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=begin
 
お題
XORゲートは4つのNANDゲートで構成できることが知られている
この構成方法をプログラムで探索せよ
 
i番目のNANDゲートの入力を(ai,bi)、出力をciとする
XORゲートの入力を(X,Y)、出力をZとする
 
出力例
X->a1
Y->b1
X->a2
c1->b2
Y->a3
c1->b3
c2->a4
c3->b4
c4->Z 
 
=end
 
# 自由度は入力の接続先。出力のどれかと必ず接続する。
# 入力同士は接続できる (同じ出力に接続できる)
# 出力同士は接続できない
#   どこにもつながらない出力は無いはず
# 出力	X,Y, c1,c2,c3,c4				0..5
# 入力	a1,b1, a2,b2, a3,b3, a4,b4		0..7
#		(c1..4) -> Z
 
 
	$ans = 0
	ab = [ 0,0, 0,0, 0,0, 0,0 ]
 
def print_map( ab, z )
	tbl  = %w{ X Y c1 c2 c3 c4 }
	chAB = %w{ a b }
	ab.each_with_index{|n,i|
		m, a = i.divmod(2)
		puts " %3s -> %s%d" % [ tbl[n], chAB[a], m+1 ]
#		print "#{tbl[n]} "
	}
	puts "  c#{z+1} -> Z"
	$ans += 1
end
 
 
def check( ab )
	return false	unless ab.index(0) && ab.index(1)	# X,Y 入力を使わない物は枝刈り
	cnum = [0,0,0,0]	# 出力ビットテーブル f(x,y) -> c_
	2.times{|x|
		2.times{|y|
			lg = [ nil,nil, nil,nil, nil,nil, nil,nil ]		# 入力値 [a_,b_] * 4
			c = [ nil, nil, nil, nil ]						# 出力値 c1..c4
			ab.each_with_index{|n,i|
				case n
				when 0;	lg[i] = x
				when 1;	lg[i] = y
				end
			}
			4.times{		# ロジック最大段数 (3で良いはず)
				4.times{|cn|
					next	if c[cn]
					if lg[2*cn] && lg[2*cn+1]
						c[cn] = (lg[2*cn] & lg[2*cn+1]) ^ 1		# nand
						ab.each_with_index{|n,i|
							case n
							when 2;	lg[i] = c[0]
							when 3;	lg[i] = c[1]
							when 4;	lg[i] = c[2]
							when 5;	lg[i] = c[3]
							end
						}
					end
				}
			}
			c.size.times{|n|
				if c[n] && cnum[n]
					cnum[n] = (cnum[n] << 1) | c[n]
				else
					cnum[n] = nil
				end
			}
		}
	}
	cnum.each_with_index{|n,i|
		next	unless n == 0b0110		# xor パターン検索
		if ab.index( i + 2 )
			warn "Loop"		# 出力がループしている
			next
		end
		print_map( ab, i )
		puts
	}
end
 
 
def solve( ab, n = 0 )
	return	if n > 7
	solve( ab, n + 1 )
	check( ab )	if n == 7
	ab[n] += 1
	ab[n] += 1	if n >> 1 == ab[n] - 2		# 出力は入力につなげない (一段のループだけチェック)
	if ab[n] > 5
		ab[n] = 0
		return
	end
	solve( ab, n )
end
 
#####################################################################
 
	solve( ab )
	puts "Done. #{$ans}"

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Time limit exceeded #stdin #stdout 5s 6328KB

