Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 56 (2016) 7 – 12
9th International Conference on Digital Enterprise Technology – DET 2016 – “Intelligent Manufacturing in the knowledge Economy Era”
Precedence Constraint Knowledge-based Assembly Sequence Planning for Open-Architecture Products Hongqin Maa, Qingjin Pengb*, Jian Zhanga, Peihua Gua b
a Shantou University, Shantou, 515063, China University of Manitoba, Winnipeg, R3T 5V6, Canada
*Corresponding author. Tel: 1-204-474-6843; fax: 1-204-275-7507. E-mail address:
[email protected]
Abstract This paper discusses feasible assembly sequences for Open-architecture products (OAPs). A structure diagram of OAPs and a product assembly constraint matrix are proposed to represent the precedence constraint knowledge among parts and modules. Considering that an independent functional module may not be independent in its spatial structure, a module of OAPs is first evaluated for its possibility to be assembled as a single sub-assembly. If it cannot be assembled as a sub-assembly, it will be divided into several sub-assembles or parts to adjust the product hierarchical graph. Combining with module types of OAPs, feasible assembly sequences of modules and parts are finally generated using the hierarchical precedence method. An industrial paper-folding machine is used as an example to verify the proposed method. 2016The The Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license ©©2016 Authors. Published by Elsevier B.V. This Peer-review under responsibility of the Scientific Committee of the “9th International Conference on Digital Enterprise Technology - DET (http://creativecommons.org/licenses/by-nc-nd/4.0/). 2016. Peer-review under responsibility of the scientific committee of the 5th CIRP Global Web Conference Research and Innovation for Future Production Keywords˖Open-architecture product, assembly sequence planning, assembly modeling, assembly constraint matrix;
1. Introduction Open-architecture products (OAPs) use adaptable design methods to meet different needs of users [1]. OAPs allow users to design, manufacture or purchase personalized functional modules added on an original product to meet changeable requirements in the product lifespan [2, 3], which requires that OAPs are assembled and disassembled easily when users update their personalized modules. Introduction of assembly sequence planning (ASP) can reduce the cost and improve the operation efficiency of OAPs. As OAPs use the modular structure [4], assembly sequence planning of OAPs has to consider both operations for modules of OAPs and for parts inside a module of OAPs. One of the purposes of the OAP planning is to achieve independent functional modules to be operated separately. But due to restrictions of the function correlation, the space correlation and information interaction of components, OAP modules formed by module planning methods cannot guarantee that both functional independence and spatial structure independence are satisfied [5]. Therefore, one
module with functional independence may not be assembled as a sub-assembly. Assembly modeling needs product information, such as geometric constraints and connection relationships among parts from the 3D product model. Assembly model information includes product information, hierarchical relationships among parts in the assembly, the assembly location and directions [6]. These information details have to be represented in a property form for the assembly modeling [7, 8]. Compared to commonly used methods of the product representation, an assembly hierarchy semantic description is mostly used for retrieving the similar assembly model [9, 10]. Product bill of materials (BOM) includes parts information with a hierarchical structure of a product [11]. Assembly modeling for OAPs has to consider the connection and assembly precedence sequence in the relative space among modules of OAPs and parts in the modules. The BOM hierarchy graph can represent the hierarchical structure and parts list information, the product structure graph provides assembly constraint relations. For the ASP of OAPs, considering their characteristic and space constraints, a matrix
2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 5th CIRP Global Web Conference Research and Innovation for Future Production doi:10.1016/j.procir.2016.10.007
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Hongqin Ma et al. / Procedia CIRP 56 (2016) 7 – 12
