Spanning Tree Protocol

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for Topology Change 2 : 0 (unused) or 1 for Proposal in RST/MST/SPT BPDU 3–4 : 00 (unused) or 01 for Port Role Alternate/Backup in RST/MST/SPT BPDU 10 for Port Role Root in RST/MST/SPT BPDU 11 for Port Role Designated in RST/MST/SPT BPDU 5 : 0 (unused) or 1 for Learning in RST/MST/SPT BPDU 6 : 0 (unused) or 1 for Forwarding in RST/MST/SPT BPDU 7 : 0 (unused) or 1 for Agreement in RST/MST/SPT BPDU 8 : 0 or 1 for Topology Change Acknowledgement 5. Root ID: 8 bytes (CIST Root ID in MST/SPT BPDU) bits : usage 1–4 : Root Bridge Priority 5–16 : Root Bridge System ID Extension 17–64 : Root Bridge MAC Address 6. Root Path Cost: 4 bytes (CIST External Path Cost in MST/SPT BPDU) 7. Bridge ID: 8 bytes (CIST Regional Root ID in MST/SPT BPDU) bits : usage 1–4 : Bridge Priority 5–16 : Bridge System ID Extension 17–64 : Bridge MAC Address 8. Port ID: 2 bytes 9. Message Age: 2 bytes in 1/256 secs 10. Max Age: 2 bytes in 1/256 secs 11. Hello Time: 2 bytes in 1/256 secs 12. Forward Delay: 2 bytes in 1/256 secs 13. Version 1 Length: 1 byte (0x00 no ver 1 protocol info present. RST, MST, SPT BPDU only) 14. Version 3 Length: 2 bytes (MST, SPT BPDU only)

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appropriately. If the root bridge goes down, the protocol will automatically assign a new root bridge based on bridge ID. If all switches have the same bridge ID, such as the default ID, and the root bridge goes down, a tie situation arises and the protocol will assign one switch as root bridge based on the switch MAC addresses. Once the switches have been assigned a bridge ID and the protocol has chosen the root bridge switch, the best path to the root bridge is calculated based on port cost, path cost and port priority. Ultimately STP calculates the path cost on the basis of the bandwidth of a link, however links between switches may have the same bandwidth. Administrators can influence the protocol's choice of the preferred path by configuring the port cost, the lower the port cost the more likely it is that the protocol will choose the connected link as root port for the preferred path. The selection of how other switches in the topology choose their root port, or the least cost path to the root bridge, can be influenced by the port priority. The highest priority will mean the path will ultimately be less preferred. If all ports of a switch have the same priority, the port with the lowest number is chosen to forward frames.

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RSTP and, in effect, classic STP too. MSTP does this by encoding an additional region of information after the standard RSTP BPDU as well as a number of MSTI messages (from 0 to 64 instances, although in practice many bridges support fewer). Each of these MSTI configuration messages conveys the spanning tree information for each instance. Each instance can be assigned a number of configured VLANs and frames assigned to these VLANs operate in this spanning tree instance whenever they are inside the MST region. In order to avoid conveying their entire VLAN to spanning tree mapping in each BPDU, bridges encode an MD5 digest of their VLAN to instance table in the MSTP BPDU. This digest is then used by other MSTP bridges, along with other administratively configured values, to determine if the neighboring bridge is in the same MST region as itself.

530: 502: 941: 835: 1085:. In 1990, the IEEE published the first standard for the protocol as 802.1D, based on the algorithm designed by Perlman. Subsequent versions were published in 1998 and 2004, incorporating various extensions. The original Perlman-inspired Spanning Tree Protocol, called DEC STP, is not a standard and differs from the IEEE version in message format as well as timer settings. Some bridges implement both the IEEE and the DEC versions of the Spanning Tree Protocol, but their interworking can create issues for the network administrator. 591:

not all switches are directly connected to the root bridge they communicate amongst each other using STP BPDUs. Each switch adds the cost of its own path to the cost received from the neighboring switches to determine the total cost of a given path to the root bridge. Once the cost of all possible paths to the root bridge have been added up, each switch assigns a port as root port which connects to the path with the lowest cost, or highest bandwidth, that will eventually lead to the root bridge.

