
||
|
end
|
||
|
24.times do |j|
|
||
|
kn[m] |= BIGBYTE[j] if pcr[PC2[j]] != 0
|
||
|
kn[n] |= BIGBYTE[j] if pcr[PC2[j+24]] != 0
|
||
|
end
|
||
|
end
|
||
|
|
||
|
kn
|
||
|
end
|
||
|
|
||
|
# corresponds to "cookey"
|
||
|
def prepare_key_stage2(raw1)
|
||
|
cook = []
|
||
|
|
||
|
16.times do |i|
|
||
|
a = raw1[i * 2 + 0]
|
||
|
b = raw1[i * 2 + 1]
|
||
|
x = (a & 0x00fc0000) << 6
|
||
|
x |= (a & 0x00000fc0) << 10
|
||
|
x |= (b & 0x00fc0000) >> 10
|
||
|
x |= (b & 0x00000fc0) >> 6
|
||
|
cook << x
|
||
|
x = (a & 0x0003f000) << 12
|
||
|
x |= (a & 0x0000003f) << 16
|
||
|
x |= (b & 0x0003f000) >> 4
|
||
|
x |= (b & 0x0000003f)
|
||
|
cook << x
|
||
|
end
|
||
|
|
||
|
cook
|
||
|
end
|
||
|
|
||
|
SP1 = [
|
||
|
0x01010400, 0x00000000, 0x00010000, 0x01010404,
|
||
|
0x01010004, 0x00010404, 0x00000004, 0x00010000,
|
||
|
0x00000400, 0x01010400, 0x01010404, 0x00000400,
|
||
|
0x01000404, 0x01010004, 0x01000000, 0x00000004,
|
||
|
0x00000404, 0x01000400, 0x01000400, 0x00010400,
|
||
|
0x00010400, 0x01010000, 0x01010000, 0x01000404,
|
||
|
0x00010004, 0x01000004, 0x01000004, 0x00010004,
|
||
|
0x00000000, 0x00000404, 0x00010404, 0x01000000,
|
||
|
0x00010000, 0x01010404, 0x00000004, 0x01010000,
|
||
|
0x01010400, 0x01000000, 0x01000000, 0x00000400,
|
||
|
0x01010004, 0x00010000, 0x00010400, 0x01000004,
|
||
|
0x00000400, 0x00000004, 0x01000404, 0x00010404,
|
||
|
0x01010404, 0x00010004, 0x01010000, 0x01000404,
|
||
|
0x01000004, 0x00000404, 0x00010404, 0x01010400,
|
||
|
0x00000404, 0x01000400, 0x01000400, 0x00000000,
|
||
|
0x00010004, 0x00010400, 0x00000000, 0x01010004
|
||
|
]
|
||
|
|
||
|
SP2 = [
|
||
|
0x80108020, 0x80008000, 0x00008000, 0x00108020,
|
||
|
0x00100000, 0x00000020, 0x80100020, 0x80008020,
|
||
|
0x80000020, 0x80108020, 0x80108000, 0x80000000,
|
||
|
0x80008000, 0x00100000, 0x00000020, 0x80100020,
|
||
|
0x00108000, 0x00100020, 0x80008020, 0x00000000,
|
||
|
0x80000000, 0x00008000, 0x00108020, 0x80100000,
|
||
|
0x00100020, 0x80000020, 0x00000000, 0x00108000,
|
||
|
0x00008020, 0x80108000, 0x80100000, 0x00008020,
|
||
|
0x00000000, 0x00108020, 0x80100020, 0x00100000,
|
||
|
0x80008020, 0x80100000, 0x80108000, 0x00008000,
|
||
|
0x80100000, 0x80008000, 0x00000020, 0x80108020,
|
||
|
0x00108020, 0x00000020, 0x00008000, 0x80000000,
|
||
|
0x00008020, 0x80108000, 0x00100000, 0x80000020,
|
||
|
0x00100020, 0x80008020, 0x80000020, 0x00100020,
|
||
|
0x00108000, 0x00000000, 0x80008000, 0x00008020,
|
||
|
0x80000000, 0x80100020, 0x80108020, 0x00108000
|
||
|
]
|
||
|
|
||
|
SP3 = [
|
||
|
