$30
AAA-Encoding Game State Solved
1 Introduction
In this section, we will develop a way of encoding the state of the game. A single state represents the current board position — it should contain all the information necessary for the game (and successor function) to operate correctly.
2 Forsyth–Edwards Notation
Forsyth–Edwards Notation (FEN) is a standard way of encoding chess positions as a string. For the game Congo, the FEN string will consist of three fields, each separated by a blank space:
<position of pieces> <side to move> <move number>
2.1 Position of pieces
In our FEN representation, we will specify the placement of each piece on the board. Each piece is encoded as a single character—white pieces uses capital letters, and black pieces use the corresponding lowercase letter. The pieces are: pawn (P), giraffe (G), monkey (M), elephant (E), lion (L), crocodile (C), zebra (Z) and superpawn (S).
The string describes each rank (row), starting from rank 7 to rank 1. The string for each rank specifices the location of a piece on that rank, and any number of empty squares. Each rank is separated by a /. The easiest way to understand this encoding is to look at some examples, as illustrated below.
Z
Z Z
Z
po
pop
op
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
PO
POP
OP
Z
Z Z
Z
7
6
5
4
3
2
1
a b c d e f g
(a) The starting position with the representation gmelecz/ppppppp/7/7/7/PPPPPPP/GMELECZ. This string indicates that rank 7 consists of black pieces only and that they are: giraffe, monkey, elephant, lion, elephant, crocodile, zebra. The next rank is 6, which contains all black pawns. The next rank is 5 which has the representation 7. This indicates that there are 7 empty squares. The same is true for ranks 4–3. Rank 2 consists of only white pawns, while rank 1 (GMELECZ) indicates white giraffe, monkey, elephant, lion, elephant, crocodile, zebra.
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z
Z0
OP
Z0Z
PZ
0Z
0Z0
Zp
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) The above board is represented by
2l4/7/4z2/4c2/PP2EP1/3L2p/7. The 7th rank
(2l4) has two empty squares, a black lion, and 4 empty squares. The 6th rank has 7 empty squares. The 5th rank (4z2) has 4 empty squares, a black zebra and 2 empty squares. The 4th rank (4c2) has 4 empty squares, a black crocodile and 2 empty squares. The 3rd rank (PP2EP1) has two white pawns, then two empty spaces, a white elephant, a white pawn and an empty space. The 2nd rank (3L2p) has 3 empty squares, a white lion, two empty squares and a black pawn. Finally, rank 1 has 7 empty squares.
Figure 1
2.2 Side to move
The side to move is just a single character W or B that indicates whose turn it is to play
2.3 Move number
The move number records the number of moves played in the game. It is incremented only after black plays a move, and so a value of N indicates that both white and black have made N moves.
1. Position of pieces is a string that specifies the placement of each piece on the board. Each rank is described, starting from rank 7 and ending with rank 1.
Input
The first line of input is N, the number of FEN strings that must be read in as input. N lines follow, with each line consisting of a single FEN string.
Output
For each FEN string i, output the location of all pieces on the board, as well as the side to move. Separate each board description with a blank line. Your output should have the following form:
white pawn: <square> <square> ... black pawn: <square> <square> ... white superpawn: <square> <square> ... black superpawn: <square> <square> ... white giraffe: <square> <square> ... black giraffe: <square> <square> ... white monkey: <square> <square> ... black monkey: <square> <square> ... white elephant: <square> <square> ... black elephant: <square> <square> ... white lion: <square> <square> ... black lion: <square> <square> ... white crocodile: <square> <square> ... black crocodile: <square> <square> ... white zebra: <square> <square> ... black zebra: <square> <square> ... side to play: <black|white>
where each <square> is the file and rank (e.g. a1) and squares are separated by blank spaces. If there is more than one square on a line, the squares should be output in alphabetical order.
