Title of Invention: COMMUNICATION SYSTEM, IDENTIFIER ASSIGNMENT DEVICE, BASE STATION, IDENTIFIER AS¬ SIGNMENT METHOD, AND NON-TRANSITORY COMPUTER READABLE MEDIUM EMBODYING INSTRUCTIONS FOR CONTROLLING A DEVICE Technical Field [0001] The exemplary embodiments relates to a method of assigning an identifier to a cell. Background Art [0002] The speed and capacity of communication between servers and backplane boards are increasing today. Accordingly, there is a possibility that the radio environment changes after assigning a PCI (Physical Cell Identifier), which is one type of a cell identifier. Therefore, in PCI assignment, it is necessary to select a PCI that can maintain collision-free and confusion-free even when the radio environment changes. [0003] However, enormous work is required to measure the actual radio environment. Further, detailed information elements such as obstacles are required to estimate the radio environment, and it is difficult to manage such enormous information. Therefore, there is a demand for a communication system in which a PCI that is likely to maintain collision-free and confusion-free can be assigned. [0004] Techniques related to PCT assignment are described in Japanese Unexamined Patent Application Publication No. 2011-004377, Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2010-537479, and Japanese Un examined Patent Application Publication No. 2010-268463. [0005] According to the handover method disclosed in Japanese Unexamined Patent Ap plication Publication No. 201 1-004377, a reconnection procedure is executed in the event PCI confusion occurs. [0006] Further, according to the conflict resolution method disclosed in Japanese Un examined Patent Application Publication (Translation of PCT Application) No. 2010-537479, when a detection node detects that a first cell identifier related to a first conflict cell is the same as a second cell identifier related to a second conflict cell, one of the first and second conflict cells is selected. Then, a different cell identifier is de termined for the selected cell. [0007] However, both of the above techniques detect the overlap of an identifier such as a PCI between adjacent cells and then resolve the detected overlap of an identifier. Therefore, it is unable in PCI assignment to select a PCI that can maintain collisionfree and confusion-free even when radio environment changes. [0008] A technique related to selection of a PCI in consideration of maintaining collisionfree and confusion-free is disclosed in Japanese Unexamined Patent Application Pub lication No.2010-268463, for example. [0009] According to the PCI assignment method disclosed in Japanese Unexamined Patent Application Publication No. 2010-268463, a SON (Self-Organizing Network) functional node pieces together information of an adjacent cells reported from each base station under the control thereof. Then, the SON functional node then assigns a PCI to a cell based on the adjacent cell information. [0010] However, in this technique, only identifier information of adjacent cells of a cell formed by a base station connected to the SON functional node is transmitted to the SON functional node. This causes a problem that, when assigning an identifier such as a PCI, the SON functional node can consider the identifier information of adjacent cells of the cell formed by the base station connected to itself but cannot consider the identifier information of cells adjacent to those adjacent cells. As a result, a serious problem occurs that it is difficult to maintain collision-free and confusion-free in the event radio environment changes. [001 1] This problem is caused by the fact that there is no way for the SON functional node to know the identifier information of adjacent cells of a cell formed by a base station that is not connected to the SON functional node. Citation List Patent Literature [0012] PL 1Japanese Unexamined Patent Application Publication No.201 1-004377 PL 2:Japanese Unexamined Patent Application Publication (Translation of PCT Ap plication) No. 2010-537479 PL 3:Japanese Unexamined Patent Application Publication No.2010-268463 Summary of Invention Technical Problem [0013] In view of the above problem, an exemplary object of the invention is to provide a communication system in which an identifier assignment device can know identifier information of adjacent cells of a cell formed by a base station that is not connected to the identifier assignment device. [0014] However, exemplary embodiments are not required to achieve here, objectives described above, and an exemplary embodiment may not achieve any of the objectives described above. Solution to Problem [0015] In an exemplary aspect of the invention, a communication system includes a first base station that forms a first cell, a second base station that