Patent Publication Number: US-2012026954-A1

Title: Resource allocation signaling of wireless communication networks

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. provisional application No. 61/363,068 filed on Jul. 9, 2010, the contents of which is hereby incorporated by reference herein. 
    
    
     BACKGROUND 
     In an advanced broadband wireless system, an air link refers to a communication channel between the BS (Base Station) and an MS (Mobile Station) using the air as media. A scheduling-based media access control (MAC) is used to manage/control the usage of the air link resources. With the scheduling-based MAC, the BS uses collected information about resource requirements to allocate air link resource for the MSs, where the resource allocations are specified in the control signal, called Advanced MAP (A-MAP) Information Elements (IEs). An A-MAP IE specifies who, when, where, and how to transmit/receive. The when and where specifies the air link resources in an orthogonal frequency division multiple access (OFDMA) two-dimensional frame structure in both time-domain and frequency-domain. 
     SUMMARY 
     A method for resource allocation in assignment of information elements (IEs) comprises defining sets of selective starting locations (L) and allocation sizes (S) in combinations (L,S) for resource allocations, based on a predetermined total number of available logical resource units (LRUs) and valid resource allocations; and defining a mapping of a resource index to each combination (L,S), wherein the location size S is a number of LRUs. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more detailed understanding may be had from the following description, given by way of example in conjunction with the accompanying drawings wherein: 
         FIG. 1A  is a system diagram of an example communications system in which one or more disclosed embodiments may be implemented; 
         FIG. 1B  is a system diagram of an example wireless transmit/receive unit (WTRU) that may be used within the communications system illustrated in  FIG. 1A ; 
         FIG. 1C  is a system diagram of an example radio access network and an example core network that may be used within the communications system illustrated in  FIG. 1A ; 
         FIG. 2A  is an example of a downlink (DL) physical (PHY) structure with frequency partitions and different types of logical resource units (LRUs); 
         FIG. 2B  shows an example mapping for the PHY structure shown in  FIG. 2A ; and 
         FIG. 3  is an example of control channel allocations. 
     
    
    
     DETAILED DESCRIPTION 
     Resource allocation constraints may be used to reduce the number of valid allocations so that the required signaling information field in the assignment A-MAP IEs may be efficiently coded by only signaling the valid allocations. For example, one allocation may not cross two different LRU types (e.g., miniband LRU (NLRU), subband LRU (SLRU) or distributed LRU (DLRU), but not mixed), and/or one allocation may be contained in the same frequency partition and may not span multiple frequency partitions. 
     The A-MAP IE mapping may be constrained and reduced by not mapping to resource locations for resources occupied by the downlink and uplink control channels in a subframe. 
     The assignable allocation sizes may be limited, the allocation starting position may be limited, or both the sizes and the starting locations may be limited to reduce the required RI (Resource Index) mapping. 
     Information regarding the maximum allocation size, the given STC_rate and the TTI_length may be used to derive the value range of the number of LRUs for an allocation so that the number of allocations that need to be signaled in the assignment A-MAP IEs may be effectively reduced. 
     The size of RI (Resource Index) may be extended by one or more additional bits that are reserved and unused, or by reshuffling some other fields of the current assignment A-MAP IE. 
     Additionally, other mechanisms may be used to support allocations of discrete LRUs. 
     These embodiments may be used independently or in any combination. 
       FIG. 1A  is a diagram of an example communications system  100  in which one or more disclosed embodiments may be implemented. The communications system  100  may be a multiple access system that provides content, such as voice, data, video, messaging, broadcast, etc., to multiple wireless users. The communications system  100  may enable multiple wireless users to access such content through the sharing of system resources, including wireless bandwidth. For example, the communications systems  100  may employ one or more channel access methods, such as code division multiple access (CDMA), time division multiple access (TDMA), frequency division multiple access (FDMA), orthogonal FDMA (OFDMA), single-carrier FDMA (SC-FDMA), and the like. 
     As shown in  FIG. 1A , the communications system  100  may include wireless transmit/receive units (WTRUs)  102   a ,  102   b ,  102   c ,  102   d , a radio access network (RAN)  104 , a core network  106 , a public switched telephone network (PSTN)  108 , the Internet  110 , and other networks  112 , though it will be appreciated that the disclosed embodiments contemplate any number of WTRUs, base stations, networks, and/or network elements. Each of the WTRUs  102   a ,  102   b ,  102   c ,  102   d  may be any type of device configured to operate and/or communicate in a wireless environment. By way of example, the WTRUs  102   a ,  102   b ,  102   c ,  102   d  may be configured to transmit and/or receive wireless signals and may include user equipment (UE), a mobile station, a fixed or mobile subscriber unit, a pager, a cellular telephone, a personal digital assistant (PDA), a smartphone, a laptop, a netbook, a personal computer, a wireless sensor, consumer electronics, an advanced mobile station (MS), and the like. 
     The communications systems  100  may also include a base station  114   a  and a base station  114   b . Each of the base stations  114   a ,  114   b  may be any type of device configured to wirelessly interface with at least one of the WTRUs  102   a ,  102   b ,  102   c ,  102   d  to facilitate access to one or more communication networks, such as the core network  106 , the Internet  110 , and/or the networks  112 . By way of example, the base stations  114   a ,  114   b  may be a base transceiver station (BTS), a Node-B, an eNode B, a Home Node B, a Home eNode B, a site controller, an access point (AP), a wireless router, an advanced base station (BS), and the like. While the base stations  114   a ,  114   b  are each depicted as a single element, it will be appreciated that the base stations  114   a ,  114   b  may include any number of interconnected base stations and/or network elements. 
     The base station  114   a  may be part of the RAN  104 , which may also include other base stations and/or network elements (not shown), such as a base station controller (BSC), a radio network controller (RNC), relay nodes, etc. The base station  114   a  and/or the base station  114   b  may be configured to transmit and/or receive wireless signals within a particular geographic region, which may be referred to as a cell (not shown). The cell may further be divided into cell sectors. For example, the cell associated with the base station  114   a  may be divided into three sectors. Thus, in one embodiment, the base station  114   a  may include three transceivers, i.e., one for each sector of the cell. In another embodiment, the base station  114   a  may employ multiple-input multiple output (MIMO) technology and, therefore, may utilize multiple transceivers for each sector of the cell. 
     The base stations  114   a ,  114   b  may communicate with one or more of the WTRUs  102   a ,  102   b ,  102   c ,  102   d  over an air interface  116 , which may be any suitable wireless communication link (e.g., radio frequency (RF), microwave, infrared (IR), ultraviolet (UV), visible light, etc.). The air interface  116  may be established using any suitable radio access technology (RAT). 
     More specifically, as noted above, the communications system  100  may be a multiple access system and may employ one or more channel access schemes, such as CDMA, TDMA, FDMA, OFDMA, SC-FDMA, and the like. For example, the base station  114   a  in the RAN  104  and the WTRUs  102   a ,  102   b ,  102   c  may implement a radio technology such as Universal Mobile Telecommunications System (UMTS) Terrestrial Radio Access (UTRA), which may establish the air interface  116  using wideband CDMA (WCDMA). WCDMA may include communication protocols such as High-Speed Packet Access (HSPA) and/or Evolved HSPA (HSPA+). HSPA may include High-Speed Downlink Packet Access (HSDPA) and/or High-Speed Uplink Packet Access (HSUPA). 
     In another embodiment, the base station  114   a  and the WTRUs  102   a ,  102   b ,  102   c  may implement a radio technology such as Evolved UMTS Terrestrial Radio Access (E-UTRA), which may establish the air interface  116  using Long Term Evolution (LTE) and/or LTE-Advanced (LTE-A). 
     In other embodiments, the base station  114   a  and the WTRUs  102   a ,  102   b ,  102   c  may implement radio technologies such as IEEE 802.16 (i.e., Worldwide Interoperability for Microwave Access (WiMAX)), CDMA2000, CDMA2000 1X, CDMA2000 EV-DO, Interim Standard 2000 (IS-2000), Interim Standard 95 (IS-95), Interim Standard 856 (IS-856), Global System for Mobile communications (GSM), Enhanced Data rates for GSM Evolution (EDGE), GSM EDGE (GERAN), and the like. 
     The base station  114   b  in  FIG. 1A  may be a wireless router, Home Node B, Home eNode B, BS, or access point, for example, and may utilize any suitable RAT for facilitating wireless connectivity in a localized area, such as a place of business, a home, a vehicle, a campus, and the like. In one embodiment, the base station  114   b  and the WTRUs  102   c ,  102   d  may implement a radio technology such as IEEE 802.11 to establish a wireless local area network (WLAN). In another embodiment, the base station  114   b  and the WTRUs  102   c ,  102   d  may implement a radio technology such as IEEE 802.15 to establish a wireless personal area network (WPAN). In yet another embodiment, the base station  114   b  and the WTRUs  102   c ,  102   d  may utilize a cellular-based RAT (e.g., WCDMA, CDMA2000, GSM, LTE, LTE-A, etc.) to establish a picocell or femtocell. As shown in  FIG. 1A , the base station  114   b  may have a direct connection to the Internet  110 . Thus, the base station  114   b  may not be required to access the Internet  110  via the core network  106 . 
     The RAN  104  may be in communication with the core network  106 , which may be any type of network configured to provide voice, data, applications, and/or voice over internet protocol (VoIP) services to one or more of the WTRUs  102   a ,  102   b ,  102   c ,  102   d . For example, the core network  106  may provide call control, billing services, mobile location-based services, pre-paid calling, Internet connectivity, video distribution, etc., and/or perform high-level security functions, such as user authentication. Although not shown in  FIG. 1A , it will be appreciated that the RAN  104  and/or the core network  106  may be in direct or indirect communication with other RANs that employ the same RAT as the RAN  104  or a different RAT. For example, in addition to being connected to the RAN  104 , which may be utilizing an E-UTRA radio technology, the core network  106  may also be in communication with another RAN (not shown) employing a GSM radio technology. 
     The core network  106  may also serve as a gateway for the WTRUs  102   a ,  102   b ,  102   c ,  102   d  to access the PSTN  108 , the Internet  110 , and/or other networks  112 . The PSTN  108  may include circuit-switched telephone networks that provide plain old telephone service (POTS). The Internet  110  may include a global system of interconnected computer networks and devices that use common communication protocols, such as the transmission control protocol (TCP), user datagram protocol (UDP) and the internet protocol (IP) in the TCP/IP internet protocol suite. The networks  112  may include wired or wireless communications networks owned and/or operated by other service providers. For example, the networks  112  may include another core network connected to one or more RANs, which may employ the same RAT as the RAN  104  or a different RAT. 
     Some or all of the WTRUs  102   a ,  102   b ,  102   c ,  102   d  in the communications system  100  may include multi-mode capabilities, i.e., the WTRUs  102   a ,  102   b ,  102   c ,  102   d  may include multiple transceivers for communicating with different wireless networks over different wireless links. For example, the WTRU  102   c  shown in  FIG. 1A  may be configured to communicate with the base station  114   a , which may employ a cellular-based radio technology, and with the base station  114   b , which may employ an IEEE 802 radio technology. 
       FIG. 1B  is a system diagram of an example WTRU  102 . As shown in  FIG. 1B , the WTRU  102  may include a processor  118 , a transceiver  120 , a transmit/receive element  122 , a speaker/microphone  124 , a keypad  126 , a display/touchpad  128 , non-removable memory  106 , removable memory  132 , a power source  134 , a global positioning system (GPS) chipset  136 , and other peripherals  138 . It will be appreciated that the WTRU  102  may include any sub-combination of the foregoing elements while remaining consistent with an embodiment. 
     The processor  118  may be a general purpose processor, a special purpose processor, a conventional processor, a digital signal processor (DSP), a plurality of microprocessors, one or more microprocessors in association with a DSP core, a controller, a microcontroller, Application Specific Integrated Circuits (ASICs), Field Programmable Gate Array (FPGAs) circuits, any other type of integrated circuit (IC), a state machine, and the like. The processor  118  may perform signal coding, data processing, power control, input/output processing, and/or any other functionality that enables the WTRU  102  to operate in a wireless environment. The processor  118  may be coupled to the transceiver  120 , which may be coupled to the transmit/receive element  122 . While  FIG. 1B  depicts the processor  118  and the transceiver  120  as separate components, it will be appreciated that the processor  118  and the transceiver  120  may be integrated together in an electronic package or chip. 
     The transmit/receive element  122  may be configured to transmit signals to, or receive signals from, a base station (e.g., the base station  114   a ) over the air interface  116 . For example, in one embodiment, the transmit/receive element  122  may be an antenna configured to transmit and/or receive RF signals. In another embodiment, the transmit/receive element  122  may be an emitter/detector configured to transmit and/or receive IR, UV, or visible light signals, for example. In yet another embodiment, the transmit/receive element  122  may be configured to transmit and receive both RF and light signals. It will be appreciated that the transmit/receive element  122  may be configured to transmit and/or receive any combination of wireless signals. 
     In addition, although the transmit/receive element  122  is depicted in  FIG. 1B  as a single element, the WTRU  102  may include any number of transmit/receive elements  122 . More specifically, the WTRU  102  may employ MIMO technology. Thus, in one embodiment, the WTRU  102  may include two or more transmit/receive elements  122  (e.g., multiple antennas) for transmitting and receiving wireless signals over the air interface  116 . 
     The transceiver  120  may be configured to modulate the signals that are to be transmitted by the transmit/receive element  122  and to demodulate the signals that are received by the transmit/receive element  122 . As noted above, the WTRU  102  may have multi-mode capabilities. Thus, the transceiver  120  may include multiple transceivers for enabling the WTRU  102  to communicate via multiple RATs, such as UTRA and IEEE 802.11, for example. 
     The processor  118  of the WTRU  102  may be coupled to, and may receive user input data from, the speaker/microphone  124 , the keypad  126 , and/or the display/touchpad  128  (e.g., a liquid crystal display (LCD) display unit or organic light-emitting diode (OLED) display unit). The processor  118  may also output user data to the speaker/microphone  124 , the keypad  126 , and/or the display/touchpad  128 . In addition, the processor  118  may access information from, and store data in, any type of suitable memory, such as the non-removable memory  106  and/or the removable memory  132 . The non-removable memory  106  may include random-access memory (RAM), read-only memory (ROM), a hard disk, or any other type of memory storage device. The removable memory  132  may include a subscriber identity module (SIM) card, a memory stick, a secure digital (SD) memory card, and the like. In other embodiments, the processor  118  may access information from, and store data in, memory that is not physically located on the WTRU  102 , such as on a server or a home computer (not shown). 
     The processor  118  may receive power from the power source  134 , and may be configured to distribute and/or control the power to the other components in the WTRU  102 . The power source  134  may be any suitable device for powering the WTRU  102 . For example, the power source  134  may include one or more dry cell batteries (e.g., nickel-cadmium (NiCd), nickel-zinc (NiZn), nickel metal hydride (NiMH), lithium-ion (Li-ion), etc.), solar cells, fuel cells, and the like. 
     The processor  118  may also be coupled to the GPS chipset  136 , which may be configured to provide location information (e.g., longitude and latitude) regarding the current location of the WTRU  102 . In addition to, or in lieu of, the information from the GPS chipset  136 , the WTRU  102  may receive location information over the air interface  116  from a base station (e.g., base stations  114   a ,  114   b ) and/or determine its location based on the timing of the signals being received from two or more nearby base stations. It will be appreciated that the WTRU  102  may acquire location information by way of any suitable location-determination method while remaining consistent with an embodiment. 
     The processor  118  may further be coupled to other peripherals  138 , which may include one or more software and/or hardware modules that provide additional features, functionality and/or wired or wireless connectivity. For example, the peripherals  138  may include an accelerometer, an e-compass, a satellite transceiver, a digital camera (for photographs or video), a universal serial bus (USB) port, a vibration device, a television transceiver, a hands free headset, a Bluetooth® module, a frequency modulated (FM) radio unit, a digital music player, a media player, a video game player module, an Internet browser, and the like. 
       FIG. 1C  is a system diagram of the RAN  104  and the core network  106  according to an embodiment. The RAN  104  may be an access service network (ASN) that employs IEEE 802.16 radio technology to communicate with the WTRUs  102   a ,  102   b ,  102   c  over the air interface  116 . As will be further discussed below, the communication links between the different functional entities of the WTRUs  102   a ,  102   b ,  102   c , the RAN  104 , and the core network  106  may be defined as reference points. 
     As shown in  FIG. 1C , the RAN  104  may include base stations  140   a ,  140   b ,  140   c , and an ASN gateway  142 , though it will be appreciated that the RAN  104  may include any number of base stations and ASN gateways while remaining consistent with an embodiment. The base stations  140   a ,  140   b ,  140   c  may each be associated with a particular cell (not shown) in the RAN  104  and may each include one or more transceivers for communicating with the WTRUs  102   a ,  102   b ,  102   c  over the air interface  116 . In one embodiment, the base stations  140   a ,  140   b ,  140   c  may implement MIMO technology. Thus, the base station  140   a , for example, may use multiple antennas to transmit wireless signals to, and receive wireless signals from, the WTRU  102   a . The base stations  140   a ,  140   b ,  140   c  may also provide mobility management functions, such as handoff triggering, tunnel establishment, radio resource management, traffic classification, quality of service (QoS) policy enforcement, and the like. The ASN gateway  142  may serve as a traffic aggregation point and may be responsible for paging, caching of subscriber profiles, routing to the core network  106 , and the like. A scheduling-based MAC may be implemented within the base stations  140   a ,  140   b ,  140   c  and/or the ASN gateway  142  for execution of the resource mapping according to the methods described herein. The base stations,  140   a ,  140   b , and  140   c  may provide the resource mapping descriptions/instructions for the subscribers, where the ASN gateway and/or other network entities may provide information to the BS to make the right resource allocation decisions. 
     The air interface  116  between the WTRUs  102   a ,  102   b ,  102   c  and the RAN  104  may be defined as an R1 reference point that implements the IEEE 802.16 specification. In addition, each of the WTRUs  102   a ,  102   b ,  102   c  may establish a logical interface (not shown) with the core network  106 . The logical interface between the WTRUs  102   a ,  102   b ,  102   c  and the core network  106  may be defined as an R2 reference point, which may be used for authentication, authorization, IP host configuration management, and/or mobility management. 
     The communication link between each of the base stations  140   a ,  140   b ,  140   c  may be defined as an R8 reference point that includes protocols for facilitating WTRU handovers and the transfer of data between base stations. The communication link between the base stations  140   a ,  140   b ,  140   c  and the ASN gateway  215  may be defined as an R6 reference point. The R6 reference point may include protocols for facilitating mobility management based on mobility events associated with each of the WTRUs  102   a ,  102   b ,  100   c.    
     As shown in  FIG. 1C , the RAN  104  may be connected to the core network  106 . The communication link between the RAN  104  and the core network  106  may defined as an R3 reference point that includes protocols for facilitating data transfer and mobility management capabilities, for example. The core network  106  may include a mobile IP home agent (MIP-HA)  144 , an authentication, authorization, accounting (AAA) server  146 , and a gateway  148 . While each of the foregoing elements are depicted as part of the core network  106 , it will be appreciated that any one of these elements may be owned and/or operated by an entity other than the core network operator. 
     The MIP-HA may be responsible for IP address management, and may enable the WTRUs  102   a ,  102   b ,  102   c  to roam between different ASNs and/or different core networks. The MIP-HA  144  may provide the WTRUs  102   a ,  102   b ,  102   c  with access to packet-switched networks, such as the Internet  110 , to facilitate communications between the WTRUs  102   a ,  102   b ,  102   c  and IP-enabled devices. The AAA server  146  may be responsible for user authentication and for supporting user services. The gateway  148  may facilitate interworking with other networks. For example, the gateway  148  may provide the WTRUs  102   a ,  102   b ,  102   c  with access to circuit-switched networks, such as the PSTN  108 , to facilitate communications between the WTRUs  102   a ,  102   b ,  102   c  and traditional land-line communications devices. In addition, the gateway  148  may provide the WTRUs  102   a ,  102   b ,  102   c  with access to the networks  112 , which may include other wired or wireless networks that are owned and/or operated by other service providers. 
     Although not shown in  FIG. 1C , it will be appreciated that the RAN  104  may be connected to other ASNs and the core network  106  may be connected to other core networks. The communication link between the RAN  104  the other ASNs may be defined as an R4 reference point, which may include protocols for coordinating the mobility of the WTRUs  102   a ,  102   b ,  102   c  between the RAN  104  and the other ASNs. The communication link between the core network  106  and the other core networks may be defined as an R5 reference, which may include protocols for facilitating interworking between home core networks and visited core networks. 
     With respect to the A-MAP information elements (IEs) used to specify downlink and uplink resource allocations, a 20 MHz channel may be specified having 96 logical resource units (LRUs), for a total number of 4656 possible allocations to be indexed. While this would require a 13-bit Resource Index (RI), one current specification calls for a smaller 11-bit RI, which cannot accommodate the full 4696 possible allocations. One solution is to compress the indexes by incrementing an allocation location index L and an allocation size index S which reduces the total number of indexes. The allocation location index L is denotes a starting location of the allocated LRUs, and the allocation size index S represents the number of allocated LRUs (i.e., an LRU allocation consists of S contiguous LRUs starting from the LRU with index L). 
     Examples of index L and index S that utilize an 11-bit RI, include the following: when 14&lt;=5&lt;=24, L may be incremented by 2 LRUs; when 28&lt;=5&lt;=48, L may be incremented by 4 LRUs; and when 56&lt;=5&lt;=88, L may be incremented by 8 LRUs. However, using these assignment granularities of 1, 2, 4, or 8 LRUs for index L, air link resources may be wasted when the required size does not fit exactly into one of the allowed sizes. For example, if the required size is 57 LRUs, which is not an allowed size, the next allowed size is 64, thus 7 extra LRUs are needed (i.e., 7/57=12.28% extra). In addition, the number of LRUs specified in the assignment IEs is for one subframe. The number of extra LRUs due to this allocation granularity issue may become much worse in the long transmission time interval (TTI) cases and/or the space time control (STC) case where STC_rate&gt;1, because the allocation size is the product of STC_rate, long TTI factor, and the number of LRUs specified in the assignment IE. 
     Rate matching is the process where the number of bits to be transmitted is reduced to fit the allocated size. Typically, some redundant bits (generated by a forward error correction scheme) in the stream are removed to reduce the size of the block to be transmitted. When the rate-matching scheme is used, and the required number of LRUs is not an assignable size, the number of allocated LRUs may be either smaller or greater than the required number of LRUs. In this case, the offset may be as big as 4 LRUs (e.g., when the required number of LRUs is 60, and the two closest assignable sizes are 56 and 64). An offset of 4 LRUs is significant. The methods and apparatus described herein may improve the encoding efficiency of resource allocation signaling in the assignment IEs, and also improve the resource usage efficiency allocation granularity. 
     The downlink/uplink basic assignment A-MAP IE may apportion a single allocation of resources, comprising a set of contiguous LRUs in a downlink/uplink advanced air interface (AAI) subframe, where the allocated set of contiguous LRUs may be contained within the same frequency partition (i.e., the allocated set of contiguous LRUs may not span multiple frequency partitions). The allocated set of contiguous LRUs may be of the same type (e.g., DLRU, NLRU, or SLRU). 
     Using the same frequency partition and the same type of LRUs for resource allocation improves the resource allocation specification encodings, by elimination of invalid combinations of allocation starting points and allocation sizes. 
       FIG. 2A  shows an example of a downlink PHY structure based on a subframe divided into frequency partitions (multi-cell), each partition having a set of physical resource units (PRUs) across a total number of available OFDMA symbols. Each frequency partition can include contiguous (localized) and/or distributed PRUs (cell specific). The PRU is the basic physical unit for resource allocation having a number of consecutive subcarriers (SC 1 , SC 2  . . . SCn) by a number of consecutive OFDMA symbols. 
       FIG. 2B  shows an example of resource mapping from PRUs to LRUs, which includes subband partitioning, miniband partitioning, and frequency partitioning. The PRUs are first partitioned by subbands PRUsB and minbands PRU MB . As shown in  FIG. 2 , there are 7 subbands. A permutation on the minibands is performed based on the channel bandwidth, shown as PRU MB  to PPRU MB , to ensure frequency diverse PRUs are allocated to each frequency partition. The subbands PRUsB and the minibands PRU MB  are then allocated to one or more frequency partitions, shown as PRU FP0  to PRU FP3 , according to a frequency partition count (FPCT). In this example, FPCT=4, as there are four frequency partitions. The allocation is also based on a defined frequency partition size (FPS) (e.g., FPS=12) as the number of PRUs allocated to the i-th frequency partition, along with the number of subbands allocated to the i-th frequency partition (e.g., downlink frequency partition subband count (DFPSC=2). 
     Finally, a cell-specific resource mapping may be performed that maps the frequency partitions to LRUs, which are divided into contiguous resource units (CRUs) and distributed resource units (DRUs). The CRUs include miniband CRUs (NRLUs) and subband CLUs (SRLUs). In the A-MAP assignment IEs, an ordered LRU list, LRU[1] to LRU[NMAX], may be used to specify an allocation, where the LRU list is specified by mapping the DRUs, NLRUs, and SLRUs in different frequency partitions in a certain order. For an example where there are four frequency partitions, the mapping order may be: FP0(DLRUs, NLRUs, SLRUs), FP1(DLRUs, NLRUs, SLRUs), FP2(DLRUs, NLRUs, SLRUs), and FP3(DLRUs, NLRUs, SLRUs). 
     When applying the constraints of same frequency partition and the same type of LRUs for a resource allocation, the number of valid allocations in a subframe may be significantly reduced for the PHY subframe structure with multiple frequency partitions and/or multiple types of LRUs. As an example, for the mapping shown in  FIG. 2B , the number of valid allocations can be reduced to 172, when compared to 1186 valid allocations that would exist without applying the constraints of the same frequency and the same LRU type, which results in an 85.37% reduction.  FIG. 2B  shows 172 valid allocations, and 1186 possible combinations of (L, S). These numbers come from calculations for the combinations of starting location (L) and allocation size (S) shown in the following table. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 DL PHY with 10 MHz, 4 FRs, multiple 
               