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regardless of the number of MSTP bridges inside the region itself. In order to further facilitate this view of an MSTP region as a single RSTP bridge, the MSTP protocol uses a variable known as remaining hops as a time to live counter instead of the message age timer used by RSTP. The message age time is only incremented once when spanning-tree information enters an MST region, and therefore RSTP bridges will see a region as only one

870:. The bridge priority default is 32,768 and can be configured only in multiples of 4096. When comparing two bridge IDs, the priority portions are compared first and the MAC addresses are compared only if the priorities are equal. The switch with the lowest priority of all the switches will be the root; if there is a tie, then the switch with the lowest priority and lowest MAC address will be the root. For example, if switches 1593:, and in that case, the port with the lowest port ID would become the designated port for that network segment, and put into forwarding mode, while its other ports on that same network segment became non-designated ports put into blocking mode. Not all bridge manufacturers follow that rule, some making all ports designated ports and putting them all into forwarding mode. 990:

may have multiple candidates for its root port. In these cases, candidates for the root port have already received BPDUs offering equally-low (i.e. the "best") root path costs and equally-low (i.e. the "best") bridge IDs, and the final tiebreaker goes to the port that received the lowest (i.e. the "best") port priority ID, or port ID.

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explicit configuration. RSTP improves convergence on point-to-point links by reducing the Max-Age time to 3 times Hello interval, removing the STP listening state, and exchanging a handshake between two switches to quickly transition the port to forwarding state. RSTP does not do anything differently from STP on shared links.

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802.1d-1998 section 8.3.2 b) A Bridge that receives a Configuration BPDU on what it decides is its Root Port conveying better information (i.e. highest priority Root Identifier, lowest Root Path Cost, highest priority transmitting Bridge and Port), passes that information on to all the LANs for which

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MSTP is fully compatible with RSTP bridges in that an MSTP BPDU can be interpreted by an RSTP bridge as an RSTP BPDU. This not only allows compatibility with RSTP bridges without configuration changes but also causes any RSTP bridges outside of an MSTP region to see the region as a single RSTP bridge

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1. Protocol ID: 2 bytes (0x0000 IEEE 802.1D) 2. Version ID: 1 byte (0x00 Config & TCN / 0x02 RST / 0x03 MST / 0x04 SPT BPDU) 3. BPDU Type: 1 byte (0x00 STP Config BPDU, 0x80 TCN BPDU, 0x02 RST/MST Config BPDU) 4. Flags: 1 byte bits : usage 1 : 0 or 1

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After STP enabled switches in a LAN have elected the root bridge, all non-root bridges assign one of their ports as root port. This is either the port that connects the switch to the root bridge, or if there are several paths, the port with the preferred path as calculated by the root bridge. Because

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Spanning tree is an older protocol with a longer convergence time. Improper use or implementation can contribute to network disruptions. Blocking links is a crude approach to high availability and preventing loops. Modern networks can make use of all connected links by use of protocols that inhibit,

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supplied by the bridge. Prior to IEEE 802.1D-2004, the first two bytes gave a 16-bit bridge priority. Since IEEE 802.1D-2004, the first four bits are a configurable priority, and the last twelve bits carry the bridge system ID extension. In the case of MST, the bridge system ID extension carries the

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in turn developed and implemented its VLAN Spanning Tree Protocol (VSTP) to provide compatibility with Cisco's PVST, so that the switches from both vendors can be included in one LAN. The VSTP protocol is only supported by the EX and MX Series from Juniper Networks. There are two restrictions to the

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VLAN encapsulation. Both standards implement a separate spanning tree for every VLAN. Cisco switches now commonly implement PVST+ and can only implement Spanning Trees for VLANs if the other switches in the LAN implement the same VLAN STP protocol. HP provides PVST and PVST+ compatibility in some of

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always goes into the forwarding state, albeit after a delay of about 30 seconds while it goes through the listening and learning states. The time spent in the listening and learning states is determined by a value known as the forward delay (default 15 seconds and set by the root bridge). If another

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Provided there is more than one link between two switches, the STP root bridge calculates the cost of each path based on bandwidth. STP will select the path with the lowest cost, that is the highest bandwidth, as the preferred link. STP will enable this preferred link as the only path to be used for