For example, the string 2l4/7/4z2/4c2/PP2EP1/3L2p/7 b 23 which is illustrated by Figure
1b would produce the output
white pawn: a3 b3 f3 black pawn: g2 white superpawn: black superpawn: white giraffe: black giraffe:
white monkey: black monkey: white elephant: e3 black elephant: white lion: d2 black lion: c7 white crocodile: black crocodile: e4 white zebra: black zebra: e5 side to play: black
Example Input-Output
Sample Input
2 gmelecz/ppppppp/7/7/7/PPPPPPP/GMELECZ w 0
1m1El2/P1P2P1/1S4C/4S2/1E3S1/1P3c1/2GL3 b 79
Sample Output
white pawn: a2 b2 c2 d2 e2 f2 g2 black pawn: a6 b6 c6 d6 e6 f6 g6 white superpawn: black superpawn: white giraffe: a1 black giraffe: a7 white monkey: b1 black monkey: b7 white elephant: c1 e1 black elephant: c7 e7 white lion: d1 black lion: d7 white crocodile: f1 black crocodile: f7 white zebra: g1 black zebra: g7 side to play: white
white pawn: a6 b2 c6 f6 black pawn:
white superpawn: b5 e4 f3 black superpawn: white giraffe: c1 black giraffe: white monkey: black monkey: b7
white elephant: b3 d7 black elephant: white lion: d1 black lion: e7 white crocodile: g5 black crocodile: f2 white zebra: black zebra: side to play: black
Automatically generated positions
Z0
Z Z
0Z
Z
0o0
Z0
Z0
Z0o
0Z
0Z
0Z0
Zp
Zp
Z Z
0Z
Z
0ZP
Zp
Z0
Z0Z
0Z
77
66
55
44
33
22
11
a b c d e f g
(a) 3l3/E2p3/4p2/6p/1pLS3/s3P1p/7
Z0
Z0Z
0Z
0Z
0Zp
Z0
ZP
O0Z
0Z
0Z
0ZP
Z0
Z0
Z0Z
0Z
0Z
Z0
Z0
Z0
Z Z
0Z
a b c d e f g
(b) 7/3lp2/1PP4/4P2/7/2e4/3L3
Z
Z0Z
Z
PZ
0Z
Z0
Z0
oPZ
0O
0Z
0O0
Z
o
Z0o
0Z
pZ
0Z
ZP
Z0
Z0Z
0Z
77
66
55
44
33
22
11
a b c d e f g
(a) 1Z3e1/P3l2/m1pP2P/3P2z/pSg1p2/p3LeP/2E4
Z0
Z0Z
0Z
0Z
0Z0
o0
o0
Z0Z
0Z
0Z
0Z0
Z0
Z0
O0O
0Z
0Z
0Z0
Z0
Z0
Z Z
0Z
a b c d e f g
(b) 4l2/5p1/p6/1S5/2P1P2/5s1/3eL2
Z
Z Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0O
0Z
0Z0
Z0
Z
ZPZ
pZ
0Z
0Z
Z0
Z0
Z0Z
0Z
77
66
55
44
33
22
11
a b c d e f g
(a) 1C1l3/7/6P/7/1Z1P1p1/3LS2/7
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
PZ
0Z
0Z
Z0
Z0
Z0Z
0Z
a b c d e f g
(b) e1l4/7/7/7/2L2P1/3Es2/7
Z0
Z Z
0Z
0Z
0Z
Z0
OP
Z0Z
pZ
Z
0Z0
Z0
ZP
O0Z
0Z
0Z
0ZP
O0
Z0
Z0Z
0Z
1
a b c d e f g
(a) 3l3/4e2/PP2Mp1/g6/1PP4/1z2PP1/4L2