               
                 types of LRUs (DLRUs, SB-CRUs, and 
               
               
                 MB-CRUs) 
               
            
           
           
               
               
               
            
               
                 Location 
                 # of valid sizes 
                 # of possible sizes 
               
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 4 
                 48 
               
               
                 2 
                 3 
                 47 
               
               
                 3 
                 2 
                 46 
               
               
                 4 
                 1 
                 45 
               
               
                 5 
                 2 
                 44 
               
               
                 6 
                 1 
                 43 
               
               
                 7 
                 6 
                 42 
               
               
                 8 
                 5 
                 41 
               
               
                 9 
                 4 
                 40 
               
               
                 10 
                 3 
                 39 
               
               
                 11 
                 2 
                 38 
               
               
                 12 
                 1 
                 37 
               
               
                 13 
                 8 
                 36 
               
               
                 14 
                 7 
                 35 
               
               
                 15 
                 6 
                 34 
               
               
                 16 
                 5 
                 33 
               
               
                 17 
                 4 
                 32 
               
               
                 18 
                 3 
                 31 
               
               
                 19 
                 2 
                 30 
               
               
                 20 
                 1 
                 29 
               
               
                 21 
                 4 
                 28 
               
               
                 22 
                 3 
                 27 
               
               
                 23 
                 2 
                 26 
               
               
                 24 
                 1 
                 25 
               
               
                 25 
                 8 
                 24 
               
               
                 26 
                 7 
                 23 
               
               
                 27 
                 6 
                 22 
               
               
                 28 
                 5 
                 21 
               
               
                 29 
                 4 
                 20 
               
               
                 30 
                 3 
                 19 
               
               
                 21 
                 2 
                 28 
               
               
                 32 
                 1 
                 17 
               
               
                 33 
                 4 
                 16 
               
               
                 34 
                 3 
                 15 
               
               
                 35 
                 2 
                 14 
               
               
                 36 
                 1 
                 13 
               
               
                 37 
                 8 
                 12 
               
               
                 38 
                 7 
                 11 
               
               
                 39 
                 6 
                 10 
               
               
                 40 
                 5 
                 9 
               
               
                 41 
                 4 
                 8 
               
               
                 42 
                 3 
                 7 
               
               
                 43 
                 2 
                 6 
               
               
                 44 
                 1 
                 5 
               
               
                 45 
                 4 
                 4 
               
               
                 46 
                 3 
                 3 
               
               
                 47 
                 2 
                 2 
               
               
                 48 
                 1 
                 1 
               
               
                   
                 172 
                 1186 
               
               
                   
                 valid allocations 
                 all possible (L, S) 
               
               
                   
                 in (L, S) 
                 combinations 
               
               
                   
                 combinations 
               
               
                   
               
            
           
         
       
     