forms a second cell, and an identifier assignment device that assigns an identifier for identifying the second cell, wherein the first base station transmits first adjacent cell information containing identifier information of adjacent cells of the first cell to the second base station, and the second base station transmits the first adjacent cell information received from the first base station to the identifier assignment device. [0016] In an exemplary aspect of the invention, an identifier assignment device in a commu nication system including a first base station forming a first cell and a second base station forming a second cell, the identifier assignment device assigning an identifier of the second cell, includes a receiving unit that receives first adjacent cell information containing identifier information of adjacent cells of the first cell from the second base station, and an identifier assignment unit that assigns an identifier of the second cell based on the first adjacent cell information received by the receiving unit. [0017] In an exemplary aspect of the invention, a base station in a communication system including a first cell, a second cell, and an identifier assignment device that assigns an identifier of the second cell, the base station forming the second cell, includes a receiving unit that receives first adjacent cell information containing identifier in formation of adjacent cells of the first cell from another base station forming the first cell, and a transmitting unit that transmits the first adjacent cell information to the identifier assignment device. [0018] In an exemplary aspect of the invention, an identifier assignment method includes a step of transmitting first adjacent cell information containing identifier information of adjacent cells of a first cell formed by a first base station to a second base station that forms a second cell, and a step of transmitting the first adjacent cell information received by the second base station to an identifier assignment device that assigns an identifier of the second cell. [0019] In an exemplary aspect of the invention, a method for an identifier assignment device in a communication system including a first base station forming a first cell and a second base station forming a second cell, the identifier assignment device assigning an identifier of the second cell, includes a receiving step of receiving first adjacent cell information containing identifier information of adjacent cells of the first cell from the second base station, and an identifier assignment step of assigning an identifier of the second cell based on the first adjacent cell information received in the receiving step. [0020] In an exemplary aspect of the invention, a method for a base station in a commu nication system including a first cell, a second cell, and an identifier assignment device that assigns an identifier of the second cell, the base station forming the second cell, includes a receiving step of receiving first adjacent cell information containing identifier information of adjacent cells of the first cell from another base station forming the first cell, and a transmitting step of transmitting the first adjacent cell in formation to the identifier assignment device. [0021] In an exemplary aspect of the invention, a non-transitory computer readable medium stores a program causing a computer to execute a step of transmitting first adjacent cell information containing identifier information of adjacent cells of a first cell formed by a first base station to a second base station that forms a second cell, and a step of transmitting the first adjacent cell information received by the second base station to an identifier assignment device that assigns an identifier of the second cell. Advantageous Effects of Invention [0022] According to the present invention, an identifier assignment device can know identifier information of a cell adjacent to a cell formed by a base station that is not connected to the identifier assignment device. [0023] In view of the above problem, an exemplary object of the invention is to provide a communication system in which an identifier assignment device can know identifier information of adjacent cells of a cell formed by a base station that is not connected to the identifier assignment device. Brief Description of Drawings [0024] [fig. 1]Fig. 1 is a block diagram showing a configuration of a communication system according to a first exemplary embodiment of the present invention. [fig.2]Fig. 2 is a block diagram showing a configuration of a second base station according to the first exemplary embodiment of the present invention. [fig.3]Fig. 3 is a block diagram showing a configuration of an identifier assignment device according to the first exemplary embodiment of the present