Z0
Z0Z
0Z
0Z
0Z0
o0
Z
Z0Z
0Z
0Z
0ZP
Z0
Z0
ZPZ
pZ
0Z
0O0
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(b) 7/3l1p1/1e5/4P2/3P1p1/3P3/2L4
Z0
Z0Z
0Z
0Z
0o
Zp
Z
Z0Z
0Z
Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0o0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 6E/3pl1p/ezZ4/G6/2L4/3p3/6C
Z
Z0Z
0Z
0Z
0ZP
Z0
O
Z Z
0Z
0Z
0Z0
O0
Z0
Z Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 1e5/4P2/PE1l3/5P1/3L3/7/7
Z0
Z0Z
0Z
0Z
0Z0
ZP
Z
o0Z
0O
0Z
0Z0
Z
Zp
Z Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
Z
7
6
5
4
3
2
1
a b c d e f g
(a) 7/3e2P/1gp1l1P/6G/1p1L3/7/4ez1
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
ZpZ
0Z
0Z
0Z0
Z0
Z0
ZPO
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 2l4/7/3p3/7/3PP2/3L3/7
Z0
Z0Z
0Z
pZ
0Z0
oP
Z0
Z0Z
PZ
0Z
0Z
Z0
Z0
Z0O
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
Z
Z0Z
0Z
Z
0oP
Z0
Z0
Z0Z
0Z
0Z
0Z0
ZP
o
Z0Z
0Z
0Z
Z0
Z0
Z0
Z0Z
0Z
11
a b c d e f g
(a) 7/pe3pP/2l2P1/4M2/4P2/4s2/2L4
a b c d e f g
(b) 1e5/s2pP2/2l4/6P/pES4/2L4/7
Z0
Z0Z
0Z
0Z
0Z
Z0
Z0
o0o
Z
0Z
0Zp
Z0
o0
Z0Z
po
0Z
0Zp
Z0
Z0
Z0Z
0Z
77
66
55
44
33
22
11
a b c d e f g
(a) 2l4/4g2/2p1pc1/4p2/p4pp/4p2/e3L2
Z0
Z0Z
0Z
0o
0o0
Z0
Z0
O Z
0Z
0Z
Z0
Zp
o
O Z
0Z
Z
Z
Zp
Z0
Z0Z
0Z
77
66
55
44
33
22
11
a b c d e f g
(a) 6e/1p1p1s1/E1Pl2e/2Z3p/pEPM3/c1L1sCp/7
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z
Z0
Z
Z0Z
0Z
0Z
pZ0
Z0
Z0
Z0Z
0Z
a b c d e f g
(b) 4l2/7/7/4E2/es5/2p4/2L4
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0O
0Z
0Z0
Z0
Z0
Z0Z
0Z
pZ
Z0
ZP
Z0
Z0Z
0Z
a b c d e f g
(b) 7/7/4l1P/7/7/p1EL2P/7
Z0
Z Z
0Z
0O
PZ0
Z0
Z0
Z0o
PZ
Z
0Z
Z0
o0
ZPZ
0Z
0o
Po
Zp
Z
Z0Z
0Z
Z0
Z0Z
0Z
Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
11
a b c d e f g
(a) 3l2C/1PP4/4pP1/e3G2/p1LPz2/1pPpc1p/1e5
a b c d e f g
Z0
Z Z
0Z
0Z
0Z
Z
Z0
Z0O
pZ
Z
0Z
Z0
Z0
o0Z
Z
0Z
0Z0
Zp
Z0
Z0Z
0Z
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
Z0
Z0
Z0
Z0Z
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
77
66
55
44
33
22
11
(b) 2l4/s4S1/6E/7/4L2/7/7
a b c d e f g
(a) 3l3/4m1E/4Pp1/E3s2/2p1gM1/6p/2G1L2
a b c d e f g
Z0
Z Z
0Z
0o
0Z0
ZP