model can be combined with the analytic hierarchy process proposed in the literature [12]. This paper proposes a suitable modeling method for OAPs. The BOM hierarchy graph is used to describe OAP module hierarchies and parts information. Using the assembly constraint matrix, modules are analyzed if they can be assembled individually as sub-assemblies. Conditions of the serial assembly and parallel assembly are used to search the assembly level of parts and modules. Following definitions and assumptions are used to conduct the research discussed in this paper. Definitions x Support platform module: In a product assembly process, a module used as the assembly baseline is called the support platform module. Other modules are added in this module sequentially to complete the assembly of an entire product. x Basic part: In a process of parts assembly inside a module, a part used as the assembly baseline is called the basic part. Other parts are connected to this part sequentially to complete the assembly of an entire module. Assumptions x Modules that cannot be assembled as a sub-assembly are divided into several sub-assemblies or parts. They still belong to the same BOM module layer. After a module is divided, a separated part is considered as a module to plan the assembly sequence with other modules. x If several assemblies have same part numbers, shape and materials, they can be divided from the module to be an independent assembly, called alike-type assemblies. Each of them should have more than two parts. x Module types of OAPs are known from the product design. 2. ASP for OAPs An assembly is composed of sub-assemblies and parts. However, sub-assemblies of an OAP may be sets of parts as well as modules. ASP steps are: (a) Modules of an OAP are first evaluated for their possibility to be assembled in a single sub-assembly. (b) ASP for parts in each module. (c) ASP for modules of the OAP based on the BOM layer. A structure diagram, assembly constraint matrix and direction matrix are established based on the product design and BOM. A module of the OAP is evaluated for its possibility to be assembled as a sub-assembly based on the simplification matrix, alike-type assembly and direction matrix. If a module cannot be assembled in a sub-assembly, it will be divided, and the BOM hierarchy graph is adjusted. Then the assembly sequence of parts inside modules is generated based on the assembly constraint matrix and conditions of sub-assemblies. 2.1 Alike-type assembly As described in the assumptions, if several assemblies have same number of parts, similar shape and materials, they are called alike-type assemblies. They can be treated as independent modules to simplify the assembly constraint matrix.
2.2 Bill of materials (BOM) A hierarchical graph can be established based on the product to describe hierarchies of OAPs. If Mk is a module, Pbk is a part of Mk, and bk is the total number of parts in Mk while k is the total number of modules. 2.3. Product structure diagram and assembly constraint matrix A product structure diagram G = {E, V, W} is used to describe the precedence constraint knowledge of OAPs. Where E = {E1, E2, ..., En}, E is a set of non-null nodes. V = {V1, V2, ... , Vm}, W is a set of undirected edges used to connect nodes, W = { W1, W2,... , Wq}, W is a set of directed edges used to connect nodes. In this paper, Assembly = {P, WS}. P = {P1, P2, ..., Pn } to represent the parts of OAPs. WS=[WSij] represents the assembly constraint relationship defined as follows: x wsij =1: a connection relation exists between Pi and Pj but Pi must be assembled before Pj; x wsij =-1: a connection relation exists between Pi and Pj but Pi must be assembled after Pj; x wsij =2: a connection relation exists between Pi and Pj but Pi can be assembled before or after Pj; x wsij =9: there is no connection between Pi and Pj, but Pi must be assembled before Pj; x wsij = -9: there is no connection between Pi and Pj, but Pi must be assembled after Pj; WSk represents the assembly constraint relationship among the parts in Mk. Remaining parts except parts in Mk of OAPs are P1, P2, …, Pi. SMk is a simplification matrix which represents the assembly constraint relations among P1k, P2k, …, Pbk, and remaining parts P1, P2, …, Pi. BMij represents the assembly constraint relation between P1i, P2i, …, Pbi of module Mi and P1j, P2j, …, Pbj of module Mj. 2.4. Direction matrix The direction matrix DM describes feasible assembly directions of parts. There are six assembly directions: x, -x, y, -y, z, –z in an x-y-z coordinate system. DM = [dmoj], where o={x, -x, y, -y, z,-z}, represents the direction sets, j = {1k, 2k,…, bk}, dmoj = 0, 1 as follows. x x
0 represents that part bk cannot be assembled. 1 represents that part bk can be assembled.