     This reduction may be useful in resolving the 11-bit RI index code deficit with respect to the maximum 4656 allocations in 20 MHz systems, requiring a 13-bit RI. 
     For each combination of system channel bandwidth (e.g., 5 MHz, 10 MHz, or 20 MH), frequency partitions, and LRU type compositions (such as the mapping shown in  FIG. 2B ), there exists a table entry in an RI table, which uses an 11-bit RI value as a table index, and each table entry includes corresponding index values (L,S), representing a valid allocation. The RI tables are used at both the WTRU  102  and the base station  114  to code and decode the assignment A-MAP IEs. Both the frequency partitioning and the LRU structure may be included in the system configuration information, which are either static or semi-static for a system deployment. 
     The downlink and uplink frequency partitions may be defined in a frame header, such as a Secondary Super Frame Header (S-SFH), by parameters Downlink Frequency Partition Configuration (DFPC) and Uplink Frequency Partition Configuration (UFPC), respectively. For both downlink and uplink, the number of defined frequency partitions varies with fast Fourier transform (FFT) sizes of the PHY system. For example, there may be n different frequency partition configurations for 2048-FFT, m configurations for 1024-FFT, and p configurations for 512-FFT, for both downlink and uplink. 
     The downlink/uplink LRU structures may also be defined in the S-SFH by parameters downlink/uplink Subband Allocation Count (DSAC/USAC), downlink/uplink Frequency Partition Subband Count (DFPSC/UFPSC), and downlink/uplink CRU Allocation Size (DCASi/UCASi). The number of different LRU structures also varies with the system FFT size. For example, for both downlink and uplink, there may be q valid subband allocations for 2048-FFT, r subband allocations for 1024-FFT, and s subband allocations for 512-FFT. 
     At least one of the following options are available for the above described resource mapping. Both the frequency partitioning and the LRU structure information may be included. Only the frequency partition information may be used. Only the LRU structure information may be used. Selecting either the frequency partition information and/or the LRU structure information only as needed (e.g., in 20 MHz bandwidth systems). 
     As an alternative method for reducing resource allocation with respect to the assignment A-MAP IEs, the uplink and downlink control channels may be pre-defined or configured to resources such that the assignment A-MAP IEs do not need to perform this mapping. The existence of the non-assignable LRUs occupied by the control channels in the allocation specification encoding design reduces the number of valid allocations in a subframe. 
       FIG. 3  shows an example of a frame structure with control channel allocations. As shown, for the downlink subframes  321 , the A-MAP regions  313  may be present in all AAI subframes. For the uplink subframes  322 , a hybrid automatic repeat request (HARQ) feedback region  317  may be present in all uplink subframes. The uplink control channels  311  may occupy the resources that are pre-defined or configured. In the uplink subframes  322 , the number of DLRUs reserved for Feedback channels  312  may be specified by a field UL FEEDBACK SIZE in the secondary superframe header (S-SFH)  316 . Thus, there is no need for the assignment A-MAP IEs to do the allocations for the uplink feedback channels  312 , thus reducing the number of allocations that need to be signaled in the assignment A-MAP IEs. By knowing the size of the A-MAP region  313  (defined as L AMAP  LRUs) in a downlink subframe  321  and the size of uplink feedback channels  312  in an uplink subframe, the number of valid allocations for the assignment IEs to signal may be determined, and the mapping between the RI codes and valid allocations in terms of location and size indexes (L, S) may be defined, as previously described. 
     For example, if L AMAP =6 LRUs in a 20 MHz channel bandwidth, excluding the control channel occupied resources, the number of allocations for the A-MAP IE is 4095 after eliminating the size of the uplink feedback channels. This is a significant reduction of the full 4656 possible allocations without excluding the control channel occupied resources. 
     The assumption of L AMAP =6 LRUs may be conservative. The A-MAP modulation/coding selections are quadrature phase-shift keying (QPSK) ½, QPSK ¼, and QPSK ⅛. One LRU may be 18 subcarriers*6 symbols=108 tones, while typically there are 6 pilot tones. This gives 102 data bits for the QPSK ½, and 51 data bits for the QPSK ¼. On the other hand, an assignment A-MAP IE is typically 56 bits (i.e., 40 bits data plus 16 bits CRC). In addition to the assignment A-MAP IEs, the A-MAP region may also contain the HARQ feedback and power control IEs. Consider the number of data bits for an LRU carrier in the DL control channel, i.e., 51 bits for QPSK ¼, which is close to, but not enough, for one A-MAP IE. So, a DL control channel with 6 LRUs may accommodate 5 A-MAP IEs, i.e., specify 5 DL resource allocations. Further, a DL control channel may also carry other control information, e.g., HARQ feedback, power control IE, etc, in addition to A-MAP IEs. So, again, this may further be an indication of a need for DL resources for DL control channels. 
     As an alternative method for resource allocation of the A-MAP IEs, the starting location L may be selectively defined to reduce the number of allocations that need to be specified in an assignment A-MAP IE. Additionally, selective sizes of resource allocations may be employed. Mechanisms may be used to identify the resource allocations in a given size of resource index field when the given resource index field cannot accommodate the allocations with all the possible combinations of locations and sizes. 
     With respect to selective locations, starting point gaps may be created for sets of allocation sizes. As a first example using a 96 LRU mapping, for allocation sizes 1-12 LRUs, the starting location L may be defined for every possible location. For allocation sizes 13-24 LRUs, the starting location L may be defined to start on odd numbered locations only. For allocation sizes 25-48 LRUs, L may be defined to start on every 4th odd numbered location (1, 5, 9, . . . ). For allocation sizes 49-88 LRUs, L may be defined to start on every 8th odd numbered location (1, 9, 17, . . . ). For allocation sizes 89-96 LRUs, L may be defined to start on every possible location. 
     As a second example, which is a variation of the above first example mapping, the gapped starting location L may defined as follows. For allocation sizes 1-12 LRUs, the starting location L may be defined for every possible location. For allocation sizes 13-24 LRUs, the starting location L may be defined to start at the locations at increments of 3 (i.e., from 1, 4, 7, . . . ). For allocation sizes 25-76 LRUs, L may be defined to start at the locations at increments of 4 (i.e., from 1, 5, 9, . . . ). For allocation sizes 77-96 LRUs, L may be defined to start at the one location for each of the allocation sizes; for a given size, the starting location may be chosen so that the allocation ends at the highest LRU index (i.e., 96). With this example variation, 2048 total allocations are possible, which may be signaled by an 11-bit RI field in the assignment IEs. 
     These defined mappings are provided as examples, and this embodiment should not be considered limited to these examples, as other similar variations may be used. 
     Using any of the above defined allocation sets having starting locations L with the “gapped allocations”, the larger size allocations may be mapped first, followed by mapping the smaller size allocations, which may start anywhere and to fill the gaps left by the large size allocations. 
     Table 2 shows valid allocations using selective locations for certain allocation sizes, in accordance with the above second example. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Assignable 
                   
                 Num- 
               
               
                 Resource 
                   
                 ber of 
               
               
                 Sizes 
                 Contiguous LRUs Index 
                 Indices 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 {1~1}, {2~2}, {3~3}, {4~4}, {5~5}, {6~6}, {7~7}, {8~8}, {9~9}, {10~10}, {11~11}, {12~12},  
                 96 
               
               
                   
                 {13~13}, {14~14}, {15~15}, {16~16}, {17~17}, {18~18}, {19~19}, {20~20}, {21~21}, {22~22},  
                   
               
               
                   
                 {23~23}, {24~24}, {25~25}, {26~26}, {27~27}, {28~28}, {29~29}, {30~30}, {31~31}, {32~32},  
                   
               
               
                   
                 {33~33}, {34~34}, {35~35}, {36~36}, {37~37}, {38~38}, {39~39}, {40~40}, {41~41}, {42~42},  
                   
               
               
                   
                 {43~43}, {44~44}, {45~45}, {46~46}, {47~47}, {48~48}, {49~49}, {50~50}, {51~51}, {52~52},  
                   
               
               
                   
                 {53~53}, {54~54}, {55~55}, {56~56}, {57~57}, {58~58}, {59~59}, {60~60}, {61~61}, {62~62},  
                   
               
               
                   
                 {63~63}, {64~64}, {65~65}, {66~66}, {67~67}, {68~68}, {69~69}, {70~70}, {71~71}, {72~72},  
                   
               
               
                   
                 {73~73}, {74~74}, {75~75}, {76~76}, {77~77}, {78~78}, {79~79}, {80~80}, {81~81}, {82~82},  
                   
               
               
                   
                 {83~83}, {84~84}, {85~85}, {86~86}, {87~87}, {88~88}, {89~89}, {90~90}, {91~91}, {92~92},  
                   
               
               
                   
                 {93~93}, {94~94}, {95~95}, {96~96} 
                   
               
               
                 2 
                 {1~2}, {2~3}, {3~4}, {4~5}, {5~6}, {6~7}, {7~8}, {8~9}, {9~10}, {10~11}, {11~12}, {12~13},  
                 95 
               
               
                   
                 {13~14}, {14~15}, {15~16}, {16~17}, {17~18}, {18~19}, {19~20}, {20~21}, {21~22}, {22~23},  
                   
               
               
                   
                 {23~24}, {24~25}, {25~26}, {26~27}, {27~28}, {28~29}, {29~30}, {30~31}, {31~32}, {32~33},  
                   
               
               
                   
                 {33~34}, {34~35}, {35~36}, {36~37}, {37~38}, {38~39}, {39~40}, {40~41}, {41~42}, {42~43},  
                   
               
               
                   
                 {43~44}, {44~45}, {45~46}, {46~47}, {47~48}, {48~49}, {49~50}, {50~51}, {51~52}, {52~53},  
                   
               
               
                   
                 {53~54}, {54~55}, {55~56}, {56~57}, {57~58}, {58~59}, {59~60}, {60~61}, {61~62}, {62~63},  
                   
               
               
                   
                 {63~64}, {64~65}, {65~66}, {66~67}, {67~68}, {68~69}, {69~70}, {70~71}, {71~72}, {72~73},  
                   
               
               
                   
                 {73~74}, {74~75}, {75~76}, {76~77}, {77~78}, {78~79}, {79~80}, {80~81}, {81~82}, {82~83},  
                   
               
               
                   
                 {83~84}, {84~85}, {85~86}, {86~87}, {87~88}, {88~89}, {89~90}, {90~91}, {91~92}, {92~93},  
                   
               
               
                   
                 {93~94}, {94~95}, {95~96} 
                   
               
               
                 3 
                 {1~3}, {2~4}, {3~5}, {4~6}, {5~7}, {6~8}, {7~9}, {8~10}, {9~11}, {10~12}, {11~13}, {12~14},  
                 94 
               
               
                   
                 {13~15}, {14~16}, {15~17}, {16~18}, {17~19}, {18~20}, {19~21}, {20~22}, {21~23}, {22~14}, 
                   
               
               
                   
                 {23~25}, {24~26}, {25~27}, {26~28}, {27~29}, {28~30}, {29~31}, {30~32}, {31~33}, {32~34},  
                   
               
               
                   
                 {33~35}, {34~36}, {35~37}, {36~38}, {37~39}, {38~40}, {39~41}, {40~42}, {41~43}, {42~44},  
                   
               
               
                   
                 {43~45}, {44~46}, {45~47}, {46~48}, {47~49}, {48~50}, {49~51}, {50~52}, {51~53}, {52~54},  
                   
               
               
                   
                 {53~55}, {54~56}, {55~57}, {56~58}, {57~59}, {58~60}, {59~61}, {60~62}, {61~63}, {62~64},  
                   
               
               
                   
                 {63~65}, {64~66}, {65~67}, {66~68}, {67~69}, {68~70}, {69~71}, {70~72}, {71~73}, {72~74},  
                   
               
               
                   
                 {73~75}, {74~76}, {75~77}, {76~78}, {77~79}, {78~80}, {79~81}, {80~82}, {81~83}, {82~84},  
                   
               
               
                   
                 {83~85}, {84~86}, {85~87}, {86~88}, {87~89}, {88~90}, {89~91}, {90~92}, {91~93}, {92~94},  
                   
               
               
                   
                 {93~95}, {94~96} 
                   
               
               
                 4 
                 {1~4}, {2~5}, {3~6}, {4~7}, {5~8}, {6~9}, {7~10}, {8~11}, {9~12}, {10~13}, {11~14}, {12~15},  
                 93 
               
               
                   
                 {13~16}, {14~17}, {15~18}, {16~19}, {17~20}, {18~21}, {19~22}, {20~23}, {21~24}, {22~25},  
                   
               
               
                   
                 {23~26}, {24~27}, {25~28}, {26~29}, {27~30}, {28~31}, {29~32}, {30~33}, {31~34}, {32~35},  
                   
               
               
                   
                 {33~36}, {34~37}, {35~38}, {36~39}, {37~40}, {38~41}, {39~42}, {40~43}, {41~44}, {42~45},  
                   
               
               
                   
                 {43~46}, {44~47}, {45~48}, {46~49}, {47~50}, {48~51}, {49~52}, {50~53}, {51~54}, {52~55},  
                   
               
               
                   
                 {53~56}, {54~57}, {55~58}, {56~59}, {57~60}, {58~61}, {59~62}, {60~63}, {61~64}, {62~65},  
                   
               
               
                   
                 {63~66}, {64~67}, {65~68}, {66~69}, {67~70}, {68~71}, {69~72}, {70~73}, {71~74}, {72~75},  
                   
               
               
                   
                 {73~76}, {74~77}, {75~78}, {76~79}, {77~80}, {78~81}, {79~82}, {80~83}, {81~84}, {82~85},  
                   
               
               
                   
                 {83~86}, {84~87}, {85~88}, {86~89}, {87~90}, {88~91}, {89~92}, {90~93}, {91~94}, {92~95},  
                   
               
               
                   
                 {93~96} 
                   
               
               
                 5 
                 {1~5}, {2~6}, {3~7}, {4~8}, {5~9}, {6~10}, {7~11}, {8~12}, {9~13}, {10~14}, {11~15}, {12~16}, 
                 92 
               
               
                   
                 {13~17}, {14~18}, {15~19}, {16~20}, {17~21}, {18~22}, {19~23}, {20~24}, {21~25}, {22~26},  
                   
               
               
                   
                 {23~27}, {24~28}, {25~29}, {26~30}, {27~31}, {28~32}, {29~33}, {30~34}, {31~35}, {32~36},  
                   
               
               
                   
                 {33~37}, {34~38}, {35~39}, {36~40}, {37~41}, {38~42}, {39~43}, {40~44}, {41~45}, {42~46},  
                   
               
               
                   
                 {43~47}, {44~48}, {45~49}, {46~50}, {47~51}, {48~52}, {49~53}, {50~54}, {51~55}, {52~56},  
                   
               
               
                   
                 {53~57}, {54~58}, {55~59}, {56~60}, {57~61}, {58~62}, {59~63}, {60~64}, {61~65}, {62~66},  
                   
               
               
                   
                 {63~67}, {64~68}, {65~69}, {66~70}, {67~71}, {68~72}, {69~73}, {70~74}, {71~75}, {72~76},  
                   
               
               
                   
                 {73~77}, {74~78}, {75~79}, {76~80}, {77~81}, {78~82}, {79~83}, {80~84}, {81~85}, {82~86},  
                   
               
               
                   
                 {83~87}, {84~88}, {85~89}, {86~90}, {87~91}, {88~92}, {89~93}, {90~94}, {91~95}, {92~96} 
                   
               
               
                 6 
                 {1~6}, {2~7}, {3~8}, {4~9}, {5~10}, {6~11}, {7~12}, {8~13}, {9~14}, {10~15}, {11~16},  
                 91 
               
               
                   
                 {12~17}, {13~18}, {14~19}, {15~20}, {16~21}, {17~22}, {18~23}, {19~24}, {20~25}, {21~26},  
                   
               
               
                   
                 {22~27}, {23~28}, {24~29}, {25~30}, {26~31}, {27~32}, {28~33}, {29~34}, {30~35}, {31~36},  
                   
               
               
                   
                 {32~37}, {33~38}, {34~39}, {35~40}, {36~41}, {37~42}, {38~43}, {39~44}, {40~45}, {41~46},  
                   
               
               
                   
                 {42~47}, {43~48}, {44~49}, {45~50}, {46~51}, {47~52}, {48~53}, {49~54}, {50~55}, {51~56},  
                   
               
               
                   
                 {52~57}, {53~58}, {54~59}, {55~60}, {56~61}, {57~62}, {58~63}, {59~64}, {60~65}, {61~66},  
                   
               
               
                   
                 {62~67}, {63~68}, {64~69}, {65~70}, {66~71}, {67~72}, {68~73}, {69~74}, {70~75}, {71~76},  
                   
               
               
                   
                 {72~77}, {73~78}, {74~79}, {75~80}, {76~81}, {77~82}, {78~83}, {79~84}, {80~85}, {81~86},  
                   
               
               
                   
                 {82~87}, {83~88}, {84~89}, {85~90}, {86~91}, {87~92}, {88~93}, {89~94}, {90~95}, {91~96} 
                   
               
               
                 7 
                 {1~7}, {2~8}, {3~9}, {4~10}, {5~11}, {6~12}, {7~13}, {8~14}, {9~15}, {10~16}, {11~17},  
                 90 
               
               
                   
                 {12~18}, {13~19}, {14~20}, {15~21}, {16~22}, {17~23}, {18~24}, {19~25}, {20~26}, {21~27},  
                   
               
               
                   
                 {22~28}, {23~29}, {24~30}, {25~31}, {26~32}, {27~33}, {28~34}, {29~35}, {30~36}, {31~37},  
                   
               
               
                   
                 {32~38}, {33~39}, {34~40}, {35~41}, {36~42}, {37~43}, {38~44}, {39~45}, {40~46}, {41~47},  
                   
               
               
                   
                 {42~48}, {43~49}, {44~50}, {45~51}, {46~52}, {47~53}, {48~54}, {49~55}, {50~56}, {51~57},  
                   
               
               
                   
                 {52~58}, {53~59}, {54~60}, {55~61}, {56~62}, {57~63}, {58~64}, {59~65}, {60~66}, {61~67},  
                   
               
               
                   
                 {62~68}, {63~69}, {64~70}, {65~71}, {66~72}, {67~73}, {68~74}, {69~75}, {70~76}, {71~77},  
                   
               
               
                   
                 {72~78}, {73~79}, {74~80}, {75~81}, {76~82}, {77~83}, {78~84}, {79~85}, {80~86}, {81~87},  
                   
               
               
                   
                 {82~88}, {83~89}, {84~90}, {85~91}, {86~92}, {87~93}, {88~94}, {89~95}, {90~96} 
                   
               
               
                 8 
                 {1~8}, {2~9}, {3~10}, {4~11}, {5~12}, {6~13}, {7~14}, {8~15}, {9~16}, {10~17}, {11~18},  
                 89 
               
               
                   
                 {12~19}, {13~20}, {14~21}, {15~22}, {16~23}, {17~24}, {18~25}, {19~26}, {20~27}, {21~28},  
                   
               
               
                   
                 {22~29}, {23~30}, {24~31}, {25~32}, {26~33}, {27~34}, {28~35}, {29~36}, {30~37}, {31~38},  
                   
               
               