0x00000208, 0x08020200, 0x00000000, 0x08020008,
|
||
|
0x08000200, 0x00000000, 0x00020208, 0x08000200,
|
||
|
0x00020008, 0x08000008, 0x08000008, 0x00020000,
|
||
|
0x08020208, 0x00020008, 0x08020000, 0x00000208,
|
||
|
0x08000000, 0x00000008, 0x08020200, 0x00000200,
|
||
|
0x00020200, 0x08020000, 0x08020008, 0x00020208,
|
||
|
0x08000208, 0x00020200, 0x00020000, 0x08000208,
|
||
|
0x00000008, 0x08020208, 0x00000200, 0x08000000,
|
||
|
0x08020200, 0x08000000, 0x00020008, 0x00000208,
|
||
|
0x00020000, 0x08020200, 0x08000200, 0x00000000,
|
||
|
0x00000200, 0x00020008, 0x08020208, 0x08000200,
|
||
|
0x08000008, 0x00000200, 0x00000000, 0x08020008,
|
||
|
0x08000208, 0x00020000, 0x08000000, 0x08020208,
|
||
|
0x00000008, 0x00020208, 0x00020200, 0x08000008,
|
||
|
0x08020000, 0x08000208, 0x00000208, 0x08020000,
|
||
|
0x00020208, 0x00000008, 0x08020008, 0x00020200
|
||
|
]
|
||
|
|
||
|
SP4 = [
|
||
|
0x00802001, 0x00002081, 0x00002081, 0x00000080,
|
||
|
0x00802080, 0x00800081, 0x00800001, 0x00002001,
|
||
|
0x00000000, 0x00802000, 0x00802000, 0x00802081,
|
||
|
0x00000081, 0x00000000, 0x00800080, 0x00800001,
|
||
|
0x00000001, 0x00002000, 0x00800000, 0x00802001,
|
||
|
0x00000080, 0x00800000, 0x00002001, 0x00002080,
|
||
|
0x00800081, 0x00000001, 0x00002080, 0x00800080,
|
||
|
0x00002000, 0x00802080, 0x00802081, 0x00000081,
|
||
|
0x00800080, 0x00800001, 0x00802000, 0x00802081,
|
||
|
0x00000081, 0x00000000, 0x00000000, 0x00802000,
|
||
|
0x00002080, 0x00800080, 0x00800081, 0x00000001,
|
||
|
0x00802001, 0x00002081, 0x00002081, 0x00000080,
|
||
|
0x00802081, 0x00000081, 0x00000001, 0x00002000,
|
||
|
0x00800001, 0x00002001, 0x00802080, 0x00800081,
|
||
|
0x00002001, 0x00002080, 0x00800000, 0x00802001,
|
||
|
0x00000080, 0x00800000, 0x00002000, 0x00802080
|
||
|
]
|
||
|
|
||
|
SP5 = [
|
||
|
0x00000100, 0x02080100, 0x02080000, 0x42000100,
|
||
|
0x00080000, 0x00000100, 0x40000000, 0x02080000,
|
||
|
0x40080100, 0x00080000, 0x02000100, 0x40080100,
|
||
|
0x42000100, 0x42080000, 0x00080100, 0x40000000,
|
||
|
0x02000000, 0x40080000, 0x40080000, 0x00000000,
|
||
|
0x40000100, 0x42080100, 0x42080100, 0x02000100,
|
||
|
0x42080000, 0x40000100, 0x00000000, 0x42000000,
|
||
|
0x02080100, 0x02000000, 0x42000000, 0x00080100,
|
||
|
0x00080000, 0x42000100, 0x00000100, 0x02000000,
|
||
|
0x40000000, 0x02080000, 0x42000100, 0x40080100,
|
||
|
0x02000100, 0x40000000, 0x42080000, 0x02080100,
|
||
|
0x40080100, 0x00000100, 0x02000000, 0x42080000,
|
||
|
0x42080100, 0x00080100, 0x42000000, 0x42080100,
|
||
|
0x02080000, 0x00000000, 0x40080000, 0x42000000,
|
||
|
