--- /dev/null
+0
+x
+1
+0
+00
+0x
+01
+x
+x0
+xx
+x1
+1
+10
+1x
+11
+0
+0 0
+0 x
+0 1
+00
+000
+00x
+001
+0x
+0x0
+0xx
+0x1
+01
+010
+01x
+011
+x
+x 0
+x x
+x 1
+x0
+x00
+x0x
+x01
+xx
+xx0
+xxx
+xx1
+x1
+x10
+x1x
+x11
+1
+1 0
+1 x
+1 1
+10
+100
+10x
+101
+1x
+1x0
+1xx
+1x1
+11
+110
+11x
+111
+0
+0 0
+0 x
+0 1
+0 0
+0 00
+0 0x
+0 01
+0 x
+0 x0
+0 xx
+0 x1
+0 1
+0 10
+0 1x
+0 11
+00
+00 0
+00 x
+00 1
+000
+0000
+000x
+0001
+00x
+00x0
+00xx
+00x1
+001
+0010
+001x
+0011
+0x
+0x 0
+0x x
+0x 1
+0x0
+0x00
+0x0x
+0x01
+0xx
+0xx0
+0xxx
+0xx1
+0x1
+0x10
+0x1x
+0x11
+01
+01 0
+01 x
+01 1
+010
+0100
+010x
+0101
+01x
+01x0
+01xx
+01x1
+011
+0110
+011x
+0111
+x
+x 0
+x x
+x 1
+x 0
+x 00
+x 0x
+x 01
+x x
+x x0
+x xx
+x x1
+x 1
+x 10
+x 1x
+x 11
+x0
+x0 0
+x0 x
+x0 1
+x00
+x000
+x00x
+x001
+x0x
+x0x0
+x0xx
+x0x1
+x01
+x010
+x01x
+x011
+xx
+xx 0
+xx x
+xx 1
+xx0
+xx00
+xx0x
+xx01
+xxx
+xxx0
+xxxx
+xxx1
+xx1
+xx10
+xx1x
+xx11
+x1
+x1 0
+x1 x
+x1 1
+x10
+x100
+x10x
+x101
+x1x
+x1x0
+x1xx
+x1x1
+x11
+x110
+x11x
+x111
+1
+1 0
+1 x
+1 1
+1 0
+1 00
+1 0x
+1 01
+1 x
+1 x0
+1 xx
+1 x1
+1 1
+1 10
+1 1x
+1 11
+10
+10 0
+10 x
+10 1
+100
+1000
+100x
+1001
+10x
+10x0
+10xx
+10x1
+101
+1010
+101x
+1011
+1x
+1x 0
+1x x
+1x 1
+1x0
+1x00
+1x0x
+1x01
+1xx
+1xx0
+1xxx
+1xx1
+1x1
+1x10
+1x1x
+1x11
+11
+11 0
+11 x
+11 1
+110
+1100
+110x
+1101
+11x
+11x0
+11xx
+11x1
+111
+1110
+111x
+1111