                   
                 {32~39}, {33~40}, {34~41}, {35~42}, {36~43}, {37~44}, {38~45}, {39~46}, {40~47}, {41~48},  
                   
               
               
                   
                 {42~49}, {43~50}, {44~51}, {45~52}, {46~53}, {47~54}, {48~55}, {49~56}, {50~57}, {51~58},  
                   
               
               
                   
                 {52~59}, {53~60}, {54~61}, {55~62}, {56~63}, {57~64}, {58~65}, {59~66}, {60~67}, {61~68},  
                   
               
               
                   
                 {62~69}, {63~70}, {64~71}, {65~72}, {66~73}, {67~74}, {68~75}, {69~76}, {70~77}, {71~78},  
                   
               
               
                   
                 {72~79}, {73~80}, {74~81}, {75~82}, {76~83}, {77~84}, {78~85}, {79~86}, {80~87}, {81~88},  
                   
               
               
                   
                 {82~89}, {83~90}, {84~91}, {85~92}, {86~93}, {87~94}, {88~95}, {89~96} 
                   
               
               
                 9 
                 {1~9}, {2~10}, {3~11}, {4~12}, {5~13}, {6~14}, {7~15}, {8~16}, {9~17}, {10~18}, {11~19},  
                 88 
               
               
                   
                 {12~20}, {13~21}, {14~22}, {15~23}, {16~24}, {17~25}, {18~26}, {19~27}, {20~28}, {21~29},  
                   
               
               
                   
                 {22~30}, {23~31}, {24~32}, {25~33}, {26~34}, {27~35}, {28~36}, {29~37}, {30~38}, {31~39},  
                   
               
               
                   
                 {32~40}, {33~41}, {34~42}, {35~43}, {36~44}, {37~45}, {38~46}, {39~47}, {40~48}, {41~49},  
                   
               
               
                   
                 {42~50}, {43~51}, {44~52}, {45~53}, {46~54}, {47~55}, {48~56}, {49~57}, {50~58}, {51~59},  
                   
               
               
                   
                 {52~60}, {53~61}, {54~62}, {55~63}, {56~64}, {57~65}, {58~66}, {59~67}, {60~68}, {61~69},  
                   
               
               
                   
                 {62~70}, {63~71}, {64~72}, {65~73}, {66~74}, {67~75}, {68~76}, {69~77}, {70~78}, {71~79},  
                   
               
               
                   
                 {72~80}, {73~81}, {74~82}, {75~83}, {76~84}, {77~85}, {78~86}, {79~87}, {80~88}, {81~89},  
                   
               
               
                   
                 {82~90}, {83~91}, {84~92}, {85~93}, {86~94}, {87~95}, {88~96} 
                   
               
               
                 10 
                 {1~10}, {2~11}, {3~12}, {4~13}, {5~14}, {6~15}, {7~16}, {8~17}, {9~18}, {10~19}, {11~20},  
                 87 
               
               
                   
                 {12~21}, {13~22}, {14~23}, {15~24}, {16~25}, {17~26}, {18~27}, {19~28}, {20~29}, {21~30},  
                   
               
               
                   
                 {22~31}, {23~32}, {24~33}, {25~34}, {26~35}, {27~36}, {28~37}, {29~38}, {30~39}, {31~40},  
                   
               
               
                   
                 {32~41}, {33~42}, {34~43}, {35~44}, {36~45}, {37~46}, {38~47}, {39~48}, {40~49}, {41~50},  
                   
               
               
                   
                 {42~51}, {43~52}, {44~53}, {45~54}, {46~55}, {47~56}, {48~57}, {49~58}, {50~59}, {51~60},  
                   
               
               
                   
                 {52~61}, {53~62}, {54~63}, {55~64}, {56~65}, {57~66}, {58~67}, {59~68}, {60~69}, {61~70},  
                   
               
               
                   
                 {62~71}, {63~72}, {64~73}, {65~74}, {66~75}, {67~76}, {68~77}, {69~78}, {70~79}, {71~80},  
                   
               
               
                   
                 {72~81}, {73~82}, {74~83}, {75~84}, {76~85}, {77~86}, {78~87}, {79~88}, {80~89}, {81~90},  
                   
               
               
                   
                 {82~91}, {83~92}, {84~93}, {85~94}, {86~95}, {87~96} 
                   
               
               
                 11 
                 {1~11}, {2~12}, {3~13}, {4~14}, {5~15}, {6~16}, {7~17}, {8~18}, {9~19}, {10~20}, {11~21},  
                 86 
               
               
                   
                 {12~22}, {13~23}, {14~24}, {15~25}, {16~26}, {17~27}, {18~28}, {19~29}, {20~30}, {21~31},  
                   
               
               
                   
                 {22~32}, {23~33}, {24~34}, {25~35}, {26~36}, {27~37}, {28~38}, {29~39}, {30~40}, {31~41},  
                   
               
               
                   
                 {32~42}, {33~43}, {34~44}, {35~45}, {36~46}, {37~47}, {38~48}, {39~49}, {40~50}, {41~51},  
                   
               
               
                   
                 {42~52}, {43~53}, {44~54}, {45~55}, {46~56}, {47~57}, {48~58}, {49~59}, {50~60}, {51~61},  
                   
               
               
                   
                 {52~62}, {53~63}, {54~64}, {55~65}, {56~66}, {57~67}, {58~68}, {59~69}, {60~70}, {61~71},  
                   
               
               
                   
                 {62~72}, {63~73}, {64~74}, {65~75}, {66~76}, {67~77}, {68~78}, {69~79}, {70~80}, {71~81},  
                   
               
               
                   
                 {72~82}, {73~83}, {74~84}, {75~85}, {76~86}, {77~87}, {78~88}, {79~89}, {80~90}, {81~91},  
                   
               
               
                   
                 {82~92}, {83~93}, {84~94}, {85~95}, {86~96} 
                   
               
               
                 12 
                 {1~12}, {2~13}, {3~14}, {4~15}, {5~16}, {6~17}, {7~18}, {8~19}, {9~20}, {10~21}, {11~22},  
                 85 
               
               
                   
                 {12~23}, {13~24}, {14~25}, {15~26}, {16~27}, {17~28}, {18~29}, {19~30}, {20~31}, {21~32},  
                   
               
               
                   
                 {22~33}, {23~34}, {24~35}, {25~36}, {26~37}, {27~38}, {28~39}, {29~40}, {30~41}, {31~42},  
                   
               
               
                   
                 {32~43}, {33~44}, {34~45}, {35~46}, {36~47}, {37~48}, {38~49}, {39~50}, {40~51}, {41~52},  
                   
               
               
                   
                 {42~53}, {43~54}, {44~55}, {45~56}, {46~57}, {47~58}, {48~59}, {49~60}, {50~61}, {51~62},  
                   
               
               
                   
                 {52~63}, {53~64}, {54~65}, {55~66}, {56~67}, {57~68}, {58~69}, {59~70}, {60~71}, {61~72},  
                   
               
               
                   
                 {62~73}, {63~74}, {64~75}, {65~76}, {66~77}, {67~78}, {68~79}, {69~80}, {70~81}, {71~82},  
                   
               
               
                   
                 {72~83}, {73~84}, {74~85}, {75~86}, {76~87}, {77~88}, {78~89}, {79~90}, {80~91}, {81~92},  
                   
               
               
                   
                 {82~93}, {83~94}, {84~95}, {85~96} 
                   
               
               
                 13 
                 {1~13}, {4~16}, {7~19}, {10~22}, {13~25}, {16~28}, {19~31}, {22~34}, {25~37}, {28~40},  
                 28 
               
               
                   
                 {31~43}, {34~46}, {37~49}, {40~52}, {43~55}, {46~58}, {49~61}, {52~64}, {55~67}, {58~70},  
                   
               
               
                   
                 {61~73}, {64~76}, {67~79}, {70~82}, {73~85}, {76~88}, {79~91}, {82~94} 
                   
               
               
                 14 
                 {1~14}, {4~17}, {7~20}, {10~23}, {13~26}, {16~29}, {19~32}, {22~35}, {25~38}, {28~41},  
                 28 
               
               
                   
                 {31~44}, {34~47}, {37~50}, {40~53}, {43~56}, {46~59}, {49~62}, {52~65}, {55~68}, {58~71},  
                   
               
               
                   
                 {61~74}, {64~77}, {67~80}, {70~83}, {73~86}, {76~89}, {79~92}, {82~95} 
                   
               
               
                 15 
                 {1~15}, {4~18}, {7~21}, {10~24}, {13~27}, {16~30}, {19~33}, {22~36}, {25~39}, {28~42},  
                 28 
               
               
                   
                 {31~45}, {34~48}, {37~51}, {40~54}, {43~57}, {46~60}, {49~63}, {52~66}, {55~69}, {58~72},  
                   
               
               
                   
                 {61~75}, {64~78}, {67~81}, {70~84}, {73~87}, {76~90}, {79~93}, {82~96} 
                   
               
               
                 16 
                 {1~16}, {4~19}, {7~22}, {10~25}, {13~28}, {16~31}, {19~34}, {22~37}, {25~40}, {28~43},  
                 27 
               
               
                   
                 {31~46}, {34~49}, {37~52}, {40~55}, {43~58}, {46~61}, {49~64}, {52~67}, {55~70}, {58~73},  
                   
               
               
                   
                 {61~76}, {64~79}, {67~82}, {70~85}, {73~88}, {76~91}, {79~94} 
                   
               
               
                 17 
                 {1~17}, {4~20}, {7~23}, {10~26}, {13~29}, {16~32}, {19~35}, {22~38}, {25~41}, {28~44},  
                 27 
               
               
                   
                 {31~47}, {34~50}, {37~53}, {40~56}, {43~59}, {46~62}, {49~65}, {52~68}, {55~71}, {58~74},  
                   
               
               
                   
                 {61~77}, {64~80}, {67~83}, {70~86}, {73~89}, {76~92}, {79~95} 
                   
               
               
                 18 
                 {1~18}, {4~21}, {7~24}, {10~27}, {13~30}, {16~33}, {19~36}, {22~39}, {25~42}, {28~45},  
                 27 
               
               
                   
                 {31~48}, {34~51}, {37~54}, {40~57}, {43~60}, {46~63}, {49~66}, {52~69}, {55~72}, {58~75},  
                   
               
               
                   
                 {61~78}, {64~81}, {67~84}, {70~87}, {73~90}, {76~93}, {79~96} 
                   
               
               
                 19 
                 {1~19}, {4~22}, {7~25}, {10~28}, {13~31}, {16~34}, {19~37}, {22~40}, {25~43}, {28~46},  
                 26 
               
               
                   
                 {31~49}, {34~52}, {37~55}, {40~58}, {43~61}, {46~64}, {49~67}, {52~70}, {55~73}, {58~76},  
                   
               
               
                   
                 {61~79}, {64~82}, {67~85}, {70~88}, {73~91}, {76~94} 
                   
               
               
                 20 
                 {1~20}, {4~23}, {7~26}, {10~29}, {13~32}, {16~35}, {19~38}, {22~41}, {25~44}, {28~47},  
                 26 
               
               
                   
                 {31~50}, {34~53}, {37~56}, {40~59}, {43~62}, {46~65}, {49~68}, {52~71}, {55~74}, {58~77},  
                   
               
               
                   
                 {61~80}, {64~83}, {67~86}, {70~89}, {73~92}, {76~95} 
                   
               
               
                 21 
                 {1~21}, {4~24}, {7~27}, {10~30}, {13~33}, {16~36}, {19~39}, {22~42}, {25~45}, {28~48},  
                 26 
               
               
                   
                 {31~51}, {34~54}, {37~57}, {40~60}, {43~63}, {46~66}, {49~69}, {52~72}, {55~75}, {58~78},  
                   
               
               
                   
                 {61~81}, {64~84}, {67~87}, {70~90}, {73~93}, {76~96} 
                   
               
               
                 22 
                 {1~22}, {4~25}, {7~28}, {10~31}, {13~34}, {16~37}, {19~40}, {22~43}, {25~46}, {28~49},  
                 25 
               
               
                   
                 {31~52}, {34~55}, {37~58}, {40~61}, {43~64}, {46~67}, {49~70}, {52~73}, {55~76}, {58~79},  
                   
               
               
                   
                 {61~82}, {64~85}, {67~88}, {70~91}, {73~94} 
                   
               
               
                 23 
                 {1~23}, {4~26}, {7~29}, {10~32}, {13~35}, {16~38}, {19~41}, {22~44}, {25~47}, {28~50},  
                 25 
               
               
                   
                 {31~53}, {34~56}, {37~59}, {40~62}, {43~65}, {46~68}, {49~71}, {52~74}, {55~77}, {58~80},  
                   
               
               
                   
                 {61~83}, {64~86}, {67~89}, {70~92}, {73~95} 
                   
               
               
                 24 
                 {1~24}, {4~27}, {7~30}, {10~33}, {13~36}, {16~39}, {19~42}, {22~45}, {25~48}, {28~51},  
                 25 
               
               
                   
                 {31~54}, {34~57}, {37~60}, {40~63}, {43~66}, {46~69}, {49~72}, {52~75}, {55~78}, {58~81},  
                   
               
               
                   
                 {61~84}, {64~87}, {67~90}, {70~93}, {73~96} 
                   
               
               
                 25 
                 {1~25}, {5~29}, {9~33}, {13~37}, {17~41}, {21~45}, {25~49}, {29~53}, {33~57}, {37~61},  
                 18 
               
               
                   
                 {41~65}, {45~69}, {49~73}, {53~77}, {57~81}, {61~85}, {65~89}, {69~93} 
                   
               
               
                 26 
                 {1~26}, {5~30}, {9~34}, {13~38}, {17~42}, {21~46}, {25~50}, {29~54}, {33~58}, {37~62},  
                 18 
               
               
                   
                 {41~66}, {45~70}, {49~74}, {53~78}, {57~82}, {61~86}, {65~90}, {69~94} 
                   
               
               
                 27 
                 {1~27}, 15~311, 19~351, {13~39}, {17~43}, {21~47}, {25~51}, {29~55}, {33~59}, {37~63},  
                 18 
               
               
                   
                 {41~67}, {45~71}, {49~75}, {53~79}, {57~83}, {61~87}, {65~91}, {69~95} 
                   
               
               
                 28 
                 {1~28}, {5~32}, {9~36}, {13~40}, {17~44}, {21~48}, {25~52}, {29~56}, {33~60}, {37~64},  
                 18 
               
               
                   
                 {41~68}, {45~72}, {49~76}, {53~80}, {57~84}, {61~88}, {65~92}, {69~96} 
                   
               
               
                 29 
                 {1~29}, {5~33}, {9~37}, {13~41}, {17~45}, {21~49}, {25~53}, {29~57}, {33~61}, {37~65},  
                 17 
               
               
                   
                 {41~69}, {45~73}, {49~77}, {53~81}, {57~85}, {61~89}, {65~93} 
                   
               
               
                 30 
                 {1~30}, {5~34}, {9~38}, {13~42}, {17~46}, {21~50}, {25~54}, {29~58}, {33~62}, {37~66},  
                 17 
               
               
                   
                 {41~70}, {45~74}, {49~78}, {53~82}, {57~86}, {61~90}, {65~94} 
                   
               
               
                 31 
                 {1~31}, {5~35}, {9~39}, {13~43}, {17~47}, {21~51}, {25~55}, {29~59}, {33~63}, {37~67},  
                 17 
               
               
                   
                 {41~71}, {45~75}, {49~79}, {53~83}, {57~87}, {61~91}, {65~95} 
                   
               
               
                 32 
                 {1~32}, {5~36}, {9~40}, {13~44}, {17~48}, {21~52}, {25~56}, {29~60}, {33~64}, {37~68},  
                 17 
               
               
                   
                 {41~72}, {45~76}, {49~80}, {53~84}, {57~88}, {61~92}, {65~96} 
                   
               
               
                 33 
                 {1~33}, {5~37}, {9~41}, {13~45}, {17~49}, {21~53}, {25~57}, {29~61}, {33~65}, {37~69},  
                 16 
               
               
                   
                 {41~73}, {45~77}, {49~81}, {53~85}, {57~89}, {61~93} 
                   
               
               