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
Z
0Z
0Zp
Z0
Z
Z Z
0Z
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z Z
0Z
0O
0Z0
Z0
Z0
Z Z
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
77
66
55
44
33
22
11
(b) 7/3E3/2l4/2S4/7/4L2/7
a b c d e f g
(a) 2El3/1p1Z2P/6s/5M1/4Lg1/4p2/1G1C3
a b c d e f g
(b) 7/7/3l3/1P1e3/2LS3/4s2/7
Z0
Z Z
0Z
0Z
0Z0
Z0
Z0
Z Z
PZ
Z
0Z
Z0
Z0
Z0Z
0O
0Z
0Z0
O0
Z0
Z0Z
0Z
1
a b c d e f g
(a) 3g3/7/3l1P1/M3C2/4Z1P/3L1P1/2G4
Z0
Z0Z
0Z
po
0Z
Z0
Z0
ZPZ
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
pZ
ZP
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(b) 7/pp2l2/3P2E/1e5/7/p1L1P2/7
Z
Z Z
0Z
PZ
PZ0
O0
Z
Z0Z
0Z
0Z
0Z
Z0
Z
Z0Z
Z
0O
0Z0
Z0
Z0
Z Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 1m1El2/P1P2P1/1S4C/4S2/1E3S1/1P3c1/2GL3
Z
Z0Z
0Z
0Z
0Z0
O0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 1E5/5P1/2l4/7/S3L2/7/7
Z0
Z0Z
0Z
0Z
0Z0
ZP
Z
Z Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 7/6P/1e1l3/5Z1/2L4/3SC2/7
Z0
Z0Z
0Z
0Z
0Zp
Z0
Z
Z Z
0Z
0Z
0Z0
Z0
Z
Z0Z
pZ
0Z
Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/4p2/1S1l3/7/1e3p1/2EL3/7
Z0
0Z
OP
Z0Z
0Z0
Z0o
Z ZP
0Z
7
6
5
4
3
2
1
Z0
0Z
Z0
Z0Z
0Z
Z0Z
0Z
O0
Z
0Z
0Z0
Zp
Z
0Z0
Z0
ZP
0O Z0
Z0Z
Zp
Z Z
PO o0 0Z
Z0
0Z
Z0
Z0Z
0O
Z0Z
0o
Z0
0Z
1
a b c d e f g a b c d e f g
(a) 2l2Ce/1s4P/PP2p2/3M2p/1P2LPP/1PG1pp1/Z2c3 (b) 7/4lP1/5E1/e2S3/6p/3PL2/7
Z0 o Zp
Z0Z
Z0 Z0Z
0Z
Zp
Z
7
6
5
4
3
2
1
Z0
0Z
Zp
Z0Z
0Z0
Z Z
0Z Z0 pZ
0Z
0Z
Zp
0Z
PZ0
Z0
ZP pZ Z0
OZ
0o
Z0Z
O
Z
0Z
Z0
0Z
Z0
Z0Z
0Z0
Z Z
0Z
Z0
0Z
7
6
5
4
3
2
1
a b c d e f g a b c d e f g
(a) c3E2/GplM2p/gp2sES/4S1p/1PPL1ZP/p2pSSz/7 (b) 7/7/1p1l1p1/2P4/7/3L3/3e3
Z0 po O0
Z0Z
Z
OpO
0Z
Zp
0O
7
6
5
4
3
2
1
Z0
0Z
O0
Z0Z
PZ0
Z0Z
0Z
O0
0Z
0Z
Z0
Z0
0Z
0Z0
Z0
O0
0O
Z0
ZpZ
0o
Z Z
0Z o0 0Z
Z0
0Z
Z0
Z0Z
0Z0
Z0Z
0Z
Z0
0Z
7
6
5
4
3
2
1
a b c d e f g a b c d e f g
(a) 6e/ppS1l1p/P1PpP1P/2Zg3/P1zpL2/1P1pcp1/3M3 (b) 4l2/2P2P1/P6/7/2L4/7/7
Z0
Z0Z
0Z
0Z
0Z0
Z
Z0
Z Z
0Z
0Z
0Z0
Z0
Z0
Z Z
0Z
0Z
0Zp
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(a) 6Z/5eG/2gl3/7/3L3/1M2p2/4e2
Z0
Z0Z
0Z
0Z
0Z0
O0
Z0
Z0Z
0Z
Z
0o0
Z0
Z0
Z0Z
0Z
o
0Z0