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Standard input is empty

stdout

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   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
   Y -> a3
  c1 -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
   Y -> a3
  c1 -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
  c1 -> a3
   Y -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
  c1 -> a3
   Y -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
  c2 -> a3
  c4 -> b3
   Y -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
  c2 -> a3
  c4 -> b3
  c1 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
  c4 -> a3
  c2 -> b3
   Y -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
   X -> a2
  c1 -> b2
  c4 -> a3
  c2 -> b3
  c1 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
   X -> a3
  c1 -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
   X -> a3
  c1 -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
  c1 -> a3
   X -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
  c1 -> a3
   X -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
  c2 -> a3
  c4 -> b3
   X -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
  c2 -> a3
  c4 -> b3
  c1 -> a4
   X -> b4
  c3 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
  c4 -> a3
  c2 -> b3
   X -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
   Y -> a2
  c1 -> b2
  c4 -> a3
  c2 -> b3
  c1 -> a4
   X -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
   Y -> a3
  c1 -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
   Y -> a3
  c1 -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
  c1 -> a3
   Y -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
  c1 -> a3
   Y -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
  c2 -> a3
  c4 -> b3
   Y -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
  c2 -> a3
  c4 -> b3
  c1 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
  c4 -> a3
  c2 -> b3
   Y -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   X -> b2
  c4 -> a3
  c2 -> b3
  c1 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
   X -> a3
  c1 -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
   X -> a3
  c1 -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
  c1 -> a3
   X -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
  c1 -> a3
   X -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
  c2 -> a3
  c4 -> b3
   X -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
  c2 -> a3
  c4 -> b3
  c1 -> a4
   X -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
  c4 -> a3
  c2 -> b3
   X -> a4
  c1 -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c1 -> a2
   Y -> b2
  c4 -> a3
  c2 -> b3
  c1 -> a4
   X -> b4
  c3 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
   X -> a3
  c1 -> b3
   Y -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
   X -> a3
  c1 -> b3
  c1 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
   Y -> a3
  c1 -> b3
   X -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
   Y -> a3
  c1 -> b3
  c1 -> a4
   X -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
  c1 -> a3
   X -> b3
   Y -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
  c1 -> a3
   X -> b3
  c1 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
  c1 -> a3
   Y -> b3
   X -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c3 -> a2
  c4 -> b2
  c1 -> a3
   Y -> b3
  c1 -> a4
   X -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
   X -> a3
  c1 -> b3
   Y -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
   X -> a3
  c1 -> b3
  c1 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
   Y -> a3
  c1 -> b3
   X -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
   Y -> a3
  c1 -> b3
  c1 -> a4
   X -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
  c1 -> a3
   X -> b3
   Y -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
  c1 -> a3
   X -> b3
  c1 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
  c1 -> a3
   Y -> b3
   X -> a4
  c1 -> b4
  c2 -> Z

   X -> a1
   Y -> b1
  c4 -> a2
  c3 -> b2
  c1 -> a3
   Y -> b3
  c1 -> a4
   X -> b4
  c2 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
   Y -> a3
  c2 -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
   Y -> a3
  c2 -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
  c1 -> a3
  c4 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
  c1 -> a3
  c4 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
  c2 -> a3
   Y -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
  c2 -> a3
   Y -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
  c4 -> a3
  c1 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

   X -> a1
  c2 -> b1
   X -> a2
   Y -> b2
  c4 -> a3
  c1 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
   Y -> a3
  c2 -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
   Y -> a3
  c2 -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
  c1 -> a3
  c4 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
  c1 -> a3
  c4 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
  c2 -> a3
   Y -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
  c2 -> a3
   Y -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
  c4 -> a3
  c1 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

   X -> a1
  c2 -> b1
   Y -> a2
   X -> b2
  c4 -> a3
  c1 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

   X -> a1
  c3 -> b1
   Y -> a2
  c3 -> b2
   X -> a3
   Y -> b3
  c1 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
  c3 -> b1
   Y -> a2
  c3 -> b2
   X -> a3
   Y -> b3
  c2 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c3 -> b1
   Y -> a2
  c3 -> b2
   Y -> a3
   X -> b3
  c1 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
  c3 -> b1
   Y -> a2
  c3 -> b2
   Y -> a3
   X -> b3
  c2 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c3 -> b1
  c1 -> a2
  c4 -> b2
   X -> a3
   Y -> b3
   Y -> a4
  c3 -> b4
  c2 -> Z