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To avoid the problems associated with redundant links in a switched LAN, STP is implemented on switches to monitor the network topology. Every link between switches, and in particular redundant links, are catalogued. The spanning-tree algorithm then blocks forwarding on redundant links by setting up

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to the first bridge confirming its superior spanning tree information. The first bridge, upon receiving this agreement, knows it can rapidly transition that port to the forwarding state bypassing the listening/learning state transition. This essentially creates a cascading effect away from the root

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RSTP calls the connection between two or more switches as a "link-type" connection. A port that operates in full-duplex mode is assumed to be point-to-point link, whereas a half-duplex port (through a hub) is considered a shared port by default. This automatic link type setting can be overridden by

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In some cases, there may still be a tie, as when the root bridge has multiple active ports on the same network segment (see above) with equally low root path costs and bridge IDs, or, in other cases, multiple bridges are connected by multiple cables and multiple ports. In each case, a single bridge

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for the segment. In the figures, there are two least-cost paths from network segment d to the root, one going through bridge 24 and the other through bridge 92. The lower bridge ID is 24, so the tiebreaker dictates that the designated port is the port through which network segment d is connected to

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Unlike some proprietary per-VLAN spanning tree implementations, MSTP includes all of its spanning tree information in a single BPDU format. Not only does this reduce the number of BPDUs required to communicate spanning tree information for each VLAN, but it also ensures backward compatibility with

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When the root bridge has more than one port on a single network segment, the bridge ID is effectively tied, as are all root path costs (all equal zero). The port on that network segment with the lowest port ID becomes the designated port. It is put into forwarding mode while all other ports on the

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IEEE 802.1aq, also known as Shortest Path Bridging (SPB), allows redundant links between switches to be active through multiple equal cost paths, and provides much larger layer-2 topologies, faster convergence, and improves the use of the mesh topologies through increased bandwidth between all

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is connected, the port may remain in blocking mode if it is determined that it would cause a loop in the network. Topology change notification (TCN) BPDUs are used to inform other switches of port changes. TCNs are injected into the network by a non-root switch and propagated to the root. Upon

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A port that would cause a switching loop if it were active. To prevent the use of looped paths, no user data is sent or received over a blocking port. BPDU data is still received in blocking state. A blocked port may go into forwarding mode if the other links in use fail and the spanning tree

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802.1d-1998 section 8.3.1: The designated port for each LAN is the bridge port for which the value of the root path cost is the lowest: if two or more ports have the same value of root path cost, then first the bridge identifier of their bridges, and their port identifiers are used as tie

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Before configuring STP, the network topology should be carefully planned. Basic configuration requires that STP be enabled on all switches in the LAN and the same version of STP chosen on each. The administrator may determine which switch will be the root bridge and configure the switches

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RSTP provides significantly faster spanning tree convergence after a topology change, introducing new convergence behaviors and bridge port roles to accomplish this. While STP can take 30 to 50 seconds to respond to a topology change, RSTP is typically able to respond to changes within

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in the spanning tree. Ports at the edge of an MSTP region connected to either an RSTP or STP bridge or an endpoint are known as boundary ports. As in RSTP, these ports can be configured as edge ports to facilitate rapid changes to the forwarding state when connected to endpoints.

1389:(MST). Under MSTP, a spanning tree can be defined for individual VLANs or for groups of VLANs. Furthermore, the administrator can define alternate paths within a spanning tree. Switches are first assigned to an MST region, then VLANs are mapped against or assigned to this MST. A 1602:

Alternatively the network administrator can configure the switch as a spanning tree root primary or secondary. When configuring the root primary and root secondary the switch will automatically change the priority accordingly, 24,576 and 28,672 respectively with the default

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When a device is first attached to a switch port, it will not immediately start to forward data. It will instead go through a number of states while it processes BPDUs and determines the topology of the network. The port attached to a host such as a computer, printer or

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Since the original Spanning Tree Protocol (STP) has been removed from the 2004 revision of IEEE Std 802.1D, an implementation of RSTP is required for any claim of conformance for an implementation of IEEE Std 802.1Q-2003 that refers to the current revision of IEEE Std