2.5. Analysis of a module to be able to be assembled in a single sub-assembly Following steps are applied in the analysis: Step 1: Each part in a module is examined if it is embedded within two or several other parts belong to different modules; Step 2: For column elements in SMk, if they are not all positive or negative values but the element 0, Mk cannot be assembled in a sub-assembly. Step 3: According to the direction matrix, if there exist one row where all elements are 1, this module can be assembled in a sub-assembly. Otherwise, it will be divided into several
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Hongqin Ma et al. / Procedia CIRP 56 (2016) 7 – 12
sub-modules or parts. If the module that cannot be assembled in one operation, it is separated for the independent sub-assembly as follows. First, alike-type assemblies are separated. Second, if an element in some rows of SMk is negative, and the corresponding parts of the row with all negative numbers are assembled into a module in advance, this module will lead to conflict with modules having columns of negative elements in SMk. Therefore, corresponding parts of rows with all negative elements should be disassembled. Third, one main assembly direction is elected, elements 0 in SMk of this direction are identified, and corresponding parts are split. According to the assumption (1), all the parts or sub-assemblies still belong to the module layer of BOM after the division. The BOM is adjusted. 3. ASP for parts in a module 3.1. Serial assembly and parallel assembly To plan an assembly sequence, the serial assembly and parallel assembly are introduced [13]. A serial assembly is defined based on following Condition 1. Condition 1: |WSi(i+1) |=|WS(i+1)i|=1 2, |WSij |=|WSji|=0 9, |j-i |>1ˈi=1, 2, …,ncon-1, j=1, 2, …, ncon. Where, |WSi(i+1) |=|WS(i+1)i|=1 2 shows that there are connections between Pi and Pi+1; |WSij |=|WSji|=0 9 shows that there are no connections between Pi and Pi+1; ncon is the total number of parts. The structure diagram and assembly constraint matrix are shown in Fig. 1 (a) and Formula (1), respectively. A parallel assembly is defined based on following Condition 2. Condition 2: |WSij |=|WSji|=1 2, |WSjl|=0 9, j z l z i, i=1, j=2, …,npara, l=3, …, npara. Where, |WSij|=|WSji|=1 2 shows that there are connections between Pi and Pj; |WSjl|=0 9 shows that there are no connections between Pi and Pl. npara is the total number of parts. The structure diagram and assembly constraint matrix of a parallel assembly are shown in Fig.1 (b) and Formula (2), respectively.
i 1 i 2
i
WS
con k
i i 1 i2 i3 i4
i WS
con k
i 1 i2 i3 i4
i3 i4
ª « « « « « «¬
0
2
2 0 0
0 1 1 0 0 2
0
0
i
i 1 i 2 i 3 i 4
ª « « « « « «¬
0
0
0
0
0
0 2 0 1
0 0 1 0
2
1
1
2
2 0 1 0
0 0
0 9
0 0
1 0 2 0
9 0
0
0
0
0
º » » » » » »¼
º » » » » » »¼
(1)
(2)
If an assembly constraint matrix satisfies both conditions 1 and 2 at the same time, it is a mixed serial and parallel assembly. 3.2. ASP for parts inside a module The assembly sequence is generated from resetting WSk. The process steps are shown in Fig. 2. 4. Generation of the assembly sequence for modules As the ASP for parts in a module, the sequence of the assembly in the module level can be planned. BMij is defined as a simplification matrix. Value 2 in the BMij is set to 0 to simplify assembly sequence planning for modules. WT=[wtij] is defined to represent the assembly constraint relations among modules. If all the elements in BMij are 0, wtij =0. If all the non-zero elements in BMij are positive and the value of those non-zero elements is 9, wtij =9, otherwise, wtij =1. If all the non-zero elements in BMij are negative and exist element -9, wtij =-9, otherwise, wtij = -1. Different from the existing module layout method, this method introduces one different factor of the module type. After this step, H={Mh1, …, Mh(a*-1)}, A={Ma1, …, Ma(a*-1)}, where a* is the number of all modules. The assembly sequence matrix of modules of OAPs can be formed finally. 5. A case study
i
i+1 (a)
i+2
i+3
i+4
Structure diagram of serial assembly
i i+1 (b)
i+2
i+3
i+3 I+4
Structure diagram of parallel assembly
Fig. 1. Structure diagram of serial and parallel assemblies
The rotation table of an industrial paper-folding machine is used as an example to verify the proposed method. As there are eight bag-clamping devices with the same number of parts, shape and materials. They are alike-type assemblies and can be divided from M2. M2-1 is a bag-clamping device. Ring gauge M2-2 is independent from the total rotation table module. The remainder is represented by M2-3. M1 is chosen as the support platform module and P14 is chosen as the base part. The detail of M2-3 is shown in Fig. 3.