   X -> a1
  c3 -> b1
  c1 -> a2
  c4 -> b2
   X -> a3
   Y -> b3
  c3 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
  c3 -> b1
  c1 -> a2
  c4 -> b2
   Y -> a3
   X -> b3
   Y -> a4
  c3 -> b4
  c2 -> Z

   X -> a1
  c3 -> b1
  c1 -> a2
  c4 -> b2
   Y -> a3
   X -> b3
  c3 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
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  c3 -> a2
   Y -> b2
   X -> a3
   Y -> b3
  c1 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
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  c3 -> a2
   Y -> b2
   X -> a3
   Y -> b3
  c2 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c3 -> b1
  c3 -> a2
   Y -> b2
   Y -> a3
   X -> b3
  c1 -> a4
  c2 -> b4
  c4 -> Z

   X -> a1
  c3 -> b1
  c3 -> a2
   Y -> b2
   Y -> a3
   X -> b3
  c2 -> a4
  c1 -> b4
  c4 -> Z

   X -> a1
  c3 -> b1
  c4 -> a2
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   X -> a3
   Y -> b3
   Y -> a4
  c3 -> b4
  c2 -> Z

   X -> a1
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  c4 -> a2
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   X -> a3
   Y -> b3
  c3 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
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  c4 -> a2
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   Y -> a3
   X -> b3
   Y -> a4
  c3 -> b4
  c2 -> Z

   X -> a1
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  c4 -> a2
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   Y -> a3
   X -> b3
  c3 -> a4
   Y -> b4
  c2 -> Z

   X -> a1
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   Y -> a2
  c4 -> b2
  c1 -> a3
  c2 -> b3
   X -> a4
   Y -> b4
  c3 -> Z

   X -> a1
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   Y -> a2
  c4 -> b2
  c1 -> a3
  c2 -> b3
   Y -> a4
   X -> b4
  c3 -> Z

   X -> a1
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   Y -> a2
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  c2 -> a3
  c1 -> b3
   X -> a4
   Y -> b4
  c3 -> Z

   X -> a1
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   Y -> a2
  c4 -> b2
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  c1 -> b3
   Y -> a4
   X -> b4
  c3 -> Z

   X -> a1
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  c1 -> a2
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   Y -> a3
  c4 -> b3
   X -> a4
   Y -> b4
  c2 -> Z

   X -> a1
  c4 -> b1
  c1 -> a2
  c3 -> b2
   Y -> a3
  c4 -> b3
   Y -> a4
   X -> b4
  c2 -> Z

   X -> a1
  c4 -> b1
  c1 -> a2
  c3 -> b2
  c4 -> a3
   Y -> b3
   X -> a4
   Y -> b4
  c2 -> Z

   X -> a1
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  c1 -> a2
  c3 -> b2
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   Y -> b3
   Y -> a4
   X -> b4
  c2 -> Z

   X -> a1
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  c3 -> a2
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   Y -> a3
  c4 -> b3
   X -> a4
   Y -> b4
  c2 -> Z

   X -> a1
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  c3 -> a2
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   Y -> a3
  c4 -> b3
   Y -> a4
   X -> b4
  c2 -> Z

   X -> a1
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  c3 -> a2
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   Y -> b3
   X -> a4
   Y -> b4
  c2 -> Z

   X -> a1
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  c3 -> a2
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   Y -> b3
   Y -> a4
   X -> b4
  c2 -> Z

   X -> a1
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  c4 -> a2
   Y -> b2
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  c2 -> b3
   X -> a4
   Y -> b4
  c3 -> Z

   X -> a1
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  c4 -> a2
   Y -> b2
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  c2 -> b3
   Y -> a4
   X -> b4
  c3 -> Z

   X -> a1
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  c4 -> a2
   Y -> b2
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  c1 -> b3
   X -> a4
   Y -> b4
  c3 -> Z