invention. [fig.4]Fig. 4 is a flowchart illustrating an operation of the communication system according to the first exemplary embodiment of the present invention. [fig.5]Fig. 5 is a block diagram showing a configuration of a communication system according to a second exemplary embodiment of the present invention. [fig.6]Fig. 6 is a block diagram showing a configuration of a SON functional unit according to the second exemplary embodiment of the present invention. [fig.7]Fig. 7 is a diagram showing an X2 interface established between eNBs according to the second exemplary embodiment of the present invention. [fig.8]Fig. 8 is a diagram showing a structure of an IE contained in an X2 setup request message. [fig.9]Fig. 9 is a diagram showing a structure of an IE contained in an X2 setup response message. [fig. 10] Fig. 10 is a diagram showing a structure of an IE contained in an ENB con figuration update message. [fig. 1l]Fig. 11 is a diagram showing cell adjacent relation according to the second exemplary embodiment of the present invention. [fig. 12] Fig. 12 is a block diagram showing a configuration of a part of the commu nication system according to the second exemplary embodiment of the present invention. [fig.l3]Fig. 13 is a diagram showing an example of an operation flow of the commu nication system according to the second exemplary embodiment of the present invention. [fig. 14] Fig. 14 is a diagram showing another example of an operation flow of the com munication system according to the second exemplary embodiment of the present invention. [fig. 15]Fig. 15 is a diagram showing a list of PCIs and EGCIs of cells adjacent to cells adjacent to adjacent cells of a cell to which a PCI is assigned according to a third exemplary embodiment of the present invention. [fig. 16] Fig. 16 is a diagram showing an example of an operation flow of the commu nication system according to the third exemplary embodiment of the present invention. [fig.l7]Fig. 17 is a block diagram showing an example of a configuration of a commu nication system according to the present invention. [fig.l8]Fig. 18 is a block diagram showing an example of a configuration of a commu nication system according to the present invention. Description of Embodiments [0025] Exemplary embodiments of the present invention are described hereinafter with reference to the drawings. The exemplary embodiments, however, do not limit the scope of the present invention. [0026] First exemplary embodiment [0027] A communication system according to the first exemplary embodiment of the present invention is described hereinafter with reference to Fig. 1. [0028] A communication system 10 according to this exemplary embodiment includes a first base station 11, a second base station 12, and an identifier assignment device 13. [0029] The first base station 11 forms a first cell. The second base station 12 forms a second cell. The identifier assignment device 13 assigns an identifier of the second cell. [0030] The first base station 11 transmits first adjacent (neighbor) cell information containing identifier information of adjacent (neighbor) cells of the first cell to the second base station 12. Further, the second base station 12 transmits the first adjacent cell information received from the first base station 11 to the identifier assignment device 13. [0031] The configuration of each of the second base station 12 and the identifier assignment device 13 is described hereinafter with reference to Figs. 2 and 3. [0032] Fig. 2 shows a configuration of the second base station 12. The second base station 12 includes a receiving unit 14 and a transmitting unit 15. The receiving unit 14 receives the first adjacent cell information transmitted from the first base station 11. The transmitting unit 15 transmits the first adjacent cell information received by the receiving unit 14 to the identifier assignment device 13. [0033] Fig. 3 shows a configuration of the identifier assignment device 13. The identifier a s signment device 13 includes a receiving unit 16 and an identifier assignment unit 17. The receiving unit 16 receives the first adjacent cell information transmitted from the second base station 12. The identifier assignment unit 17 assigns an identifier of the second cell based on the first adjacent cell information received by the receiving unit 16. [0034] A communication method in the communication system 10 according to this exemplary embodiment is described hereinafter with reference to Fig. 4. First, the first adjacent cell information is transmitted to the second base station 12 (Step SI). [0035] Next, the first adjacent cell information received by the second base station 12 is transmitted to the identifier assignment device 13 (Step S2). [0036] In the above manner, in the communication system 10 according