0x00080100, 0x02000100, 0x40000100, 0x00080000,
|
||
|
0x00000000, 0x40080000, 0x02080100, 0x40000100
|
||
|
]
|
||
|
|
||
|
SP6 = [
|
||
|
0x20000010, 0x20400000, 0x00004000, 0x20404010,
|
||
|
0x20400000, 0x00000010, 0x20404010, 0x00400000,
|
||
|
0x20004000, 0x00404010, 0x00400000, 0x20000010,
|
||
|
0x00400010, 0x20004000, 0x20000000, 0x00004010,
|
||
|
0x00000000, 0x00400010, 0x20004010, 0x00004000,
|
||
|
0x00404000, 0x20004010, 0x00000010, 0x20400010,
|
||
|
0x20400010, 0x00000000, 0x00404010, 0x20404000,
|
||
|
0x00004010, 0x00404000, 0x20404000, 0x20000000,
|
||
|
0x20004000, 0x00000010, 0x20400010, 0x00404000,
|
||
|
0x20404010, 0x00400000, 0x00004010, 0x20000010,
|
||
|
0x00400000, 0x20004000, 0x20000000, 0x00004010,
|
||
|
0x20000010, 0x20404010, 0x00404000, 0x20400000,
|
||
|
0x00404010, 0x20404000, 0x00000000, 0x20400010,
|
||
|
0x00000010, 0x00004000, 0x20400000, 0x00404010,
|
||
|
0x00004000, 0x00400010, 0x20004010, 0x00000000,
|
||
|
0x20404000, 0x20000000, 0x00400010, 0x20004010
|
||
|
]
|
||
|
|
||
|
SP7 = [
|
||
|
0x00200000, 0x04200002, 0x04000802, 0x00000000,
|
||
|
0x00000800, 0x04000802, 0x00200802, 0x04200800,
|
||
|
0x04200802, 0x00200000, 0x00000000, 0x04000002,
|
||
|
0x00000002, 0x04000000, 0x04200002, 0x00000802,
|
||
|
0x04000800, 0x00200802, 0x00200002, 0x04000800,
|
||
|
0x04000002, 0x04200000, 0x04200800, 0x00200002,
|
||
|
0x04200000, 0x00000800, 0x00000802, 0x04200802,
|
||
|
0x00200800, 0x00000002, 0x04000000, 0x00200800,
|
||
|
0x04000000, 0x00200800, 0x00200000, 0x04000802,
|
||
|
0x04000802, 0x04200002, 0x04200002, 0x00000002,
|
||
|
0x00200002, 0x04000000, 0x04000800, 0x00200000,
|
||
|
0x04200800, 0x00000802, 0x00200802, 0x04200800,
|
||
|
0x00000802, 0x04000002, 0x04200802, 0x04200000,
|
||
|
0x00200800, 0x00000000, 0x00000002, 0x04200802,
|
||
|
0x00000000, 0x00200802, 0x04200000, 0x00000800,
|
||
|
0x04000002, 0x04000800, 0x00000800, 0x00200002
|
||
|
]
|
||
|
|
||
|
SP8 = [
|
||
|
0x10001040, 0x00001000, 0x00040000, 0x10041040,
|
||
|
0x10000000, 0x10001040, 0x00000040, 0x10000000,
|
||
|
0x00040040, 0x10040000, 0x10041040, 0x00041000,
|
||
|
0x10041000, 0x00041040, 0x00001000, 0x00000040,
|
||
|
0x10040000, 0x10000040, 0x10001000, 0x00001040,
|
||
|
0x00041000, 0x00040040, 0x10040040, 0x10041000,
|
||
|
0x00001040, 0x00000000, 0x00000000, 0x10040040,
|
||
|
0x10000040, 0x10001000, 0x00041040, 0x00040000,
|
||
|
0x00041040, 0x00040000, 0x10041000, 0x00001000,
|
||
|
0x00000040, 0x10040040, 0x00001000, 0x00041040,
|
||
|
0x10001000, 0x00000040, 0x10000040, 0x10040000,
|
||
|