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Hongqin Ma et al. / Procedia CIRP 56 (2016) 7 – 12
WSki-1, i=1
Basic part selection
Basic part corresponding row and column exchanged with the ith row and column The ith row and column elements are set to zero
WSki-1
WSki All the parts connected to the current assemble part are listed into the set Hi
All the parts that can be assembled are listed into the set Li
No
Yes
No Li and Hi have same parts
Hi= Yes j -j >0 No j=i
All the parts that can be assembled are listed into the set Li The part has relative more assembly relationship are chose to assembled firstly, i ++
Yes All the same parts corresponding row and column exchanged with the last ni row and column, go on adjusting to ensure all the elements above the diagonal are positive, i ++
The assembled part corresponding row and column of WSk exchanged with the i row and column WSki
WSki
The i row and column set to zero
WSki-1 The i row and column set to zero
No
All the parts have been assembled
No
All the parts have been assembled Yes END
WSki-1 Yes
Fig. 2. Flowchart of assembly for parts inside a module
P1
Annular flow net
P9
Pneumatic rotating disk
P17
Pallet of ring gauge
P2
Driving flange
P10
Pneumatic bottom head
P18
Base plate of cylinder
P3
transmission shaft
P11
Column
P19
SDA-25*20
P4
Rotary cap base
P12
HR110DFH8R 90B
P20
Ring gauge 2
P21
M5R210-08
P22
Mountingcard
P1 P22 P2 P21 P3 P20 P4 P19 P5 P6 P7 P8 P9 P10 P11
P5
bearing block
P13
Base plate of cam divider
P17
P6
Bearing
P14
Top plate of frame
P16
P7
Bearing 2
P15
Pallet reck of ring gauge
P8
Connecting flange
P16
Bracing piece of guide rail
P18
P15 P14 P13 P12
Fig. 3. Details of rotation table M2-3
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Hongqin Ma et al. / Procedia CIRP 56 (2016) 7 – 12
5.2. Evaluation of modules to be assembled in a single sub-assembly A DM of the rotation table is generated as illustrated in Table 2. The element 0 exists in all directions. All these parts cannot be assembled as a module in one direction. The module is then divided: parts include P12, P13, represented by M2-3-1, and the other is represented by M2-3-2. But P3 of M2-3-2 is surrounded by P1, P2, P4, P11, P14 and P12. P1, P2, P4, P11 and P12 belong to M2-3, while P14 belongs to M1, those parts belong to different modules. Thus M2-3 cannot be assembled as a single sub-assembly. P3 and the parts must be assembled after P3 are divided from module M2-3. This process repeats until all remaining parts can be assembled as a sub-assembly.
Paper-bag folding machine M2
M1 M1-2
M1-1
M2-1
P14
ĊĊ
ĊĊ
ĊĊ
M2-3 P1
P13
ĊĊ
M2-2
P155
P22
ĊĊ
ĊĊ
Fig. 4. BOM of the paper-bag folding machine
P12
Table 2. Direction matrix of the rotation table
P13
P3
P14
P2
P4
P6
P11
P10
P1
P5
P7
P15
P9
P8
P17
P18
P22
P16
P19
P21
P20
5.1. Assembly modelling A BOM of the rotation table is shown in Fig. 4. Fig. 5 is structural diagrams of the rotation table. Table 1 is the assembly constraint matrix WS1.