to this exemplary embodiment, the identifier assignment device 13 can know the identifier information of adjacent cells of a cell formed by the first base station 11 even when the identifier assignment device 13 and the first base station 11 are not directly connected. [0037] Therefore, the identifier assignment device 13 according to this exemplary em bodiment can assign an identifier that is likely to maintain collision-free and confusion-free even when radio environment changes. [0038] Particularly, in the case where adjacent cells of at least one of the first cell and the second cell include the other cell, the possibility to maintain collision-free and confusion-free increases as a result that the identifier assignment device 13 obtains the first adjacent cell information. However, there is a case where the first cell and the second cell are not adjacent to each other but are close to each other. In such a case also, the possibility to maintain collision-free and confusion-free increases even when radio environment changes can increase in some cases as a result that the identifier a s signment device 13 obtains the first adjacent cell information. For example, in the case where adjacent cells of a third cell, which is the adjacent cell of the second cell, include the first cell, the possibility to maintain collision-free and confusion-free can increase as a result that the identifier assignment device 13 uses the first adjacent cell information as in Step S32 of a third exemplary embodiment, which is described later. [0039] Second exemplary embodiment [0040] A communication system 20 according to the second exemplary embodiment of the present invention is described hereinafter with reference to Fig. 5. [0041] The communication system 20 according to this exemplary embodiment is an LTE (Long Term Evolution) system having a centralized SON (Self-Organizing Network) function. The "centralized SON" means that a SON functional unit exists in an OAM (Operation Administration and Maintenance) System. The operation performed by the SON functional unit includes self-configuration, self-optimization, self-healing and the like, and, specifically, determination of a PCI, for example. Further, the centralized SON includes NM-centralized SON where NMS (Network Management System) has the SON function and EM-centralized SON where EMS (Element Management System) has the SON function. It is assumed that the communication system 20 according to this exemplary embodiment is the EM-centralized SON. Note that the NMS is a management system that manages the entire LTE network. The EMS is a management system that manages a plurality of base stations (eNB etc.). [0042] The communication system 20 according to this exemplary embodiment includes an NMS 21, EMSs 22 and 23, eNBs 2A m, and cells 25i_m. The NMS 2 1 manages the entire communication system 20. The EMS 22 manages the eNBs 24 . The EMS 23 manages the eNBs 24 + m. The eNBs 24 m are base stations and form the cells 25 , respectively. Note that, although one eNB can form a plurality of cells, it is assumed in this exemplary embodiment that each eNB forms a single cell to simplify the de scription. Thus, the eNBs 24 m form the cells 25 , respectively. [0043] The NMS 2 1 is connected to the EMS 22 and the EMS 23 through a given interface. The EMS 22 is connected to the eNBs 24 through a given interface. Likewise, the EMS 23 is connected to the eNBs 24 +1 m through a given interface. [0044] The EMSs 22 and 23 have SON functional units 26 and 27, respectively. In this exemplary embodiment, the EMSs 22 and 23 function as identifier assignment devices. [0045] Fig. 6 shows a configuration of the SON functional unit 26. Note that the con figuration of the SON functional unit 27 is the same as that of the SON functional unit 26 and thus not repeatedly described. [0046] As shown in Fig. 6, the SON functional unit 26 includes a receiving unit 28, a memory 29, and an identifier assignment unit 30. The receiving unit 28 receives neighbour information. The memory 29 stores the received neighbour information. The identifier assignment unit 30 assigns an identifier to a cell formed by an eNB connected to the EMS 22. The identifier assigned to a cell includes a PCI. [0047] Note that the neighbour information is information containing identifier information of an adjacent cell. Further, the adjacent cell means a cell to which handover can be made by a mobile terminal, and it includes a cell with which a cover area overlaps. For example, assuming that cells to which handover can be made from the cell 251 by a mobile terminal are the cell 252, the cell 25 and the cell 25i0. In this case, adjacent cells of the cell 25 are the cell 252, the cell 25 and the cell 25i0. [0048] Further, the eNBs 24i_m can establish an X2 interface with another