   X -> a1
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  c4 -> a2
   Y -> b2
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  c1 -> b3
   Y -> a4
   X -> b4
  c3 -> Z

   Y -> a1
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   X -> a2
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   Y -> a3
  c1 -> b3
  c2 -> a4
  c3 -> b4
  c4 -> Z

   Y -> a1
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   X -> a2
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   Y -> a3
  c1 -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   Y -> a1
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   X -> a2
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  c1 -> a3
   Y -> b3
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  c3 -> b4
  c4 -> Z

   Y -> a1
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   X -> a2
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   Y -> b3
  c3 -> a4
  c2 -> b4
  c4 -> Z

   Y -> a1
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   X -> a2
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  c4 -> b3
   Y -> a4
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  c3 -> Z

   Y -> a1
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   X -> a2
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  c4 -> b3
  c1 -> a4
   Y -> b4
  c3 -> Z

   Y -> a1
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   X -> a2
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  c4 -> a3
  c2 -> b3
   Y -> a4
  c1 -> b4
  c3 -> Z

   Y -> a1
   X -> b1
   X -> a2
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  c4 -> a3
  c2 -> b3
  c1 -> a4
   Y -> b4
  c3 -> Z

   Y -> a1
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   Y -> a2
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   X -> a3
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  c2 -> a4
  c3 -> b4
  c4 -> Z

   Y -> a1
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   Y -> a2
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  c3 -> a4
  c2 -> b4
  c4 -> Z

   Y -> a1
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   Y -> a2
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   X -> b3
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  c3 -> b4
  c4 -> Z

   Y -> a1
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   Y -> a2
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   X -> b3
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  c4 -> Z

   Y -> a1
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   Y -> a2
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  c4 -> b3
   X -> a4
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  c3 -> Z

   Y -> a1
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   Y -> a2
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  c4 -> b3
  c1 -> a4
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  c3 -> Z

   Y -> a1
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   Y -> a2
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  c4 -> a3
  c2 -> b3
   X -> a4
  c1 -> b4
  c3 -> Z

   Y -> a1
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   Y -> a2
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  c2 -> b3
  c1 -> a4
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  c3 -> Z

   Y -> a1
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   Y -> a1
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   Y -> a1
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   Y -> b3
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   Y -> a1
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  c2 -> b4
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   Y -> a1
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   Y -> a4
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   Y -> a1
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   Y -> a4
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   Y -> a1
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   Y -> a1
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  c3 -> b4
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   Y -> a1
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  c2 -> b4
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   Y -> a1
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   Y -> a1
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   Y -> a1
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   Y -> a4
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   Y -> a1
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   Y -> a1
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   X -> a4
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   Y -> a1
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   Y -> a1
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   Y -> a4
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   Y -> a1
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   Y -> a1
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   Y -> a1
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   Y -> a4
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  c2 -> Z

   Y -> a1
  c4 -> b1
  c4 -> a2
   X -> b2
  c1 -> a3
  c2 -> b3
   X -> a4
   Y -> b4
  c3 -> Z

   Y -> a1
  c4 -> b1
  c4 -> a2
   X -> b2
  c1 -> a3
  c2 -> b3
   Y -> a4
   X -> b4
  c3 -> Z

   Y -> a1
  c4 -> b1
  c4 -> a2
   X -> b2
  c2 -> a3
  c1 -> b3
   X -> a4
   Y -> b4
  c3 -> Z