1
2
-1 -9 -9
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22
2
1
0
-1 -1 -9 -9 -9
9
1
0
1
9
9
9
4
9
1
-1
0
-1 -9 -9
-9 -9 -9
-9 -9
-9
1
0
-1 -9 -9
-9 -9
-9
9
1
-1
-9 -9
1
-1
-9
9
-1
0
-9
-9 -1
-9 -9
-9
-9
9
1
9
0
-9 -1
-9 -9
-9
-9 -9 -9
-9 -9
-9
9 11
9 9
9
12
-9
9
-9
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
z
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
-y
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
Table 3. Assembly constraint matrix of parts 23 14 13 12 14
0 -1
9
9
11 -1
-9
0
1
15 -9
-9
9
-9
-9 -9
22
9
9
1
1
9
9
1
0
-1
9
21
9
9
9
9
1
9
9
9
9
-1
1
9
9
9
9
9
9
9
-9
-1
-1
9
9
9
1
1
9
9
1
1
9
9
9
1
9
9
9
9
-1
0
1
-1
0
-9
1
1
0
1
-1
0 0
1
-1
0
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
-1
-9
-9
0
9
-1
-9
-9
-9
0
-9
-9
-9
-9
5
-9
-9
-9
-9
-9
8
-9
-9
-9
-9
-9
-1
9
9
6
-9
-9
-1
-9
-9
-9
-9
0
1
4
-9
-1
-9
-9
-9
-9
-9
2
-1
-9
-9
-9
-9
1
-9
-9
-9 -1
0
-1
1
1
0
1
-1
0
1
-1
0 0 0
-1
1
0
22 21
9
0
-1
21
4
9
-9
19 20
1
-9
-9 -9
9
6
9
-1
7
-9 -9
9
8
9
-1
10 -9
-1
9
5
9
19
0
9
9
9
-9
18
-9 -9
0
7
9
2
1
1 1
0
1
9
0
9
1
1 0
9
-1
11 15 17 16 20 18 19 10
-1
9
9
3
1
12
9
9
0
13 -1
9
0
10 11 12 13 14 15 16 17 18 19 20 21 22
-x
1
18
22
0
y
9
16 17
9 0
9
1
14
8 0
9
13 15
7 0
20
9
10
6 0
16
9
0
5 0
9
6
-1
4 0
-9
7 8
3 0
17 -9
-9
3 5
2 0
3
Table 1. Assembly constraint matrix WS1 0
1 1
5.3. Assembly sequence planning for parts inside a module of the rotational table P14 is chosen as the base part. Parts that meet the parallel assembly are searched in Step 2. P23 is then chosen to be a support part of P3 in Step 3. After then, an assembly constraint matrix WSk23 is generated as shown in Table 3. Set elements in WSk23 as 0, the assembly sequence matrix WSk23-1 can be formed.
Fig. 5. Structural diagrams of the rotation table
1
0 x
1 0
1
-1
0
1
1
-1
0
9
9
9
9
9
9
9
9
9
-1
0
1
-9
-1
0
1
1
9
-1
0
9
9
-9
-1
-9
0
1
-9
-9
-9
-1
0
1
9
-1
0
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Hongqin Ma et al. / Procedia CIRP 56 (2016) 7 – 12
5.4. Assembly sequence planning for modules
Acknowledgements
The assemble constraint matrix WT of modules is formed based on module layers in BOM as shown in Table 4. The final assembly sequence can be planned as follows. Only P14 is listed in the first level, it connects to M1-1 by analyzing WT0, that is Mh1= Mb2= {P14}. The corresponding row and column elements of P14 in WT0 are exchanged with the second row and column elements, WT1 is generated. Then set them to 0, WT1-1 is achieved. All remaining modules that can be assembled are put into the second layer as M2-3-1 and M2-2, Mh2 = {M2-3-1, M2-2}. While Mb2= {M2-3-1, M2-2}, M2-3-1 belongs to customized modules and M2-2 is the common platform module. Therefore, M2-2 is assembled firstly in this step. WT2 and WT2-1 are formed. This process doesn’t end until all modules are assembled. After this step, H= {Mh1, …, Mh(17)}, A={Ma1, …, Ma(17)}. The final assembly sequences are formed as follows:
The authors wish to acknowledge that this research has been supported by the National Natural Science Foundation of China (Grant No. 51375287, 51505269) and the Leading Talent Project of Guangdong Province, China. References [1] Zhao C, Peng Q, Gu P. Development of a paper-bag-folding machine using open architecture for adaptability. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture 2015; 229(1): 155-169. [1] Koren Y, Hu SJ, Gu P, Shpitalni M. Open-architecture products. CIRP Annals-Manufacturing Technology 2013; 62(2): 719-729. [2] Berry C, Wang H, Hu SJ. Product architecting for personalization. Journal of Manufacturing Systems 2013; 32(3): 404-411. [3] Peng Q, Liu Y, Gu P, Fan Z. Development of an Open-Architecture Electric Vehicle Using Adaptable Design. Lecture Notes in Mechanical Engineering 2013; 79-90. [4] Bettig B, Gershenson JK. Module Interface Representation. ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2006; 1-935. [5] Wang Y, Liu J. Subassembly identification for assembly sequence planning. The International Journal of Advanced Manufacturing Technology 2013; 68(1-4): 781-793. [6] Chen X, Gao S. Guo S, Bai J. A flexible assembly retrieval approach for model reuse. Computer-Aided Design, 2012, 44(6): 554-574. [7] Luo Y, Peng Q. Disassembly Sequence Planning for Product Maintenance. ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2012; (5): 601-609. [8] Xing Y, Chen G, Lai X, Jin S, Zhou J. Assembly sequence planning of automobile body components based on liaison graph. Assembly Automation 2007; 27(2): 157-164. [9] Kashkoush M, EIMaraghy H. Consensus tree method for generating master assembly sequence. Production Engineering 2014; 8(1-2): 233-242. [10] Blaha MR, Premerlani WJ, Bender A R, Salemme R M. Bill-of-material configuration generation. Proceedings of Sixth International Conference on Data Engineering 1990; 237-244. [11] Zhang YZ, Ni J, Lin ZQ, Lai XM. Automated sequencing and sub-assembly detection in automobile body assembly planning. Journal of Materials Processing Technology 2002; 129(1-3): 490-494. [12] Kobalashi M, Higashi M, Layout Optimization Method Considering Disassemblability for the Facilitation of Reuse and Recycle. 10th world Congress on Structural and Multidisciplinary Optimization, Orlando, Florida, USA, May. 19-24, 2013.
(a) M1-1, P14, M2-2, M2-3-1, P3, P11, P15, M2-3-2, P10, P7, M2-3-3, P5, P6, P8, P4, P2, P1; (b) M1-1, P14, M2-2, M2-3-1, P3, P11, P15, M2-3-2, P10, M2-3-3, P7, P5, P6, P8, P4, P2, P1. 6. Conclusions OAPs’ modules and precedence constraint knowledge are discussed in this paper to generate an assembly sequence for OAPs. ASP is important to reduce cost in the development and application of OAPs. Unlike ASP for common products, ASP for OAPs is conducted with two steps of ASP for components in modules, and ASP for modules in the product. The precedence constraint knowledge among parts and modules is used to form the product structural diagram and assembly constraint matrix. The matrix, parallel and serial assembly conditions are combined to plan the assembly sequence for parts inside modules. Based on the module type and hierarchical precedence method, the assembly sequence for modules is also formed.
Table 4. Assembly constraint matrix of modules 1
2
3
4
5
6
7
8
P1
P2
P3
P4
P5
P6
P7
P8 M 2-3-3 P10
-9
-9
-9
-9
9
9
-9
-9
1
P1
0
-1
-9
-9
2
1
0
-1
-1
3
P2 P3
9
1
0
1
4
P4
9
1
-1
0
5
P5
9
1
0
1
-1
1
6
P6
9
-9
9
-1
0
-9
1
9
-9
9
1
9
0
P7 P8 9 M 2-3-3 10 P10 11 P11 7 8
9 9 9
9
12 M 2-3-1
-9
9
10
11
P14
15
P15
16 M 2-3-2 17 M 2-1 18 M 2-2
13
-1
9
16
17
18
-9 -1
-9
-9 -1
9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-1
-9
-9
-9 -9
-9
-1
-9
-9
-1
0
-9
-9
-9
-9
-9
-9
1
9
0
-9
-9
-9
-9
-9
9
9
9
9
9
9
0
-1
-9
-9
-9
9
9
1
1
9
9
1
0
-1
1
9
1
0 0
-9
15
P15 M 2-3-2 M 2-1 M 2-2
-9
1
9
14
P14
-9
13 M 1-1 14
12
P11 M 2-3-1 M 1-1
-1
1
9
9
9
9
9
9
9
1
0
9
9
9
9
9
9
9
9
9
-1
-9
0
1
9
9
9
9
9
9
9
-9
-9
-1
0
-1
1
0 -1
0