eNB. The X2 interface is an interface specified by the 3GPP (3rd Generation Partnership Project) standard. Typically, the X2 interface is often established between eNBs that form adjacent cells. In this exemplary embodiment, the X2 interface is established between eNBs connected by a solid line as shown in Fig. 7. Note that Fig. 7 shows the con figuration in the case of m=12, that is, the communication system 20 includes eNBs 24 1-12- [0049] The eNBs that are connected to each other through the X2 interface can transmit and receive neighbour information of the cell formed by themselves by transmitting and receiving a message. The message transmitted and received by the eNBs is an X2 setup request message, an X2 setup response message, or an ENB configuration update message. The X2 setup request message and the X2 setup response message are messages transmitted and received at the time of newly establishing the X2 interface between eNBs. The ENB configuration update message is a message transmitted and received between eNBs when an information element such as the neighbour in formation is changed. Figs. 8 to 10 show IE (Information Element) contained in each message. As shown in Figs. 8 to 10, the neighbour information is composed of a list containing a combination of ECGI (E-UTRAN Cell Global Identifier), PCI, and EARFCN (E-UTRAN Absolute Radio Frequency Channel Number). The ECGI is an identifier that uniquely identifies a cell. The PCI is one of radio resources, and it is a physical cell identifier that is assigned to a cell. In the LTE, 504 different PCIs, from 0 to 503, are used. The EARFCN is one of radio resources, and it corresponds to a frequency used by a cell. [0050] Fig. 11 shows the adjacent relation of cells 25 _ 2 formed by the eNBs 24 _ 2. In Fig. 11, cells connected by a solid line with no arrow mean that they are adjacent cells that are adjacent to each other. Accordingly, the neighbour information of one cell contains the identifier information of the other cell. Cells connected by a solid line with an arrow mean that adjacent cells of the cell from which the arrow starts include the cell to which the arrow is pointing but adjacent cells of the cell to which the arrow is pointing do not include the cell from which the arrow starts. Accordingly, the neighbour information of the cell from which the arrow starts contains the identifier in formation of the cell to which the arrow is pointing. On the other hand, the neighbour information of the cell to which the arrow is pointing does not contain the identifier in formation of the cell from which the arrow starts. In other words, the neighbour in formation of one cell does not contain the identifier information of the other cell. [005 1] The ECGI, PCI and EARFCN are assigned to each of the cells 25i_i2. The ECGIs assigned to the cells 25i_i2 are ECGIi_i2, respectively. Because the ECGI is an identifier unique to a cell, the ECGI 2 are different from one another. On the other hand, the EARFCNs assigned to the cells 25 2 are all common. Further, the PCIs assigned to the cells 25 2 are PCIi_i2, respectively. Although the same PCI value can be assigned to a plurality of cells, the PCI needs to be collision-free and confusion-free. [0052] The collision-free means that the PCI of an area covered by a cell is one, that is, the areas covered by cells having the same PCI do not overlap. In this exemplary em bodiment, when a combination of EARFCN and PCI of a certain cell is different from a combination of EARFCN and PCI of a cell contained in the neighbor information of that cell, collision-free is achieved. [0053] The confusion-free means that adjacent cells of a certain cell do not include a plurality of cells having the same PCI. In this exemplary embodiment, when the neighbour information of a certain cell does not contain two or more cells having the same EARFCN and the same PCI, confusion-free is achieved. [0054] The operation of the communication system 20 according to this exemplary em bodiment is described hereinafter. The case of assigning a PCI to the cell 251 formed by the eNB 24i is described in this example. [0055] Fig. 12 shows the relation of the EMS 22 and the eNBs 24i 2 ,9 ,io included in the com munication system 20. As shown in Fig. 12, the eNB 24i that forms the cell 251 and the eNB 242 that forms the cell 252 are connected to the EMS 22 having the SON functional unit 26, and the eNB 24 that forms the cell 25 and the eNB 24 that forms the cell 25 0 are not connected to the EMS 22. Further, the X2 interface is established between the eNB 24 and each of the eNB 242, eNB 24 and eNB 2410 . Further, the X2 interface is established between the eNB 242 and eNB 24 and between the eNB 2410 and eNB 24 . See Fig. 11 for the adjacent relation of the cells. Referring to Fig. 11, adjacent