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(b) 7/5P1/2l4/E2p3/2L4/ep5/7
Z
Z0Z
0Z
pO
pZ
O0
Z0
Z0Z
Z
0Z
0ZP
Z
Z0
Z Z
0o
0Z
Z0
oP
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 1z5/pPp1lP1/5es/4P1e/3mL1p/2s2pP/c6
Z0
Z0Z
0Z
0Z
ZP
op
Z0
Z0Z
0Z
0Z
0O0
Z0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 4l2/2E1Ppp/7/3P3/7/7/4L2
Z
Z Z
0Z
0Z
0Z0
Z0
Z0
ZPZ
pZ
0Z
0Z0
Z0
Z0
ZpZ
Z
0Z
0Z0
ZP
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 1M1m3/7/2lP1p1/7/2speE1/1z4P/4L2
Z0
Z0Z
0Z
0O
0Z0
Z0
Z0
Z Z
0Z
0Z
0Z0
Z0
Zp
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 4l2/1P5/3S3/7/1p5/3L3/7
Z0
0Z
Z0
Z0Z
0Z
Z0o
0Z Zp pZ
7
6
5
4
3
2
1
Z0
0Z
ZP
Z0Z
0Z0
Z0Z
0Z
Z0
0Z
0Z
0Z0
Z0
PZ
0Z0
Z0
Z0
0Z Z0
Z Z
0O0
Z0Z
0Z o
Z
Z0 po Z0
Z0Z
0Z0
Z0Z
Z
Z0
0Z
1
a b c d e f g
(a) 7/3elsp/4ppg/1Z5/e1sL3/1E1P1pc/C4E1
a b c d e f g
Z0
0Z
Z
Z0Z
0Z
ZPO
0Z o
O
7
6
5
4
3
2
1
Z0
0Z
Zp
Z0Z
0Z0
Z Z
Z
Z0
Z
0Z
0Z
Z0
0Z
0Zp
Z0
Z0
O
Z0
o0o POp Z0Z
0Z
Z0
0Z
O0
0Z
Z0
Z Z
0Z0
Z0Z
0O
Z0
0Z
7
6
5
4
3
2
1
a b c d e f g a b c d e f g
(a) 7/1s2lps/CZ1PPEP/1e2M2/2p1p1S/cPPPp2/2L1e2 (b) 5e1/7/1p1l1E1/4p2/P1Ls2P/7/7
Z0
0Z
Z0
Z0Z
0Z0 o Z
0Z
Z
0Z
7
6
5
4
3
2
1
Z0
0Z
Z0
Z0Z
0Z0
Z0Z
0Z
Z0
0Z
0Z
0Z0
Z
0Z
0Z0
Z
Z0
0Z
Z0
ZpZ
0Z
Z0Z
0o
Z0
0Z
Z0
0Z
Z0
Z0Z
PZ0
Z0Z
0Z
Z0
0Z
7
6
5
4
3
2
1
a b c d e f g a b c d e f g
(a) 6E/6c/2plE2/6z/3p2p/4L2/7 (b) 7/7/2l4/6S/7/2P4/4L2
(b) 4l2/7/1P4e/P6/5S1/pp5/2L4
Z0
Z Z
Z
0Z
PZ0
O0
Z0
Z0Z
0Z
pZ
0Z0
Z0
Z0
Z0Z
0O
0Z
0Z0
Z0
Z
Z0Z
0Z
1
a b c d e f g
(a) 3l1E1/2P2P1/6S/p6/4L1P/1S3m1/1M5
Z0
Z0Z
0Z
0Z
0o
Z0
Z0
Z0Z
Z
0Z
0O0
Z0
Zp
O0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(b) 7/3pl2/5e1/3P3/1pP4/7/2L4
Z0
Z0Z
0Z
0Z
0Z0
Z
Z0
Z0Z
0Z
0Z
0Z0
Z
Z0
Z Z
Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 7/3l2g/7/6M/3m1e1/1Z5/2L1e2
Z0
Z0Z
0Z
pZ
0Z0
o0
Z0
Z Z
0Z
PZ
0Z0
Z0
Z0
Z0Z
0Z
0Z
pZ0
Z0
Z0
Z Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/p4p1/3le2/P6/6E/2p4/3L3
Z0
Z Z
0Z
0Z
0ZP
Z0
oP
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z Z
0Z
0O
0Z0
o0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 3l3/1c2P2/pP4C/7/3z3/1P1m1p1/4L1M
Z0
Z0Z
0Z
0Z
0O0
Z0
Z
Z0Z
0Z
0o
0Z0
Z0
Z0
Z Z
0Z
0Z
ZP