                 34 
                 {1~34}, {5~38}, {9~42}, {13~46}, {17~50}, {21~54}, {25~58}, {29~62}, {33~66}, {37~70},  
                 16 
               
               
                   
                 {41~74}, {45~78}, {49~82}, {53~86}, {57~90}, {61~94} 
                   
               
               
                 35 
                 {1~35}, {5~39}, {9~43}, {13~47}, {17~51}, {21~55}, {25~59}, {29~63}, {33~67}, {37~71},  
                 16 
               
               
                   
                 {41~75}, {45~79}, {49~83}, {53~87}, {57~91}, {61~95} 
                   
               
               
                 36 
                 {1~36}, {5~40}, {9~44}, {13~48}, {17~52}, {21~56}, {25~60}, {29~64}, {33~68}, {37~72},  
                 16 
               
               
                   
                 {41~76}, {45~80}, {49~84}, {53~88}, {57~92}, {61~96} 
                   
               
               
                 37 
                 {1~37}, {5~41}, {9~45}, {13~49}, {17~53}, {21~57}, {25~61}, {29~65}, {33~69}, {37~73},  
                 15 
               
               
                   
                 {41~77}, {45~81}, {49~85}, {53~89}, {57~93} 
                   
               
               
                 38 
                 {1~38}, {5~42}, {9~46}, {13~50}, {17~54}, {21~58}, {25~62}, {29~66}, {33~70}, {37~74},  
                 15 
               
               
                   
                 {41~78}, {45~82}, {49~86}, {53~90}, {57~94} 
                   
               
               
                 39 
                 {1~39}, {5~43}, {9~47}, {13~51}, {17~55}, {21~59}, {25~63}, {29~67}, {33~71}, {37~75},  
                 15 
               
               
                   
                 {41~79}, {45~83}, {49~87}, {53~91}, {57~95} 
                   
               
               
                 40 
                 {1~40}, {5~44}, {9~48}, {13~52}, {17~56}, {21~60}, {25~64}, {29~68}, {33~72}, {37~76},  
                 15 
               
               
                   
                 {41~80}, {45~84}, {49~88}, {53~92}, {57~96} 
                   
               
               
                 41 
                 {1~41}, {5~45}, {9~49}, {13~53}, {17~57}, {21~61}, {25~65}, {29~69}, {33~73}, {37~77},  
                 14 
               
               
                   
                 {41~81}, {45~85}, {49~89}, {53~93} 
                   
               
               
                 42 
                 {1~42}, {5~46}, {9~50}, {13~54}, {17~58}, {21~62}, {25~66}, {29~70}, {33~74}, {37~78},  
                 14 
               
               
                   
                 {41~82}, {45~86}, {49~90}, {53~94} 
                   
               
               
                 43 
                 {1~43}, {5~47}, {9~51}, {13~55}, {17~59}, {21~63}, {25~67}, {29~71}, {33~75}, {37~79},  
                 14 
               
               
                   
                 {41~83}, {45~87}, {49~91}, {53~95} 
                   
               
               
                 44 
                 {1~44}, {5~48}, {9~52}, {13~56}, {17~60}, {21~64}, {25~68}, {29~72}, {33~76}, {37~80},  
                 14 
               
               
                   
                 {41~84}, {45~88}, {49~92}, {53~96} 
                   
               
               
                 45 
                 {1~45}, {5~49}, {9~53}, {13~57}, {17~61}, {21~65}, {25~69}, {29~73}, {33~77}, {37~81},  
                 13 
               
               
                   
                 {41~85}, {45~89}, {49~93} 
                   
               
               
                 46 
                 {1~46}, {5~50}, {9~54}, {13~58}, {17~62}, {21~66}, {25~70}, {29~74}, {33~78}, {37~82},  
                 13 
               
               
                   
                 {41~86}, {45~90}, {49~94} 
                   
               
               
                 47 
                 {1~47}, {5~51}, {9~55}, {13~59}, {17~63}, {21~67}, {25~71}, {29~75}, {33~79}, {37~83},  
                 13 
               
               
                   
                 {41~87}, {45~91}, {49~95} 
                   
               
               
                 48 
                 {1~48}, {5~52}, {9~56}, {13~60}, {17~64}, {21~68}, {25~72}, {29~76}, {33~80}, {37~84},  
                 13 
               
               
                   
                 {41~88}, {45~92}, {49~96} 
                   
               
               
                 49 
                 {1~49}, {5~53}, {9~57}, {13~61}, {17~65}, {21~69}, {25~73}, {29~77}, {33~81}, {37~85},  
                 12 
               
               
                   
                 {41~89}, {45~93} 
                   
               
               
                 50 
                 {1~50}, {5~54}, {9~58}, {13~62}, {17~66}, {21~70}, {25~74}, {29~78}, {33~82}, {37~86},  
                 12 
               
               
                   
                 {41~90}, {45~94} 
                   
               
               
                 51 
                 {1~51}, {5~55}, {9~59}, {13~63}, {17~67}, {21~71}, {25~75}, {29~79}, {33~83}, {37~87},  
                 12 
               
               
                   
                 {41~91}, {45~95} 
                   
               
               
                 52 
                 {1~52}, {5~56}, {9~60}, {13~64}, {17~68}, {21~72}, {25~76}, {29~80}, {33~84}, {37~88},  
                 12 
               
               
                   
                 {41~92}, {45~96} 
                   
               
               
                 53 
                 {1~53}, {5~57}, {9~61}, {13~65}, {17~69}, {21~73}, {25~77}, {29~81}, {33~85}, {37~89},  
                 11 
               
               
                   
                 {41~93} 
                   
               
               
                 54 
                 {1~54}, {5~58}, {9~62}, {13~66}, {17~70}, {21~74}, {25~78}, {29~82}, {33~86}, {37~90},  
                 11 
               
               
                   
                 {41~94} 
                   
               
               
                 55 
                 {1~55}, {5~59}, {9~63}, {13~67}, {17~71}, {21~75}, {25~79}, {29~83}, {33~87}, {37~91},  
                 11 
               
               
                   
                 {41~95} 
                   
               
               
                 56 
                 {1~56}, {5~60}, {9~64}, {13~68}, {17~72}, {21~76}, {25~80}, {29~84}, {33~88}, {37~92},  
                 11 
               
               
                   
                 {41~96} 
                   
               
               
                 57 
                 {1~57}, {5~61}, {9~65}, {13~69}, {17~73}, {21~77}, {25~81}, {29~85}, {33~89}, {37~93} 
                 10 
               
               
                 58 
                 {1~58}, {5~62}, {9~66}, {13~70}, {17~74}, {21~78}, {25~82}, {29~86}, {33~90}, {37~94} 
                 10 
               
               
                 59 
                 {1~59}, {5~63}, {9~67}, {13~71}, {17~75}, {21~79}, {25~83}, {29~87}, {33~91}, {37~95} 
                 10 
               
               
                 60 
                 {1~60}, {5~64}, {9~68}, {13~72}, {17~76}, {21~80}, {25~84}, {29~88}, {33~92}, {37~96} 
                 10 
               
               
                 61 
                 {1~61}, {5~65}, {9~69}, {13~73}, {17~77}, {21~81}, {25~85}, {29~89}, {33~93} 
                 9 
               
               
                 62 
                 {1~62}, {5~66}, {9~70}, {13~74}, {17~78}, {21~82}, {25~86}, {29~90}, {33~94} 
                 9 
               
               
                 63 
                 {1~63}, {5~67}, {9~71}, {13~75}, {17~79}, {21~83}, {25~87}, {29~91}, {33~95} 
                 9 
               
               
                 64 
                 {1~64}, {5~68}, {9~72}, {13~76}, {17~80}, {21~84}, {25~88}, {29~92}, {33~96} 
                 9 
               
               
                 65 
                 {1~65}, {5~69}, {9~73}, {13~77}, {17~81}, {21~85}, {25~89}, {29~93} 
                 8 
               
               
                 66 
                 {1~66}, {5~70}, {9~74}, {13~78}, {17~82}, {21~86}, {25~90}, {29~94} 
                 8 
               
               
                 67 
                 {1~67}, {5~71}, {9~75}, {13~79}, {17~83}, {21~87}, {25~91}, {29~95} 
                 8 
               
               
                 68 
                 {1~68}, {5~72}, {9~76}, {13~80}, {17~84}, {21~88}, {25~92}, {29~96} 
                 8 
               
               
                 69 
                 {1~69}, {5~73}, {9~77}, {13~81}, {17~85}, {21~89}, {25~93} 
                 7 
               
               
                 70 
                 {1~70}, {5~74}, {9~78}, {13~82}, {17~86}, {21~90}, {25~94} 
                 7 
               
               
                 71 
                 {1~71}, {5~75}, {9~79}, {13~83}, {17~87}, {21~91}, {25~95} 
                 7 
               
               
                 72 
                 {1~72}, {5~76}, {9~80}, {13~84}, {17~88}, {21~92}, {25~96} 
                 7 
               
               
                 73 
                 {1~73}, {5~77}, {9~81}, {13~85}, {17~89}, {21~93} 
                 6 
               
               
                 74 
                 {1~74}, {5~78}, {9~82}, {13~86}, {17~90}, {21~94} 
                 6 
               
               
                 75 
                 {1~75}, {5~79}, {9~83}, {13~87}, {17~91}, {21~95} 
                 6 
               
               
                 76 
                 {1~76}, {5~80}, {9~84}, {13~88}, {17~92}, {21~96} 
                 6 
               
               
                 77 
                 {20~96} 
                 1 
               
               
                 78 
                 {19~96} 
                 1 
               
               
                 79 
                 {18~96} 
                 1 
               
               
                 80 
                 {17~96} 
                 1 
               
               
                 81 
                 {16~96} 
                 1 
               
               
                 82 
                 {15~96} 
                 1 
               
               
                 83 
                 {14~96} 
                 1 
               
               
                 84 
                 {13~96} 
                 1 
               
               
                 85 
                 {12~96} 
                 1 
               
               
                 86 
                 {11~96} 
                 1 
               
               
                 87 
                 {10~96} 
                 1 
               
               
                 88 
                 {9~96} 
                 1 
               
               
                 89 
                 {8~96} 
                 1 
               
               
                 90 
                 {7~96} 
                 1 
               
               
                 91 
                 {6~96} 
                 1 
               
               
                 92 
                 {5~96} 
                 1 
               
               
                 93 
                 {4~96} 
                 1 
               
               
                 94 
                 {3~96} 
                 1 
               
               
                 95 
                 {2~96} 
                 1 
               
               
                 96 
                 {1~96} 
                 1 
               
               
                   
                   
                 Total = 
               
               
                   
                   
                 2048 
               
               
                   
               
            
           
         
       
     
     Based on the defined selective locations L for certain allocation sizes as shown in Table 1, an example 11-bit RI index assignment may be generated as shown in Table 3. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Index 
                 Start 
                 Length 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 1 
                 1 
               