cells of the cell 25 are the cell 252 and the cell 25 . [0056] Fig. 13 shows an operation flow of the communication system 20. First, the eNB 24i and the eNB 242 transmit the neighbour information containing the identifier in formation of adjacent cells of the cell 25 and the cell 252 formed by themselves to the SON functional unit 26 (Step SI 1). The receiving unit 28 of the SON functional unit 26 receives the neighbour information of each of the cell 25 and the cell 252, and the memory 29 stores them. Note that, although the neighbour information of the cell 25 and the cell 252 are first transmitted to the SON functional unit 26, this operation may be performed at some point between Step S12 and Step S16, which are described later. [0057] The eNB 24 transmits the neighbour information containing the identifier in formation of adjacent cells of the cell 25 formed by itself to the eNB 24i (Step S12). For example, the eNB 24 transmits the neighbour information of the cell 25 to the eNB 24i by adding it to the ENB configuration update message. [0058] The eNB 24i receives the neighbour information of the cell 25 and then transmits the received neighbour information to the SON functional unit 26 (Step S13). The receiving unit 28 of the SON functional unit 26 receives the neighbour information of the cell 25 received from the eNB 2 Then, the memory 29 of the SON functional unit 26 stores the neighbour information of the cell 25 received by the receiving unit 28. [0059] Likewise, the neighbour information containing the identifier information of adjacent cells of the cell 25 0 is transmitted to the SON functional unit 26 through the eNB 24i (Steps S14, S15). Note that, because the eNB 2410 is connected also to the eNB 242 through the X2 interface, the neighbour information of the cell 25 may be transmitted to the SON functional unit 26 through the eNB 242. [0060] In the above manner, the SON functional unit 26 can store not only the neighbour in formation of the cell 251 and the cell 252 formed by the eNB 241 and the eNB 242 that are connected to the EMS 22 but also the neighbour information of the cell 259 and the cell 2510 formed by the eNB 249 and the eNB 2410 that are not connected to the EMS 22. [0061] In the event it becomes necessary to assign a PCI to the cell 25i, the identifier a s signment unit 30 of the SON functional unit 26 creates a PCI candidate list of the cell 25 (Step S16). Note that a procedure to create the PCI candidate list of the cell 251by the identifier assignment unit 30 is described later. [0062] Next, the identifier assignment unit 30 determines a PCI to be assigned to the cell 251 from the PCI candidate list created in Step S16 (Step S17). The identifier assignment unit 30 then notifies the selected PCI to the eNB 24 to make PCI assignment to the [0063] The procedure to create the PCI candidate list of the cell 25 by the identifier a s signment unit 30 in Step S16 is described hereinafter. [0064] First, the identifier assignment unit 30 creates a first PCI candidate list (Step S22). The first PCI candidate list is a list of all PCIs that can be assigned (for example, PCI0to 503)· [0065] Next, the identifier assignment unit 30 excludes the PCIs of adjacent cells of the cell 25 from the PCI candidate list (Step S23). Specifically, the identifier assignment unit 30 reads the neighbour information of the cell 25 stored in the memory 29. The neighbour information of the cell 25 contains ECGI information and PCI information of the cell 252 and the cell 25 , which are the adjacent cells of the cell 25 . Then, the identifier assignment unit 30 creates a second PCI candidate list by excluding PCI2 and PCI9, which are the PCIs of the cell 252 and the cell 25 , from the first PCI candidate list. [0066] Then, the identifier assignment unit 30 excludes the PCIs of cells whose adjacent cells include the cell 25 from the PCI candidate list (Step S24). Specifically, the identifier assignment unit 30 reads neighbour information of a plurality of cells stored in the memory 29 and determines that the cells whose neighbour information contains the identifier information of the cell 25 are the cell 25 and the cell 25 0. The identifier assignment unit 30 then creates a third PCI candidate list by excluding the PCI and PCIio, which are the PCIs of the cell 25 and the cell 25 0, from the second PCI candidate list. [0067] Then, the identifier assignment unit 30 excludes the PCIs of adjacent cells of the cells whose adjacent cells include the cell 25 from the PCI candidate list (Step S25). Specifically, the identifier assignment unit 30 reads the neighbour information of the PCI and PCI10 whose adjacent cells include the cell 25 from the memory 29. The adjacent cells of the cell 25 are the cell 25 , the cell 252, the cell 253, the cell 25 , the cell 25io a n