0x10040040, 0x10000000, 0x00040000, 0x10001040,
|
||
|
0x00000000, 0x10041040, 0x00040040, 0x10000040,
|
||
|
0x10040000, 0x10001000, 0x10001040, 0x00000000,
|
||
|
0x10041040, 0x00041000, 0x00041000, 0x00001040,
|
||
|
0x00001040, 0x00040040, 0x10000000, 0x10041000
|
||
|
]
|
||
|
|
||
|
def desfunc block, keys
|
||
|
leftt = block[0]
|
||
|
right = block[1]
|
||
|
|
||
|
work = ((leftt >> 4) ^ right) & 0x0f0f0f0f
|
||
|
right ^= work
|
||
|
leftt ^= (work << 4)
|
||
|
work = ((leftt >> 16) ^ right) & 0x0000ffff
|
||
|
right ^= work
|
||
|
leftt ^= (work << 16)
|
||
|
work = ((right >> 2) ^ leftt) & 0x33333333
|
||
|
leftt ^= work
|
||
|
right ^= (work << 2)
|
||
|
work = ((right >> 8) ^ leftt) & 0x00ff00ff
|
||
|
leftt ^= work
|
||
|
right ^= (work << 8)
|
||
|
right = ((right << 1) | ((right >> 31) & 1)) & 0xffffffff
|
||
|
work = (leftt ^ right) & 0xaaaaaaaa
|
||
|
leftt ^= work
|
||
|
right ^= work
|
||
|
leftt = ((leftt << 1) | ((leftt >> 31) & 1)) & 0xffffffff
|
||
|
|
||
|
8.times do |i|
|
||
|
work = (right << 28) | (right >> 4)
|
||
|
work ^= keys[i * 4 + 0]
|
||
|
fval = SP7[ work & 0x3f]
|
||
|
fval |= SP5[(work >> 8) & 0x3f]
|
||
|
fval |= SP3[(work >> 16) & 0x3f]
|
||
|
fval |= SP1[(work >> 24) & 0x3f]
|
||
|
work = right ^ keys[i * 4 + 1]
|
||
|
fval |= SP8[ work & 0x3f]
|
||
|
fval |= SP6[(work >> 8) & 0x3f]
|
||
|
fval |= SP4[(work >> 16) & 0x3f]
|
||
|
fval |= SP2[(work >> 24) & 0x3f]
|
||
|
leftt ^= fval
|
||
|
work = (leftt << 28) | (leftt >> 4)
|
||
|
work ^= keys[i * 4 + 2]
|
||
|
fval = SP7[ work & 0x3f]
|
||
|
fval |= SP5[(work >> 8) & 0x3f]
|
||
|
fval |= SP3[(work >> 16) & 0x3f]
|
||
|
fval |= SP1[(work >> 24) & 0x3f]
|
||
|
work = leftt ^ keys[i * 4 + 3]
|
||
|
fval |= SP8[ work & 0x3f]
|
||
|
fval |= SP6[(work >> 8) & 0x3f]
|
||
|
fval |= SP4[(work >> 16) & 0x3f]
|
||
|
fval |= SP2[(work >> 24) & 0x3f]
|
||
|
right ^= fval
|
||
|
end
|
||
|
|
||
|
right = ((right << 31) | (right >> 1)) & 0xffffffff
|
||
|
work = (leftt ^ right) & 0xaaaaaaaa
|
||
|
leftt ^= work
|
||
|
right ^= work
|
||
|
leftt = ((leftt << 31) | (leftt >> 1)) & 0xffffffff
|
||
|
work = ((leftt >> 8) ^ right) & 0x00ff00ff
|
||
|
right ^= work
|
||
|
leftt ^= (work << 8)
|
||
|
work = ((leftt >> 2) ^ right) & 0x33333333
|
||
|
right ^= work
|
||
|
leftt ^= (work << 2)
|
||
|
work = ((right >> 16) ^ leftt) & 0x0000ffff
|
||
|
leftt ^= work
|
||
|
right ^= (work << 16)
|
||
|
work = ((right >> 4) ^ leftt) & 0x0f0f0f0f
|
||
|
leftt ^= work
|
||
|
right ^= (work << 4)
|
||
|
|
||
|
[right, leftt]
|
||
|
end
|
||
|
end
|
||
|
end
|
||
|
end
|
||
|
|