               
                 2 
                 2 
                 1 
               
               
                 3 
                 3 
                 1 
               
               
                 4 
                 4 
                 1 
               
               
                 5 
                 5 
                 1 
               
               
                 6 
                 6 
                 1 
               
               
                 7 
                 7 
                 1 
               
               
                 8 
                 8 
                 1 
               
               
                 9 
                 9 
                 1 
               
               
                 10 
                 10 
                 1 
               
               
                 11 
                 11 
                 1 
               
               
                 12 
                 12 
                 1 
               
               
                 13 
                 13 
                 1 
               
               
                 14 
                 14 
                 1 
               
               
                 15 
                 15 
                 1 
               
               
                 16 
                 16 
                 1 
               
               
                 17 
                 17 
                 1 
               
               
                 18 
                 18 
                 1 
               
               
                 19 
                 19 
                 1 
               
               
                 20 
                 20 
                 1 
               
               
                 21 
                 21 
                 1 
               
               
                 22 
                 22 
                 1 
               
               
                 23 
                 23 
                 1 
               
               
                 24 
                 24 
                 1 
               
               
                 25 
                 25 
                 1 
               
               
                 26 
                 26 
                 1 
               
               
                 27 
                 27 
                 1 
               
               
                 28 
                 28 
                 1 
               
               
                 29 
                 29 
                 1 
               
               
                 30 
                 30 
                 1 
               
               
                 31 
                 31 
                 1 
               
               
                 32 
                 32 
                 1 
               
               
                 33 
                 33 
                 1 
               
               
                 34 
                 34 
                 1 
               
               
                 35 
                 35 
                 1 
               
               
                 36 
                 36 
                 1 
               
               
                 37 
                 37 
                 1 
               
               
                 38 
                 38 
                 1 
               
               
                 39 
                 39 
                 1 
               
               
                 40 
                 40 
                 1 
               
               
                 41 
                 41 
                 1 
               
               
                 42 
                 42 
                 1 
               
               
                 43 
                 43 
                 1 
               
               
                 44 
                 44 
                 1 
               
               
                 45 
                 45 
                 1 
               
               
                 46 
                 46 
                 1 
               
               
                 47 
                 47 
                 1 
               
               
                 48 
                 48 
                 1 
               
               
                 49 
                 49 
                 1 
               
               
                 50 
                 50 
                 1 
               
               
                 51 
                 51 
                 1 
               
               
                 52 
                 52 
                 1 
               
               
                 53 
                 53 
                 1 
               
               
                 54 
                 54 
                 1 
               
               
                 55 
                 55 
                 1 
               
               
                 56 
                 56 
                 1 
               
               
                 57 
                 57 
                 1 
               
               
                 58 
                 58 
                 1 
               
               
                 59 
                 59 
                 1 
               
               
                 60 
                 60 
                 1 
               
               
                 61 
                 61 
                 1 
               
               
                 62 
                 62 
                 1 
               
               
                 63 
                 63 
                 1 
               
               
                 64 
                 64 
                 1 
               
               
                 65 
                 65 
                 1 
               
               
                 66 
                 66 
                 1 
               
               
                 67 
                 67 
                 1 
               
               
                 68 
                 68 
                 1 
               
               
                 69 
                 69 
                 1 
               
               
                 70 
                 70 
                 1 
               
               
                 71 
                 71 
                 1 
               
               
                 72 
                 72 
                 1 
               
               
                 73 
                 73 
                 1 
               
               
                 74 
                 74 
                 1 
               
               
                 75 
                 75 
                 1 
               
               
                 76 
                 76 
                 1 
               
               
                 77 
                 77 
                 1 
               
               
                 78 
                 78 
                 1 
               
               
                 79 
                 79 
                 1 
               
               
                 80 
                 80 
                 1 
               
               
                 81 
                 81 
                 1 
               
               
                 82 
                 82 
                 1 
               
               
                 83 
                 83 
                 1 
               
               
                 84 
                 84 
                 1 
               
               
                 85 
                 85 
                 1 
               
               
                 86 
                 86 
                 1 
               
               
                 87 
                 87 
                 1 
               
               
                 88 
                 88 
                 1 
               
               
                 89 
                 89 
                 1 
               
               
                 90 
                 90 
                 1 
               
               
                 91 
                 91 
                 1 
               
               
                 92 
                 92 
                 1 
               
               
                 93 
                 93 
                 1 
               
               
                 94 
                 94 
                 1 
               
               
                 95 
                 95 
                 1 
               
               
                 96 
                 96 
                 1 
               
               
                 97 
                 1 
                 2 
               
               
                 98 
                 2 
                 2 
               
               
                 99 
                 3 
                 2 
               
               
                 100 
                 4 
                 2 
               
               
                 101 
                 5 
                 2 
               
               
                 102 
                 6 
                 2 
               
               
                 103 
                 7 
                 2 
               
               
                 104 
                 8 
                 2 
               
               
                 105 
                 9 
                 2 
               
               
                 106 
                 10 
                 2 
               
               
                 107 
                 11 
                 2 
               
               
                 108 
                 12 
                 2 
               
               
                 109 
                 13 
                 2 
               
               
                 110 
                 14 
                 2 
               
               
                 111 
                 15 
                 2 
               
               
                 112 
                 16 
                 2 
               
               
                 113 
                 17 
                 2 
               
               
                 114 
                 18 
                 2 
               
               
                 115 
                 19 
                 2 
               
               
                 116 
                 20 
                 2 
               
               
                 117 
                 21 
                 2 
               
               
                 118 
                 22 
                 2 
               
               
                 119 
                 23 
                 2 
               
               
                 120 
                 24 
                 2 
               
               
                 121 
                 25 
                 2 
               
               
                 122 
                 26 
                 2 
               
               
                 123 
                 27 
                 2 
               
               
                 124 
                 28 
                 2 
               
               
                 125 
                 29 
                 2 
               
               
                 126 
                 30 
                 2 
               
               
                 127 
                 31 
                 2 
               
               
                 128 
                 32 
                 2 
               
               
                 129 
                 33 
                 2 
               
               
                 130 
                 34 
                 2 
               
               
                 131 
                 35 
                 2 
               
               
                 132 
                 36 
                 2 
               
               
                 133 
                 37 
                 2 
               
               
                 134 
                 38 
                 2 
               
               
                 135 
                 39 
                 2 
               
               
                 136 
                 40 
                 2 
               
               
                 137 
                 41 
                 2 
               
               
                 138 
                 42 
                 2 
               
               
                 139 
                 43 
                 2 
               
               
                 140 
                 44 
                 2 
               
               
                 141 
                 45 
                 2 
               
               
                 142 
                 46 
                 2 
               
               
                 143 
                 47 
                 2 
               
               
                 144 
                 48 
                 2 
               
               
                 145 
                 49 
                 2 
               
               
                 146 
                 50 
                 2 
               
               
                 147 
                 51 
                 2 
               
               
                 148 
                 52 
                 2 
               
               
                 149 
                 53 
                 2 
               
               
                 150 
                 54 
                 2 
               
               
                 151 
                 55 
                 2 
               
               
                 152 
                 56 
                 2 
               
               
                 153 
                 57 
                 2 
               
               
                 154 
                 58 
                 2 
               
               
                 155 
                 59 
                 2 
               
               
                 156 
                 60 
                 2 
               
               
                 157 
                 61 
                 2 
               
               
                 158 
                 62 
                 2 
               
               
                 159 
                 63 
                 2 
               
               
                 160 
                 64 
                 2 
               
               
                 161 
                 65 
                 2 
               
               
                 162 
                 66 
                 2 
               
               
                 163 
                 67 
                 2 
               
               
                 164 
                 68 
                 2 
               
               
                 165 
                 69 
                 2 
               
               
                 166 
                 70 
                 2 
               
               
                 167 
                 71 
                 2 
               
               
                 168 
                 72 
                 2 
               
               
                 169 
                 73 
                 2 
               
               
                 170 
                 74 
                 2 
               
               
                 171 
                 75 
                 2 
               
               
                 172 
                 76 
                 2 
               
               
                 173 
                 77 
                 2 
               
               
                 174 
                 78 
                 2 
               
               
                 175 
                 79 
                 2 
               
               
                 176 
                 80 
                 2 
               
               
                 177 
                 81 
                 2 
               
               
                 178 
                 82 
                 2 
               
               
                 179 
                 83 
                 2 
               
               
                 180 
                 84 
                 2 
               
               
                 181 
                 85 
                 2 
               
               
                 182 
                 86 
                 2 
               
               
                 183 
                 87 
                 2 
               
               
                 184 
                 88 
                 2 
               
               
                 185 
                 89 
                 2 
               
               
                 186 
                 90 
                 2 
               
               
                 187 
                 91 
                 2 
               
               
                 188 
                 92 
                 2 
               
               
                 189 
                 93 
                 2 
               
               
                 190 
                 94 
                 2 
               
               
                 191 
                 95 
                 2 
               
               
                 192 
                 1 
                 3 
               
               
                 193 
                 2 
                 3 
               
               
                 194 
                 3 
                 3 
               
               
                 195 
                 4 
                 3 
               
               
                 196 
                 5 
                 3 
               
               
                 197 
                 6 
                 3 
               
               
                 198 
                 7 
                 3 
               
               
                 199 
                 8 
                 3 
               
               
                 200 
                 9 
                 3 
               
               
                 201 
                 10 
                 3 
               
               
                 202 
                 11 
                 3 
               
               
                 203 
                 12 
                 3 
               
               
                 204 
                 13 
                 3 
               
               
                 205 
                 14 
                 3 
               
               
                 206 
                 15 
                 3 
               
               
                 207 
                 16 
                 3 
               
               
                 208 
                 17 
                 3 
               
               
                 209 
                 18 
                 3 
               
               
                 210 
                 19 
                 3 
               
               
                 211 
                 20 
                 3 
               
               
                 212 
                 21 
                 3 
               
               
                 213 
                 22 
                 3 
               
               
                 214 
                 23 
                 3 
               
               
                 215 
                 24 
                 3 
               
               
                 216 
                 25 
                 3 
               
               
                 217 
                 26 
                 3 
               
               
                 218 
                 27 
                 3 
               
               
                 219 
                 28 
                 3 
               
               
                 220 
                 29 
                 3 
               
               
                 221 
                 30 
                 3 
               
               
                 222 
                 31 
                 3 
               
               
                 223 
                 32 
                 3 
               
               
                 224 
                 33 
                 3 
               
               
                 225 
                 34 
                 3 
               
               
                 226 
                 35 
                 3 
               
               
                 227 
                 36 
                 3 
               
               
                 228 
                 37 
                 3 
               
               
                 229 
                 38 
                 3 
               
               
                 230 
                 39 
                 3 
               
               
                 231 
                 40 
                 3 
               
               
                 232 
                 41 
                 3 
               
               
                 233 
                 42 
                 3 
               
               
                 234 
                 43 
                 3 
               
               
                 235 
                 44 
                 3 
               
               
                 236 
                 45 
                 3 
               
               
                 237 
                 46 
                 3 
               
               
                 238 
                 47 
                 3 
               
               
                 239 
                 48 
                 3 
               
               
                 240 
                 49 
                 3 
               
               
                 241 
                 50 
                 3 
               
               
                 242 
                 51 
                 3 
               
               
                 243 
                 52 
                 3 
               
               
                 244 
                 53 
                 3 
               
               
                 245 
                 54 
                 3 
               
               
                 246 
                 55 
                 3 
               
               
                 247 
                 56 
                 3 
               
               
                 248 
                 57 
                 3 
               
               
                 249 
                 58 
                 3 
               
               
                 250 
                 59 
                 3 
               
               
                 251 
                 60 
                 3 
               
               
                 252 
                 61 
                 3 
               
               
                 253 
                 62 
                 3 
               
               
                 254 
                 63 
                 3 
               
               
                 255 
                 64 
                 3 
               
               
                 256 
                 65 
                 3 
               
               
                 257 
                 66 
                 3 
               
               
                 258 
                 67 
                 3 
               
               
                 259 
                 68 
                 3 
               
               
                 260 
                 69 
                 3 
               
               
                 261 
                 70 
                 3 
               
               
                 262 
                 71 
                 3 
               
               
                 263 
                 72 
                 3 
               
               
                 264 
                 73 
                 3 
               
               
                 265 
                 74 
                 3 
               
               
                 266 
                 75 
                 3 
               
               
                 267 
                 76 
                 3 
               
               
                 268 
                 77 
                 3 
               
               
                 269 
                 78 
                 3 
               
               
                 270 
                 79 
                 3 
               
               
                 271 
                 80 
                 3 
               
               
                 272 
                 81 
                 3 
               
               
                 273 
                 82 
                 3 
               
               
                 274 
                 83 
                 3 
               
               
                 275 
                 84 
                 3 
               
               
                 276 
                 85 
                 3 
               
               
                 277 
                 86 
                 3 
               
               
                 278 
                 87 
                 3 
               
               
                 279 
                 88 
                 3 
               
               
                 280 
                 89 
                 3 
               
               
                 281 
                 90 
                 3 
               
               
                 282 
                 91 
                 3 
               
               
                 283 
                 92 
                 3 
               
               
                 284 
                 93 
                 3 
               
               
                 285 
                 94 
                 3 
               
               
                 286 
                 1 
                 4 
               
               
                 287 
                 2 
                 4 
               
               
                 288 
                 3 
                 4 
               
               
                 289 
                 4 
                 4 
               
               
                 290 
                 5 
                 4 
               
               
                 291 
                 6 
                 4 
               
               
                 292 
                 7 
                 4 
               
               
                 293 
                 8 
                 4 
               
               
                 294 
                 9 
                 4 
               
               
                 295 
                 10 
                 4 
               
               
                 296 
                 11 
                 4 
               
               
                 297 
                 12 
                 4 
               
               
                 298 
                 13 
                 4 
               
               
                 299 
                 14 
                 4 
               
               
                 300 
                 15 
                 4 
               
               
                 301 
                 16 
                 4 
               
               
                 302 
                 17 
                 4 
               
               
                 303 
                 18 
                 4 
               
               
                 304 
                 19 
                 4 
               
               
                 305 
                 20 
                 4 
               
               
                 306 
                 21 
                 4 
               
               
                 307 
                 22 
                 4 
               
               
                 308 
                 23 
                 4 
               
               
                 309 
                 24 
                 4 
               
               
                 310 
                 25 
                 4 
               
               
                 311 
                 26 
                 4 
               
               
                 312 
                 27 
                 4 
               
               
                 313 
                 28 
                 4 
               
               
                 314 
                 29 
                 4 
               
               
                 315 
                 30 
                 4 
               
               
                 316 
                 31 
                 4 
               
               
                 317 
                 32 
                 4 
               
               
                 318 
                 33 
                 4 
               
               
                 319 
                 34 
                 4 
               
               
                 320 
                 35 
                 4 
               
               
                 321 
                 36 
                 4 
               
               
                 322 
                 37 
                 4 
               
               
                 323 
                 38 
                 4 
               
               
                 324 
                 39 
                 4 
               
               
                 325 
                 40 
                 4 
               
               
                 326 
                 41 
                 4 
               
               
                 327 
                 42 
                 4 
               
               
                 328 
                 43 
                 4 
               
               
                 329 
                 44 
                 4 
               
               
                 330 
                 45 
                 4 
               
               
                 331 
                 46 
                 4 
               
               
                 332 
                 47 
                 4 
               
               
                 333 
                 48 
                 4 
               
               
                 334 
                 49 
                 4 
               
               
                 335 
                 50 
                 4 
               
               
                 336 
                 51 
                 4 
               
               
                 337 
                 52 
                 4 
               
               
                 338 
                 53 
                 4 
               
               
                 339 
                 54 
                 4 
               
               
                 340 
                 55 
                 4 
               
               
                 341 
                 56 
                 4 
               
               
                 342 
                 57 
                 4 
               
               
                 343 
                 58 
                 4 
               
               
                 344 
                 59 
                 4 
               
               
                 345 
                 60 
                 4 
               
               
                 346 
                 61 
                 4 
               
               
                 347 
                 62 
                 4 
               
               
                 348 
                 63 
                 4 
               
               
                 349 
                 64 
                 4 
               
               
                 350 
                 65 
                 4 
               
               
                 351 
                 66 
                 4 
               
               
                 352 
                 67 
                 4 
               
               
                 353 
                 68 
                 4 
               
               
                 354 
                 69 
                 4 
               
               
                 355 
                 70 
                 4 
               
               
                 356 
                 71 
                 4 
               
               
                 357 
                 72 
                 4 
               
               
                 358 
                 73 
                 4 
               
               
                 359 
                 74 
                 4 
               
               
                 360 
                 75 
                 4 
               
               
                 361 
                 76 
                 4 
               
               
                 362 
                 77 
                 4 
               
               
                 363 
                 78 
                 4 
               
               
                 364 
                 79 
                 4 
               
               
                 365 
                 80 
                 4 
               
               
                 366 
                 81 
                 4 
               
               
                 367 
                 82 
                 4 
               
               
                 368 
                 83 
                 4 
               
               
                 369 
                 84 
                 4 
               
               
                 370 
                 85 
                 4 
               
               
                 371 
                 86 
                 4 
               
               
                 372 
                 87 
                 4 
               
               
                 373 
                 88 
                 4 
               
               
                 374 
                 89 
                 4 
               
               
                 375 
                 90 
                 4 
               
               
                 376 
                 91 
                 4 
               
               
                 377 
                 92 
                 4 
               
               
                 378 
                 93 
                 4 
               
               
                 379 
                 1 
                 5 
               
               
                 380 
                 2 
                 5 
               
               
                 381 
                 3 
                 5 
               
               
                 382 
                 4 
                 5 
               
               
                 383 
                 5 
                 5 
               
               
                 384 
                 6 
                 5 
               
               
                 385 
                 7 
                 5 
               
               
                 386 
                 8 
                 5 
               
               
                 387 
                 9 
                 5 
               
               
                 388 
                 10 
                 5 
               
               
                 389 
                 11 
                 5 
               
               
                 390 
                 12 
                 5 
               
               
                 391 
                 13 
                 5 
               
               
                 392 
                 14 
                 5 
               
               
                 393 
                 15 
                 5 
               
               
                 394 
                 16 
                 5 
               
               
                 395 
                 17 
                 5 
               
               
                 396 
                 18 
                 5 
               
               
                 397 
                 19 
                 5 
               
               
                 398 
                 20 
                 5 
               
               
                 399 
                 21 
                 5 
               
               
                 400 
                 22 
                 5 
               
               
                 401 
                 23 
                 5 
               
               
                 402 
                 24 
                 5 
               
               
                 403 
                 25 
                 5 
               
               
                 404 
                 26 
                 5 
               
               
                 405 
                 27 
                 5 
               
               
                 406 
                 28 
                 5 
               
               
                 407 
                 29 
                 5 
               
               
                 408 
                 30 
                 5 
               
               
                 409 
                 31 
                 5 
               
               
                 410 
                 32 
                 5 
               
               
                 411 
                 33 
                 5 
               
               
                 412 
                 34 
                 5 
               
               
                 413 
                 35 
                 5 
               
               
                 414 
                 36 
                 5 
               
               
                 415 
                 37 
                 5 
               
               
                 416 
                 38 
                 5 
               
               
                 417 
                 39 
                 5 
               
               
                 418 
                 40 
                 5 
               
               
                 419 
                 41 
                 5 
               
               
                 420 
                 42 
                 5 
               
               
                 421 
                 43 
                 5 
               
               
                 422 
                 44 
                 5 
               
               
                 423 
                 45 
                 5 
               
               
                 424 
                 46 
                 5 
               
               
                 425 
                 47 
                 5 
               
               
                 426 
                 48 
                 5 
               
               
                 427 
                 49 
                 5 
               
               
                 428 
                 50 
                 5 
               
               
                 429 
                 51 
                 5 
               
               
                 430 
                 52 
                 5 
               
               
                 431 
                 53 
                 5 
               
               
                 432 
                 54 
                 5 
               
               
                 433 
                 55 
                 5 
               
               
                 434 
                 56 
                 5 
               
               
                 435 
                 57 
                 5 
               
               
                 436 
                 58 
                 5 
               
               
                 437 
                 59 
                 5 
               
               
                 438 
                 60 
                 5 
               
               
                 439 
                 61 
                 5 
               
               
                 440 
                 62 
                 5 
               
               
                 441 
                 63 
                 5 
               
               
                 442 
                 64 
                 5 
               
               
                 443 
                 65 
                 5 
               
               
                 444 
                 66 
                 5 
               
               
                 445 
                 67 
                 5 
               
               
                 446 
                 68 
                 5 
               
               
                 447 
                 69 
                 5 
               
               
                 448 
                 70 
                 5 
               
               
                 449 
                 71 
                 5 
               
               
                 450 
                 72 
                 5 
               
               
                 451 
                 73 
                 5 
               
               
                 452 
                 74 
                 5 
               
               
                 453 
                 75 
                 5 
               
               
                 454 
                 76 
                 5 
               
               
                 455 
                 77 
                 5 
               
               
                 456 
                 78 
                 5 
               
               
                 457 
                 79 
                 5 
               
               
                 458 
                 80 
                 5 
               
               
                 459 
                 81 
                 5 
               
               
                 460 
                 82 
                 5 
               
               
                 461 
                 83 
                 5 
               
               
                 462 
                 84 
                 5 
               
               
                 463 
                 85 
                 5 
               
               
                 464 
                 86 
                 5 
               
               
                 465 
                 87 
                 5 
               
               
                 466 
                 88 
                 5 
               
               
                 467 
                 89 
                 5 
               
               
                 468 
                 90 
                 5 
               
               
                 469 
                 91 
                 5 
               
               
                 470 
                 92 
                 5 
               
               
                 471 
                 1 
                 6 
               
               
                 472 
                 2 
                 6 
               
               
                 473 
                 3 
                 6 
               
               
                 474 
                 4 
                 6 
               
               
                 475 
                 5 
                 6 
               
               
                 476 
                 6 
                 6 
               
               
                 477 
                 7 
                 6 
               
               
                 478 
                 8 
                 6 
               
               
                 479 
                 9 
                 6 
               
               
                 480 
                 10 
                 6 
               
               
                 481 
                 11 
                 6 
               
               
                 482 
                 12 
                 6 
               
               
                 483 
                 13 
                 6 
               
               
                 484 
                 14 
                 6 
               
               
                 485 
                 15 
                 6 
               
               
                 486 
                 16 
                 6 
               
               
                 487 
                 17 
                 6 
               
               
                 488 
                 18 
                 6 
               
               
                 489 
                 19 
                 6 
               
               
                 490 
                 20 
                 6 
               
               
                 491 
                 21 
                 6 
               
               
                 492 
                 22 
                 6 
               
               
                 493 
                 23 
                 6 
               
               
                 494 
                 24 
                 6 
               
               
                 495 
                 25 
                 6 
               
               
                 496 
                 26 
                 6 
               
               
                 497 
                 27 
                 6 
               
               
                 498 
                 28 
                 6 
               
               
                 499 
                 29 
                 6 
               
               
                 500 
                 30 
                 6 
               
               
                 501 
                 31 
                 6 
               
               
                 502 
                 32 
                 6 
               
               
                 503 
                 33 
                 6 
               
               
                 504 
                 34 
                 6 
               
               
                 505 
                 35 
                 6 
               
               
                 506 
                 36 
                 6 
               
               
                 507 
                 37 
                 6 
               
               
                 508 
                 38 
                 6 
               
               
                 509 
                 39 
                 6 
               
               
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                 916 
                 1 
                 11 
               