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/3P3/1S2l2/1p5/3e3/2L1P2/7
Z0
Z0Z
Z
PZ
0Z0
Z0
ZP
Z0Z
PZ
0Z
0Zp
Z
O0
Z0Z
PZ
0Z
0Z0
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(a) z3CE1/P2l3/1PS2P1/4p1E/P4P1/5S1/4L1m
Z0
Z0Z
0Z
0Z
0Z0
ZP
Z0
Z0Z
0Z
0O
0Z0
o0
Z0
Z0Z
0Z
0Z
0o0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/6P/4l2/1P3p1/7/3p3/4L2
Z0
Z0Z
0Z
pO
Z
Zp
ZP
Z Z
0Z
0Z
0ZP
o0
o0
Z o
pZ
0Z
0Z0
OP
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 7/pPEzC1p/GP1lM2/4Pp1/p2mpp1/3c1PP/4L2
Z0
Z0Z
0Z
PZ
0Z
Z0
Z0
Z0Z
0Z
0O
0Z0
Z0
o0
Z0Z
0Z
0Z
pZ0
O0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) E6/P3l2/7/1P5/p6/2pL1P1/7
Z0
Z0Z
0Z
0Z
0Z0
Z0
o0
OpZ
0Z
pZ
0O0
Z0
Z0
Z0Z
0Z
0Z
pZ0
Z
Z0
Z Z
Z
7
6
5
4
3
2
1
a b c d e f g
(a) 2l4/1c5/p1PpM2/p2P3/4e2/2p3m/3L1E1
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z Z
0Z
0o
0Z0
Z0
Z0
ZpZ
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/1S5/3l3/1p5/3p3/4S2/2L4
Z0
Z0Z
0Z
0Z
Z0
Z0
Z0
ZPZ
0Z
0Z
0o0
Z0
Z0
OPZ
0Z
0Z
pZ0
Z0
Z0
Z Z
0Z
1
a b c d e f g
(a) c5E/2e4/3Pl1E/3p3/2PP3/2pe3/Z2L3
Z0
Z0Z
0Z
0Z
0Z0
Z0
o
Z0Z
0Z
0Z
0Z0
Z0
O0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(b) 4l2/7/pE5/7/P1L4/1e5/7
Z0
Z0Z
Z
Z
0Z
Z0
O0
Z0Z
0Z
0Z
0Z0
Z
Z0
ZpO
PZ
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 5g1/Sm1lS2/P6/5Sc/3pPP1/3L1Z1/2M4
Z0
Z0Z
0Z
0Z
Z0
Z0
Z0
Z0Z
0Z
0Z
pZ0
Z0
Z0
Z0Z
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/2El3/7/2p4/7/1e2L2/7
Z0
Z0Z
Z
Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z
Z0
Z
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 2l2c1/Me5/G6/7/7/1s2L2/1E5
Z0
Z0Z
0Z
0Z
0Z0
O0
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/5P1/4l2/7/3L3/5e1/7
Z0
0O Z0
Z Z
PoP ZpZ
0Z o0 0o
7
6
5
4
3
2
1
Z0
0Z
Z0
ZZ
PZ0
Z0Z
0Z
Z0
0Z
0Z
Z0
Z0
0Z
0Z0
Z0
ZP
0o Z0
Z0o
PZ
Z0Z
0Z
Z
0Z
Z0
0Z
Z0
Z0Z
0Z0
Z0Z
0Z
Z0
0Z
1
a b c d e f g a b c d e f g
(a) 3eC2/1PPpPp1/G1lp2p/2c4/1PS1p2/1pPeg1s/M1L4 (b) 3l3/2P4/7/7/e1L4/7/7
Z0
Z Z
0Z
0Z
0O0
Z
Z
ZPZ
0Z
Z
PZ0
Z0
Z0
Z Z
PZ
Z
PZ0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) c2l3/3P2E/1S1P3/C1P4/3eLP1/GmP2S1/2e4
Z0
Z0Z
0Z
0Z
0Z0
Z0
Zp
Z0Z
0Z
0Z
pZ0
Z0
Z0
Z0Z