   Y -> a1
  c4 -> b1
  c4 -> a2
   X -> b2
  c2 -> a3
  c1 -> b3
   Y -> a4
   X -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
   Y -> a3
  c2 -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
   Y -> a3
  c2 -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
  c1 -> a3
  c4 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
  c1 -> a3
  c4 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
  c2 -> a3
   Y -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
  c2 -> a3
   Y -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
  c4 -> a3
  c1 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   X -> a2
   Y -> b2
  c4 -> a3
  c1 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
   Y -> a3
  c2 -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
   Y -> a3
  c2 -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
  c1 -> a3
  c4 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
  c1 -> a3
  c4 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
  c2 -> a3
   Y -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
  c2 -> a3
   Y -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
  c4 -> a3
  c1 -> b3
   Y -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   X -> b1
   Y -> a2
   X -> b2
  c4 -> a3
  c1 -> b3
  c2 -> a4
   Y -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
   X -> a3
  c2 -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
   X -> a3
  c2 -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
  c1 -> a3
  c4 -> b3
   X -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
  c1 -> a3
  c4 -> b3
  c2 -> a4
   X -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
  c2 -> a3
   X -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
  c2 -> a3
   X -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
  c4 -> a3
  c1 -> b3
   X -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   X -> a2
   Y -> b2
  c4 -> a3
  c1 -> b3
  c2 -> a4
   X -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
   X -> a3
  c2 -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
   X -> a3
  c2 -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
  c1 -> a3
  c4 -> b3
   X -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
  c1 -> a3
  c4 -> b3
  c2 -> a4
   X -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
  c2 -> a3
   X -> b3
  c1 -> a4
  c3 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
  c2 -> a3
   X -> b3
  c3 -> a4
  c1 -> b4
  c4 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
  c4 -> a3
  c1 -> b3
   X -> a4
  c2 -> b4
  c3 -> Z

  c2 -> a1
   Y -> b1
   Y -> a2
   X -> b2
  c4 -> a3
  c1 -> b3
  c2 -> a4
   X -> b4
  c3 -> Z

  c2 -> a1
  c3 -> b1
   X -> a2
  c4 -> b2
   Y -> a3
  c4 -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
   X -> a2
  c4 -> b2
   Y -> a3
  c4 -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
   X -> a2
  c4 -> b2
  c4 -> a3
   Y -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
   X -> a2
  c4 -> b2
  c4 -> a3
   Y -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
   Y -> a2
  c4 -> b2
   X -> a3
  c4 -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
   Y -> a2
  c4 -> b2
   X -> a3
  c4 -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
   Y -> a2
  c4 -> b2
  c4 -> a3
   X -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
   Y -> a2
  c4 -> b2
  c4 -> a3
   X -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   X -> b2
   Y -> a3
  c4 -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   X -> b2
   Y -> a3
  c4 -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   X -> b2
  c4 -> a3
   Y -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   X -> b2
  c4 -> a3
   Y -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   Y -> b2
   X -> a3
  c4 -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   Y -> b2
   X -> a3
  c4 -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   Y -> b2
  c4 -> a3
   X -> b3
   X -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c3 -> b1
  c4 -> a2
   Y -> b2
  c4 -> a3
   X -> b3
   Y -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   X -> a2
  c3 -> b2
   X -> a3
   Y -> b3
   Y -> a4
  c3 -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   X -> a2
  c3 -> b2
   X -> a3
   Y -> b3
  c3 -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   X -> a2
  c3 -> b2
   Y -> a3
   X -> b3
   Y -> a4
  c3 -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   X -> a2
  c3 -> b2
   Y -> a3
   X -> b3
  c3 -> a4
   Y -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   Y -> a2
  c3 -> b2
   X -> a3
   Y -> b3
   X -> a4
  c3 -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   Y -> a2
  c3 -> b2
   X -> a3
   Y -> b3
  c3 -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   Y -> a2
  c3 -> b2
   Y -> a3
   X -> b3
   X -> a4
  c3 -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
   Y -> a2
  c3 -> b2
   Y -> a3
   X -> b3
  c3 -> a4
   X -> b4
  c1 -> Z

  c2 -> a1
  c4 -> b1
  c3 -> a2

https://ideone.com/OJiVYh

xor

language:

Ruby (ruby 2.5.5)

created:

visibility:

public

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