               
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                 2 
                 11 
               
               
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                 3 
                 11 
               
               
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                 4 
                 11 
               
               
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                 5 
                 11 
               
               
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                 6 
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                 28 
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                 29 
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                 30 
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                 31 
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                 32 
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                 11 
               
               
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                 970 
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                 11 
               
               
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                 11 
               
               
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                 11 
               
               
                 999 
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                 11 
               
               
                 1000 
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                 11 
               
               
                 1001 
                 86 
                 11 
               
               
                 1002 
                 1 
                 12 
               
               
                 1003 
                 2 
                 12 
               
               
                 1004 
                 3 
                 12 
               
               
                 1005 
                 4 
                 12 
               
               
                 1006 
                 5 
                 12 
               
               
                 1007 
                 6 
                 12 
               
               
                 1008 
                 7 
                 12 
               
               
                 1009 
                 8 
                 12 
               
               
                 1010 
                 9 
                 12 
               
               
                 1011 
                 10 
                 12 
               
               
                 1012 
                 11 
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                 18 
               
               
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                 18 
               
               
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                 18 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 20 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 21 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 22 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 23 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
                 1398 
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                 24 
               
               
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                 24 
               
               
                 1400 
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                 24 
               
               
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                 24 
               
               
                 1402 
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                 24 
               
               
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                 24 
               
               
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                 24 
               
               
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                 25 
               
               
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                 25 
               
               
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                 25 
               
               
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                 25 
               
               
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                 25 
               
               
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                 25 
               
               
                 1415 
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                 25 
               
               
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                 25 
               
               
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                 25 
               
               
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                 25 
               
               
                 1419 
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                 25 
               
               
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                 25 
               
               
                 1421 
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                 1422 
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                 25 
               
               
                 1423 
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                 1429 
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                 26 
               
               
                 1430 
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                 26 
               
               
                 1431 
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                 26 
               
               
                 1432 
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                 26 
               
               
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                 26 
               
               
                 1434 
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                 26 
               
               
                 1435 
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                 26 
               
               
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                 26 
               
               
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                 26 
               
               
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                 26 
               
               
                 1439 
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                 26 
               
               
                 1440 
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                 27 
               
               
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                 27 
               
               
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                 27 
               
               
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                 27 
               
               
                 1445 
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                 27 
               
               
                 1446 
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                 27 
               
               
                 1447 
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                 27 
               
               
                 1448 
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                 27 
               
               
                 1449 
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                 27 
               
               
                 1450 
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                 27 
               
               
                 1451 
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                 27 
               
               
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                 27 
               
               
                 1453 
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                 27 
               
               
                 1454 
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                 27 
               
               
                 1455 
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                 27 
               
               
                 1456 
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                 27 
               
               
                 1457 
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                 27 
               
               
                 1458 
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                 27 
               
               
                 1459 
                 1 
                 28 
               
               
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                 28 
               
               
                 1461 
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                 28 
               
               
                 1462 
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                 28 
               
               
                 1463 
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                 28 
               
               
                 1464 
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                 28 
               
               
                 1465 
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                 28 
               
               
                 1466 
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                 28 
               
               
                 1467 
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                 28 
               
               
                 1468 
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                 28 
               
               
                 1469 
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                 28 
               
               
                 1470 
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                 28 
               
               
                 1471 
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                 28 
               
               
                 1472 
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                 28 
               
               
                 1473 
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                 28 
               
               
                 1474 
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                 28 
               
               
                 1475 
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                 28 
               
               
                 1476 
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                 28 
               
               
                 1477 
                 1 
                 29 
               
               
                 1478 
                 5 
                 29 
               
               
                 1479 
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                 29 
               
               
                 1480 
                 13 
                 29 
               
               
                 1481 
                 17 
                 29 
               
               
                 1482 
                 21 
                 29 
               
               
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                 25 
                 29 
               
               
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                 29 
                 29 
               
               
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                 33 
                 29 
               
               
                 1486 
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                 29 
               
               
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                 45 
                 29 
               
               
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                 29 
               
               
                 1490 
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                 1491 
                 57 
                 29 
               
               
                 1492 
                 61 
                 29 
               
               
                 1493 
                 65 
                 29 
               
               
                 1494 
                 1 
                 30 
               
               
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                 5 
                 30 
               
               
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                 9 
                 30 
               
               
                 1497 
                 13 
                 30 
               
               
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                 17 
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                 1499 
                 21 
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                 25 
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                 1501 
                 29 
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                 33 
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                 30 
               
               
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                 1 
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                 5 
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                 9 
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                 1 
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                 1 
                 33 
               
               
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                 5 
                 33 
               
               
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                 9 
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                 17 
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                 1 
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                 5 
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                 9 
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                 17 
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                 21 
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                 1 
                 35 
               
               
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                 5 
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                 9 
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                 13 
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                 17 
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                 21 
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                 1 
                 36 
               
               
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                 5 
                 36 
               
               
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                 9 
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                 13 
                 36 
               
               
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                 17 
                 36 
               
               
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                 21 
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                 25 
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                 1600 
                 29 
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                 33 
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                 37 
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                 41 
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                 61 
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                 1 
                 37 
               
               
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                 5 
                 37 
               
               
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                 9 
                 37 
               
               
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                 13 
                 37 
               
               
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                 17 
                 37 
               
               
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                 21 
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                 25 
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                 29 
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                 33 
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                 37 
               
               
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                 41 
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                 49 
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                 57 
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                 1 
                 38 
               
               
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                 5 
                 38 
               
               
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                 9 
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                 13 
                 38 
               
               
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                 17 
                 38 
               
               
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                 21 
                 38 
               
               
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                 25 
                 38 
               
               
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                 29 
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                 33 
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                 37 
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                 41 
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                 1 
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                 5 
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                 9 
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                 13 
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                 17 
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                 21 
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                 25 
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                 29 
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                 33 
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                 1 
                 40 
               
               
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                 5 
                 40 
               
               
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                 9 
                 40 
               
               
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                 13 
                 40 
               
               
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                 17 
                 40 
               
               
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                 21 
                 40 
               
               
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                 25 
                 40 
               
               
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                 29 
                 40 
               
               
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                 33 
                 40 
               
               
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                 37 
                 40 
               
               
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                 41 
                 40 
               
               
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                 45 
                 40 
               
               
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                 49 
                 40 
               
               
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                 53 
                 40 
               
               
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                 40 
               
               
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                 1 
                 41 
               
               
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                 5 
                 41 
               
               
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                 9 
                 41 
               
               
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                 13 
                 41 
               
               
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                 17 
                 41 
               
               
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                 21 
                 41 
               
               
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                 25 
                 41 
               
               
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                 29 
                 41 
               
               
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                 33 
                 41 
               
               
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                 37 
                 41 
               
               
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                 41 
                 41 
               
               
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                 45 
                 41 
               
               
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                 49 
                 41 
               
               
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                 53 
                 41 
               
               
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                 1 
                 42 
               
               
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                 5 
                 42 
               
               
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                 9 
                 42 
               
               
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                 13 
                 42 
               
               
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                 17 
                 42 
               
               
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                 21 
                 42 
               
               
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                 25 
                 42 
               
               
                 1690 
                 29 
                 42 
               
               
                 1691 
                 33 
                 42 
               
               
                 1692 
                 37 
                 42 
               
               
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                 41 
                 42 
               
               
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                 45 
                 42 
               
               
                 1695 
                 49 
                 42 
               
               
                 1696 
                 53 
                 42 
               
               
                 1697 
                 1 
                 43 
               
               
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                 5 
                 43 
               
               
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                 9 
                 43 
               