0Z
0Z
Z0
Zp
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/3l3/1p5/2p4/7/2L3p/7
Z
Z0Z
0Z
pZ
Z0
Z
o0
Z0Z
0O
0Z
0O0
Z
Zp
Z0Z
0Z
0O
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 1M2l2/p1s3G/p5P/3P2z/1p4s/1P1L3/2m4
Z0
Z0Z
0Z
pZ
0Z0
Z0
Z0
O0o
0Z
0Z
0Z0
Z0
Z0
Z Z
0O
0Z
0ZP
Z0
Z0
Z Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 4E2/p2l3/2P1p2/7/3e2P/4P2/3L3
Z0
Z0Z
0Z
po
pZ0
Z
Zp
Z Z
Z
0o
0Z0
Z0
Z0
Z Z
0Z
PZ
0Z0
Z
Z0
Z0Z
0Z
1
a b c d e f g
(a) 7/pppl2s/1p1e1Se/1p5/3L3/P5E/6C
Z0
Z0Z
0Z
0Z
Z0
Z0
Z0
Z0Z
0Z
0Z
0Z0
o0
Z0
Z0Z
0Z
0Z
0Z
O0
Z0
Z0Z
0Z
1
a b c d e f g
(b) 7/2l4/7/5p1/e6/4LP1/7
Z0
Z Z
0Z
pZ
pZ
Z0
Zp
Z0Z
0Z
0Z
Z0
Z0
Z
ZpZ
PO
o
0Z0
Z0
Z0
Z Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 3l3/p1p1s2/1p4e/2z4/1s1p1PP/Gp3m1/3L3
Z0
Z0Z
0Z
0Z
0o0
Z0
Z0
ZpZ
0Z
0O
0Z0
o0
Z0
Z Z
Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 4l2/3p3/3pE2/1P3p1/3e1S1/3L3/7
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
ZpZ
0Z
0Z
0Z
Z0
Z0
Z Z
pZ
0Z
0Z0
o0
Z0
Z0Z
Z
7
6
5
4
3
2
1
a b c d e f g
(a) 6C/7/3pl2/4z2/s2L1p1/5p1/5Z1
Z0
Z0Z
0Z
pZ
0Z
Z0
Z0
Z0Z
O
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
PZ0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/p3l2/5eP/5E1/7/1sP2s1/4L2
Z0
Z0Z
Z
Z
0Z0
Z
Z0
Z0Z
PZ
0o
0ZP
Z0
Z0
Z0o
PZ
PZ
0O0
Z0
Z0
Z0Z
0Z
Z0
Z0Z
0Z
0Z
Z0
Z0
Z0
Z0Z
0Z
0Z
PZ0
Z0
O0
Z0Z
0Z
pZ
0Z
Z
Z0
Z0Z
0Z
11
a b c d e f g
(a) 2m2E1/Z5S/E3lPM/1p2P2/2g1pP1/P2P3/z1L4
a b c d e f g
(b) 7/2l4/7/2P4/P6/p3L1S/7
Z0
Z0Z
Z
PZ
0Z0
Z
O
Z Z
pZ
Z
0Z0
ZP
O0
Z Z
po
Z
PO0
Z0
Z0
Z0Z
0Z
Z0
Z Z
0Z
0Z
0Z0
Z0
Z0
O0Z
0Z
0Z
0Z0
Z0
Z
Z Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
77
66
55
44
33
22
11
a b c d e f g
(a) 5e1/P2l2Z/Pssm1p1/s5P/P2L1pp/s1PP3/7
a b c d e f g
(b) 3l3/7/2P4/7/1E1L3/7/7
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
Z
0Z
Z0
o0
Z Z
0Z
pZ
0Z0
Z0
Z
Z0Z
0Z
Z0
Z0Z
0Z
0O
Z0
Z0
Z0
Z Z
0Z
pZ
0Z0
Z0
O0
ZpZ
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
77
66
55
44
33
22
11
a b c d e f g
(a) 6c/3l3/7/g3C2/p1Le3/pE5/1m4G
a b c d e f g
(b) 7/1PE4/3l3/p6/P2p3/7/2L4
Z0
Z0Z
0Z
0Z
0Z0
O0
Z0
O0Z
0Z
PZ
0Z0
Z0
Z0
Z O
po
pZ
0Z
oP
Z0
Z Z
0Z
1
a b c d e f g
(a) 4l2/5P1/2P4/P6/3EPpp/p2zSpP/2Lm2E
Z0
Z0Z
0Z
0Z
pZ0
O0
O0
Z Z
pZ
pZ
0Z0
Z0
Z0
Z Z
0Z
0Z
0O0
Z0
Z0
Z Z
0Z
1
a b c d e f g
(b) 7/2p2P1/P2l1p1/p6/3L3/3P3/3e3
Z0
Z0Z
0Z
Z
0O0
Z0
Z0
Z Z
0o
0Z
0Z0
Zp
Z
ZpZ
O
0Z
Z0
Z
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 7/s2P1e1/2ls2p/3Z2p/1s1p1MP/2sL1SC/7
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z0
O0
ZP
Z0Z
pZ
0Z
Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/7/2l4/5P1/1PE2p1/2L4/7
Z0
Z0Z
0Z
Z
0Z0
Z0
Z0
Z Z
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
0Z
0Z
Z
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 4Z2/gc1e3/3l3/4E2/S6/4L1m/e1E4
Z0
Z0Z
0Z
0Z
0Z0
ZP
Z0
ZPO
0Z
pZ
0Z0
Z0
Z0
Z0Z
0Z
0Z
0Z
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 7/3l2P/3PP1e/p6/2L4/4E2/7
Z0
Z Z
0Z
o
0Z
Z0
Zp
Z0Z
0Z
0Z
PZ
Z0
Z0
Z Z
0o
0Z
Z0
Z0
Z0
Z Z
0Z
1
a b c d e f g
(a) 2Zzl2/Sp2g2/ep5/2P1m2/2Le2p/2EM1E1/3G3
Z0
Z0Z
0Z
0Z
0Z
Z0
o0
Z0O
0Z
0o
0Z0
Z0
Z0
Z0Z
0o
0Z
0Z0
Z0
Z0
Z Z
0Z
1
a b c d e f g
(b) 7/3El2/p3P2/1p5/6p/7/3L3
Z0
Z0Z
0Z
0Z
0Z
Z
Z0
Z0o
0o
Z
0Z0
Z0
o0
Z0Z
0o
0Z
0Z0
Zp
Z0
Z Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 7/4l1c/4p1p/eG5/p3S1p/3L2p/3Z3
Z0
Z0Z
0Z
0Z
0Z
Z0
Z0
Z0Z
0O
0Z
0Z0
Z0
Z0
O Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) e6/4l2/6P/7/2PL3/7/7
Z0
Z0Z
0Z
Z
0Op
Zp
Z
Z Z
0Z
0Z
Zp
Z0
Z0
OPZ
0Z
0Z
pO0
ZP
Z0
Z Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(a) 7/Z2Pp1p/1Sel3/2cSp2/g1PP2z/1mpP2P/3L3
Z0
Z0Z
0Z
0Z
0Z
Z0
Z0
Z0Z
pZ
0Z
0ZP
Z0
o0
Z0Z
Z
0Z
0O
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 6E/4le1/5p1/4P2/p4S1/3PL2/7
Z0
Z Z
0Z
0Z
pZ0
Z0
o0
Z Z
PZ
pZ
Z0
Z0
ZP
Z0O
0Z
o
Z0
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(a) 3l3/2pm3/p1egEP1/p1c4/1P2P1Z/zpLe3/7
Z
Z0Z
0Z
0Z
pZ0
Z0
ZP
Z Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
pZ
Z0
Z0
Z0Z
0Z
1
a b c d e f g
(b) 1E5/2p4/1P1l3/7/7/1ep1L2/7
Z0
Z Z
0Z
Z
0Z
Z0
o0
o0Z
0Z
0Z
0Z0
ZP
Z0
Z Z
0Z
Po
0Z0
O0
Z0
Z0Z
Z
7
6
5
4
3
2
1
a b c d e f g
(a) 3gl2/C2GEE1/p1p4/3m2P/3eL2/Pp1s1P1/5e1
Z0
Z0Z
0Z
0Z
0Z0
ZP
Z0
Z0Z
0Z
0Z
0Z0
Z0
Z0
Z0Z
0Z
0Z
PZ0
Z0
Z0
Z0Z
0Z
7
6
5
4
3
2
1
a b c d e f g
(b) 4l2/6P/7/7/2L4/1eP4/7