               
                 1700 
                 13 
                 43 
               
               
                 1701 
                 17 
                 43 
               
               
                 1702 
                 21 
                 43 
               
               
                 1703 
                 25 
                 43 
               
               
                 1704 
                 29 
                 43 
               
               
                 1705 
                 33 
                 43 
               
               
                 1706 
                 37 
                 43 
               
               
                 1707 
                 41 
                 43 
               
               
                 1708 
                 45 
                 43 
               
               
                 1709 
                 49 
                 43 
               
               
                 1710 
                 53 
                 43 
               
               
                 1711 
                 1 
                 44 
               
               
                 1712 
                 5 
                 44 
               
               
                 1713 
                 9 
                 44 
               
               
                 1714 
                 13 
                 44 
               
               
                 1715 
                 17 
                 44 
               
               
                 1716 
                 21 
                 44 
               
               
                 1717 
                 25 
                 44 
               
               
                 1718 
                 29 
                 44 
               
               
                 1719 
                 33 
                 44 
               
               
                 1720 
                 37 
                 44 
               
               
                 1721 
                 41 
                 44 
               
               
                 1722 
                 45 
                 44 
               
               
                 1723 
                 49 
                 44 
               
               
                 1724 
                 53 
                 44 
               
               
                 1725 
                 1 
                 45 
               
               
                 1726 
                 5 
                 45 
               
               
                 1727 
                 9 
                 45 
               
               
                 1728 
                 13 
                 45 
               
               
                 1729 
                 17 
                 45 
               
               
                 1730 
                 21 
                 45 
               
               
                 1731 
                 25 
                 45 
               
               
                 1732 
                 29 
                 45 
               
               
                 1733 
                 33 
                 45 
               
               
                 1734 
                 37 
                 45 
               
               
                 1735 
                 41 
                 45 
               
               
                 1736 
                 45 
                 45 
               
               
                 1737 
                 49 
                 45 
               
               
                 1738 
                 1 
                 46 
               
               
                 1739 
                 5 
                 46 
               
               
                 1740 
                 9 
                 46 
               
               
                 1741 
                 13 
                 46 
               
               
                 1742 
                 17 
                 46 
               
               
                 1743 
                 21 
                 46 
               
               
                 1744 
                 25 
                 46 
               
               
                 1745 
                 29 
                 46 
               
               
                 1746 
                 33 
                 46 
               
               
                 1747 
                 37 
                 46 
               
               
                 1748 
                 41 
                 46 
               
               
                 1749 
                 45 
                 46 
               
               
                 1750 
                 49 
                 46 
               
               
                 1751 
                 1 
                 47 
               
               
                 1752 
                 5 
                 47 
               
               
                 1753 
                 9 
                 47 
               
               
                 1754 
                 13 
                 47 
               
               
                 1755 
                 17 
                 47 
               
               
                 1756 
                 21 
                 47 
               
               
                 1757 
                 25 
                 47 
               
               
                 1758 
                 29 
                 47 
               
               
                 1759 
                 33 
                 47 
               
               
                 1760 
                 37 
                 47 
               
               
                 1761 
                 41 
                 47 
               
               
                 1762 
                 45 
                 47 
               
               
                 1763 
                 49 
                 47 
               
               
                 1764 
                 1 
                 48 
               
               
                 1765 
                 5 
                 48 
               
               
                 1766 
                 9 
                 48 
               
               
                 1767 
                 13 
                 48 
               
               
                 1768 
                 17 
                 48 
               
               
                 1769 
                 21 
                 48 
               
               
                 1770 
                 25 
                 48 
               
               
                 1771 
                 29 
                 48 
               
               
                 1772 
                 33 
                 48 
               
               
                 1773 
                 37 
                 48 
               
               
                 1774 
                 41 
                 48 
               
               
                 1775 
                 45 
                 48 
               
               
                 1776 
                 49 
                 48 
               
               
                 1777 
                 1 
                 49 
               
               
                 1778 
                 5 
                 49 
               
               
                 1779 
                 9 
                 49 
               
               
                 1780 
                 13 
                 49 
               
               
                 1781 
                 17 
                 49 
               
               
                 1782 
                 21 
                 49 
               
               
                 1783 
                 25 
                 49 
               
               
                 1784 
                 29 
                 49 
               
               
                 1785 
                 33 
                 49 
               
               
                 1786 
                 37 
                 49 
               
               
                 1787 
                 41 
                 49 
               
               
                 1788 
                 45 
                 49 
               
               
                 1789 
                 1 
                 50 
               
               
                 1790 
                 5 
                 50 
               
               
                 1791 
                 9 
                 50 
               
               
                 1792 
                 13 
                 50 
               
               
                 1793 
                 17 
                 50 
               
               
                 1794 
                 21 
                 50 
               
               
                 1795 
                 25 
                 50 
               
               
                 1796 
                 29 
                 50 
               
               
                 1797 
                 33 
                 50 
               
               
                 1798 
                 37 
                 50 
               
               
                 1799 
                 41 
                 50 
               
               
                 1800 
                 45 
                 50 
               
               
                 1801 
                 1 
                 51 
               
               
                 1802 
                 5 
                 51 
               
               
                 1803 
                 9 
                 51 
               
               
                 1804 
                 13 
                 51 
               
               
                 1805 
                 17 
                 51 
               
               
                 1806 
                 21 
                 51 
               
               
                 1807 
                 25 
                 51 
               
               
                 1808 
                 29 
                 51 
               
               
                 1809 
                 33 
                 51 
               
               
                 1810 
                 37 
                 51 
               
               
                 1811 
                 41 
                 51 
               
               
                 1812 
                 45 
                 51 
               
               
                 1813 
                 1 
                 52 
               
               
                 1814 
                 5 
                 52 
               
               
                 1815 
                 9 
                 52 
               
               
                 1816 
                 13 
                 52 
               
               
                 1817 
                 17 
                 52 
               
               
                 1818 
                 21 
                 52 
               
               
                 1819 
                 25 
                 52 
               
               
                 1820 
                 29 
                 52 
               
               
                 1821 
                 33 
                 52 
               
               
                 1822 
                 37 
                 52 
               
               
                 1823 
                 41 
                 52 
               
               
                 1824 
                 45 
                 52 
               
               
                 1825 
                 1 
                 53 
               
               
                 1826 
                 5 
                 53 
               
               
                 1827 
                 9 
                 53 
               
               
                 1828 
                 13 
                 53 
               
               
                 1829 
                 17 
                 53 
               
               
                 1830 
                 21 
                 53 
               
               
                 1831 
                 25 
                 53 
               
               
                 1832 
                 29 
                 53 
               
               
                 1833 
                 33 
                 53 
               
               
                 1834 
                 37 
                 53 
               
               
                 1835 
                 41 
                 53 
               
               
                 1836 
                 1 
                 54 
               
               
                 1837 
                 5 
                 54 
               
               
                 1838 
                 9 
                 54 
               
               
                 1839 
                 13 
                 54 
               
               
                 1840 
                 17 
                 54 
               
               
                 1841 
                 21 
                 54 
               
               
                 1842 
                 25 
                 54 
               
               
                 1843 
                 29 
                 54 
               
               
                 1844 
                 33 
                 54 
               
               
                 1845 
                 37 
                 54 
               
               
                 1846 
                 41 
                 54 
               
               
                 1847 
                 1 
                 55 
               
               
                 1848 
                 5 
                 55 
               
               
                 1849 
                 9 
                 55 
               
               
                 1850 
                 13 
                 55 
               
               
                 1851 
                 17 
                 55 
               
               
                 1852 
                 21 
                 55 
               
               
                 1853 
                 25 
                 55 
               
               
                 1854 
                 29 
                 55 
               
               
                 1855 
                 33 
                 55 
               
               
                 1856 
                 37 
                 55 
               
               
                 1857 
                 41 
                 55 
               
               
                 1858 
                 1 
                 56 
               
               
                 1859 
                 5 
                 56 
               
               
                 1860 
                 9 
                 56 
               
               
                 1861 
                 13 
                 56 
               
               
                 1862 
                 17 
                 56 
               
               
                 1863 
                 21 
                 56 
               
               
                 1864 
                 25 
                 56 
               
               
                 1865 
                 29 
                 56 
               
               
                 1866 
                 33 
                 56 
               
               
                 1867 
                 37 
                 56 
               
               
                 1868 
                 41 
                 56 
               
               
                 1869 
                 1 
                 57 
               
               
                 1870 
                 5 
                 57 
               
               
                 1871 
                 9 
                 57 
               
               
                 1872 
                 13 
                 57 
               
               
                 1873 
                 17 
                 57 
               
               
                 1874 
                 21 
                 57 
               
               
                 1875 
                 25 
                 57 
               
               
                 1876 
                 29 
                 57 
               
               
                 1877 
                 33 
                 57 
               
               
                 1878 
                 37 
                 57 
               
               
                 1879 
                 1 
                 58 
               
               
                 1880 
                 5 
                 58 
               
               
                 1881 
                 9 
                 58 
               
               
                 1882 
                 13 
                 58 
               
               
                 1883 
                 17 
                 58 
               
               
                 1884 
                 21 
                 58 
               
               
                 1885 
                 25 
                 58 
               
               
                 1886 
                 29 
                 58 
               
               
                 1887 
                 33 
                 58 
               
               
                 1888 
                 37 
                 58 
               
               
                 1889 
                 1 
                 59 
               
               
                 1890 
                 5 
                 59 
               
               
                 1891 
                 9 
                 59 
               
               
                 1892 
                 13 
                 59 
               
               
                 1893 
                 17 
                 59 
               
               
                 1894 
                 21 
                 59 
               
               
                 1895 
                 25 
                 59 
               
               
                 1896 
                 29 
                 59 
               
               
                 1897 
                 33 
                 59 
               
               
                 1898 
                 37 
                 59 
               
               
                 1899 
                 1 
                 60 
               
               
                 1900 
                 5 
                 60 
               
               
                 1901 
                 9 
                 60 
               
               
                 1902 
                 13 
                 60 
               
               
                 1903 
                 17 
                 60 
               
               
                 1904 
                 21 
                 60 
               
               
                 1905 
                 25 
                 60 
               
               
                 1906 
                 29 
                 60 
               
               
                 1907 
                 33 
                 60 
               
               
                 1908 
                 37 
                 60 
               
               
                 1909 
                 1 
                 61 
               
               
                 1910 
                 5 
                 61 
               
               
                 1911 
                 9 
                 61 
               
               
                 1912 
                 13 
                 61 
               
               
                 1913 
                 17 
                 61 
               
               
                 1914 
                 21 
                 61 
               
               
                 1915 
                 25 
                 61 
               
               
                 1916 
                 29 
                 61 
               
               
                 1917 
                 33 
                 61 
               
               
                 1918 
                 1 
                 62 
               
               
                 1919 
                 5 
                 62 
               
               
                 1920 
                 9 
                 62 
               
               
                 1921 
                 13 
                 62 
               
               
                 1922 
                 17 
                 62 
               
               
                 1923 
                 21 
                 62 
               
               
                 1924 
                 25 
                 62 
               
               
                 1925 
                 29 
                 62 
               
               
                 1926 
                 33 
                 62 
               
               
                 1927 
                 1 
                 63 
               
               
                 1928 
                 5 
                 63 
               
               
                 1929 
                 9 
                 63 
               
               
                 1930 
                 13 
                 63 
               
               
                 1931 
                 17 
                 63 
               
               
                 1932 
                 21 
                 63 
               
               
                 1933 
                 25 
                 63 
               
               
                 1934 
                 29 
                 63 
               
               
                 1935 
                 33 
                 63 
               
               
                 1936 
                 1 
                 64 
               
               
                 1937 
                 5 
                 64 
               
               
                 1938 
                 9 
                 64 
               
               
                 1939 
                 13 
                 64 
               
               
                 1940 
                 17 
                 64 
               
               
                 1941 
                 21 
                 64 
               
               
                 1942 
                 25 
                 64 
               
               
                 1943 
                 29 
                 64 
               
               
                 1944 
                 33 
                 64 
               
               
                 1945 
                 1 
                 65 
               
               
                 1946 
                 5 
                 65 
               
               
                 1947 
                 9 
                 65 
               
               
                 1948 
                 13 
                 65 
               
               
                 1949 
                 17 
                 65 
               
               
                 1950 
                 21 
                 65 
               
               
                 1951 
                 25 
                 65 
               
               
                 1952 
                 29 
                 65 
               
               
                 1953 
                 1 
                 66 
               
               
                 1954 
                 5 
                 66 
               
               
                 1955 
                 9 
                 66 
               
               
                 1956 
                 13 
                 66 
               
               
                 1957 
                 17 
                 66 
               
               
                 1958 
                 21 
                 66 
               
               
                 1959 
                 25 
                 66 
               
               
                 1960 
                 29 
                 66 
               
               
                 1961 
                 1 
                 67 
               
               
                 1962 
                 5 
                 67 
               
               
                 1963 
                 9 
                 67 
               
               
                 1964 
                 13 
                 67 
               
               
                 1965 
                 17 
                 67 
               
               
                 1966 
                 21 
                 67 
               
               
                 1967 
                 25 
                 67 
               
               
                 1968 
                 29 
                 67 
               
               
                 1969 
                 1 
                 68 
               
               
                 1970 
                 5 
                 68 
               
               
                 1971 
                 9 
                 68 
               
               
                 1972 
                 13 
                 68 
               
               
                 1973 
                 17 
                 68 
               
               
                 1974 
                 21 
                 68 
               
               
                 1975 
                 25 
                 68 
               
               
                 1976 
                 29 
                 68 
               
               
                 1977 
                 1 
                 69 
               
               
                 1978 
                 5 
                 69 
               
               
                 1979 
                 9 
                 69 
               
               
                 1980 
                 13 
                 69 
               
               
                 1981 
                 17 
                 69 
               
               
                 1982 
                 21 
                 69 
               
               
                 1983 
                 25 
                 69 
               
               
                 1984 
                 1 
                 70 
               
               
                 1985 
                 5 
                 70 
               
               
                 1986 
                 9 
                 70 
               
               
                 1987 
                 13 
                 70 
               
               
                 1988 
                 17 
                 70 
               
               
                 1989 
                 21 
                 70 
               
               
                 1990 
                 25 
                 70 
               
               
                 1991 
                 1 
                 71 
               
               
                 1992 
                 5 
                 71 
               
               
                 1993 
                 9 
                 71 
               
               
                 1994 
                 13 
                 71 
               
               
                 1995 
                 17 
                 71 
               
               
                 1996 
                 21 
                 71 
               
               
                 1997 
                 25 
                 71 
               
               
                 1998 
                 1 
                 72 
               
               
                 1999 
                 5 
                 72 
               
               
                 2000 
                 9 
                 72 
               
               
                 2001 
                 13 
                 72 
               
               
                 2002 
                 17 
                 72 
               
               
                 2003 
                 21 
                 72 
               
               
                 2004 
                 25 
                 72 
               
               
                 2005 
                 1 
                 73 
               
               
                 2006 
                 5 
                 73 
               
               
                 2007 
                 9 
                 73 
               
               
                 2008 
                 13 
                 73 
               
               
                 2009 
                 17 
                 73 
               
               
                 2010 
                 21 
                 73 
               
               
                 2011 
                 1 
                 74 
               
               
                 2012 
                 5 
                 74 
               
               
                 2013 
                 9 
                 74 
               
               
                 2014 
                 13 
                 74 
               
               
                 2015 
                 17 
                 74 
               
               
                 2016 
                 21 
                 74 
               
               
                 2017 
                 1 
                 75 
               
               
                 2018 
                 5 
                 75 
               
               
                 2019 
                 9 
                 75 
               
               
                 2020 
                 13 
                 75 
               
               
                 2021 
                 17 
                 75 
               
               
                 2022 
                 21 
                 75 
               
               
                 2023 
                 1 
                 76 
               
               
                 2024 
                 5 
                 76 
               
               
                 2025 
                 9 
                 76 
               
               
                 2026 
                 13 
                 76 
               
               
                 2027 
                 17 
                 76 
               
               
                 2028 
                 21 
                 76 
               
               
                 2029 
                 20 
                 77 
               
               
                 2030 
                 19 
                 78 
               
               
                 2031 
                 18 
                 79 
               
               
                 2032 
                 17 
                 80 
               
               
                 2033 
                 16 
                 81 
               
               
                 2034 
                 15 
                 82 
               
               
                 2035 
                 14 
                 83 
               
               
                 2036 
                 13 
                 84 
               
               
                 2037 
                 12 
                 85 
               
               
                 2038 
                 11 
                 86 
               
               
                 2039 
                 10 
                 87 
               
               
                 2040 
                 9 
                 88 
               
               
                 2041 
                 8 
                 89 
               
               
                 2042 
                 7 
                 90 
               
               
                 2043 
                 6 
                 91 
               
               
                 2044 
                 5 
                 92 
               
               
                 2045 
                 4 
                 93 
               
               
                 2046 
                 3 
                 94 
               
               
                 2047 
                 2 
                 95 
               
               
                 2048 
                 1 
                 96 
               
               
                   
               
            
           
         
       
     
     Other variations of limiting the starting position or combinations of limiting the starting position and the size may be used to reduce the number of required signaling bits to indicate an index value, such as shown in Table 3. 
     An alternative method for resource allocation using A-MAP IEs relates to maximum allocation size (AS). The AS may be defined as follows: 
       AS=S*STC_rate*TTI_length  (Equation 1)
 
     where S is the number of LRUs derived from the RI field in the A-MAP IEs, STC_rate represents the space time coding (STC) rate allocated to the burst, and TTI_Length represents a length in subframes for the burst. The maximum AS value may be determined by multiple constraints. For example, a maximum value of AS may be defined as 192, and for a specific WTRU  102 , a maximum allowable STC_rate is negotiated as a basic capability parameter during network entry. The maximum value of AS may not be larger than the multiple of the max allowable STC_rate for the MS and the number of LRUs in a subframe. Thus, the maximum value of AS and a given STC_rate and TTI_length may be used to derive the value range of S, in order to narrow down the valid combinations of size S and location L for the RI to be signaled in the A-MAP IEs. 
     An alternative method for allocation resources using A-MAP IE includes defining the size of the RI field in the assignment A-MAP IEs so that additional allocations may be specified. For example, a 12-bit RI field may be defined by using the 1-bit reserved field in the current downlink/uplink Basic Assignment A-MAP IEs. Alternatively, a 13-bit RI field may be defined by using the 1-bit reserved field and a 1-bit that is released from redefined other fields in the current Basic Assignment IEs (e.g., change the size of parameter fields of MIMO encodings from 5 bits to 4 bits). 
     With the 12-bit RI re-design, there is no impact on other information fields in the current downlink/uplink Basic assignment A-MAP IEs, as it uses the currently reserved 1-bit. A 12-bit RI field gives 4096 indexes to identify different combinations of allocation locations and sizes. The total number of all combinations of allocation locations and sizes in a 20 MHz system is 4656 (i.e., still  560  more than what a 12-bit RI field can specify). Any of the above methods, either alone or in combination, may be used to resolve this RI index shortage (e.g., eliminating those invalid location/size combinations by taking advantage of the frequency partitions and/or LRU types; and/or eliminating those invalid location/size combinations by considering the LRUs occupied by control channels; and/or reducing the number of assignable locations and/or assignable sizes). 
     For example, the RI field can be extended from 11 bits to 12 bits by using the currently reserved bit in the basic assignment A-MAP IEs, and the remaining reduction of RI field indexes can be achieved by disregarding the information of control channel resource occupancy to reduce the number of allocations that may be signaled in the assignment IEs. The control channel allocation reduction may be selectively used only when needed or may be applied to all cases. The 12-bit RI field from the current 11-bit RI plus 1 reserved bit may have no impact on any other info fields in the current assignment IEs. As previously described, the consideration of control channel resource occupancy reduces the number of allocations that may be signaled in the assignment A-MAP IEs. For example, in a 20 MHz channel bandwidth, if 6 LRUs are used for control channels in a subframe, then 4095 allocations may be needed to be signaled, which may be accommodated by the 12-bit RI field. 
     With the 13-bit RI re-design scheme, all the 4656 possible combinations of allocation locations and sizes may be identified. However, impact on other information fields in the current downlink/uplink Basic Assignment A-MAP IEs cannot be avoided, as one more bit may be released from another information field, in addition to using the currently reserved one bit. In order to minimize the impact on design of other information fields, one information field may be designed to release one bit. For example, the MIMO related information fields in the downlink/uplink Basic Assignment IEs may be candidates to be re-designed so that one bit may be released. 
     An alternative method for resource allocation using the A-MAP IEs, is to define the mapping according to discrete (i.e., non-contiguous) LRUs. Currently, the downlink/uplink basic assignment resource allocation consists of a set of contiguous LRUs in a subframe. However, allowing allocations with discrete LRUs may be desirable in some cases (e.g., diversity gain, and/or filling holes). Additionally, by allowing allocations with discrete LRUs, more valid allocations may become available to be signaled in the A-MAP IEs, thus making it even more challenging to design the A-MAP IEs with a very strict limitation on its size (e.g., 40 bits as in current specifications). 
     Several mechanisms may be used to support the allocations with discrete LRUs including: a) selectively choosing the allocations with discrete LRUs (i.e., not allowing all possible discrete ones); b) grouping LRUs (e.g., for subband LRUs), using the subband grouping mechanism (i.e., 4 LRUs per subband); c) using bitmaps to signal the inclusion of LRUs or groups of LRU in an allocation; or d) using the RI tables to define the allowed allocations, including allocations with contiguous LRUs and allocations with discrete LRUs. For example, when applying the constraint of the same LRU type and same frequency partition for allocations, the number of valid allocations may be significantly reduced, which may leave many of RI code points unused. In this case, the unused RI code points may be used to signal allocations with discrete LRUs. 
     Although features and elements are described above in particular combinations, one of ordinary skill in the art will appreciate that each feature or element can be used alone or in any combination with the other features and elements. In addition, the methods described herein may be implemented in a computer program, software, or firmware incorporated in a computer-readable medium for execution by a computer or processor. Examples of computer-readable media include electronic signals (transmitted over wired or wireless connections) and computer-readable storage media. Examples of computer-readable storage media include, but are not limited to, a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs). A processor in association with software may be used to implement a radio frequency transceiver for use in a WTRU, UE, terminal, base station, RNC, or any host computer.