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devices by allowing traffic to load share across all paths on a mesh network. SPB consolidates multiple existing functionalities, including Spanning Tree Protocol (STP), Multiple Spanning Tree Protocol (MSTP), Rapid Spanning Tree Protocol (RSTP), Link aggregation, and

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When multiple paths from a bridge are least-cost paths, the chosen path uses the neighbor bridge with the lower bridge ID. The root port is thus the one connecting to the bridge with the lowest bridge ID. For example, in the figures, if switch 4 were connected to

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d instead of segment f, there would be two paths of length 2 to the root, one path going through bridge 24 and the other through bridge 92. Because there are two least-cost paths, the lower bridge ID (24) would be used as the tiebreaker in choosing which path to

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By default, VSTP uses the RSTP protocol as its core spanning-tree protocol, but usage of STP can be forced if the network includes old bridges. More information about configuring VSTP on Juniper Networks switches was published in the official documentation.

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BPDUs are exchanged regularly (every 2 seconds by default) and enable switches to keep track of network changes and to start and stop forwarding at ports as required. To prevent the delay when connecting hosts to a switch and during some topology changes,

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root bridge on that same network segment become non-designated ports and are put into blocking mode. Not all bridge manufacturers follow this rule, instead making all root bridge ports designated ports, and putting them all in forwarding mode.

1217:. RSTP still continues to monitor the port for BPDUs in case a bridge is connected. RSTP can also be configured to automatically detect edge ports. As soon as the bridge detects a BPDU coming to an edge port, the port becomes a non-edge port. 571:

one preferred link between switches in the LAN. This preferred link is used for all Ethernet frames unless it fails, in which case a non-preferred redundant link is enabled. When implemented in a network, STP designates one layer-2 switch as

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As discussed in the port role details above, RSTP maintains backup details regarding the discarding status of ports. This avoids timeouts if the current forwarding ports were to fail or BPDUs were not received on the root port in a certain

462:) as 802.1w. RSTP provides significantly faster recovery in response to network changes or failures, introducing new convergence behaviors and bridge port roles to do this. RSTP was designed to be backwards-compatible with standard STP. 1228:

its spanning tree information to its designated ports. If another RSTP bridge receives this information and determines this is the superior root information, it sets all its other ports to discarding. The bridge may send an

740:. When faster speeds became available, the default values were adjusted as otherwise speeds above 1 Gbit/s would have been indistinguishable by STP. Its successor RSTP uses a similar formula with a larger numerator: 966:

When more than one bridge on a segment leads to a least-cost path to the root, the bridge with the lower bridge ID is used to forward messages to the root. The port attaching that bridge to the network segment is the

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have to determine the root bridge and compute the port roles (root, designated, or blocked) with only the information that they have. To ensure that each bridge has enough information, the bridges use special data

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Spanning tree incorporated 802.1t, and per 802.1t, uses the 4 most-significant bits of the 802.1d two-octet priority field as priority, and the least-significant 12 bits of that field as the extended system

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receipt of the TCN, the root switch will set the topology change flag in its normal BPDUs. This flag is propagated to all other switches and instructs them to rapidly age out their forwarding table entries.

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bridge where each designated bridge proposes to its neighbors to determine if it can make a rapid transition. This is one of the major elements that allows RSTP to achieve faster convergence times than STP.

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2 seconds) or within a few milliseconds of a physical link failure. The hello time is an important and configurable time interval that is used by RSTP for several purposes; its default value is 2 seconds.

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Path tie: The least-cost path to the root from network segment e goes through bridge 92. Therefore, the designated port for network segment e is the port that connects bridge 92 to network segment e.

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Before the IEEE published a Spanning Tree Protocol standard for VLANs, a number of vendors who sold VLAN capable switches developed their own Spanning Tree Protocol versions that were VLAN capable.

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VSTP supports only 253 different spanning-tree topologies. If there are more than 253 VLANs, it is recommended to configure RSTP in addition to VSTP, and VLANs beyond 253 will be handled by RSTP.

575:. All switches then select their best connection towards the root bridge for forwarding and block other redundant links. All switches constantly communicate with their neighbors in the LAN using 1441:

The bridge ID (BID) is a field inside a BPDU packet. It is eight bytes in length. The first two bytes are the bridge priority, an unsigned integer of 0–65,535. The last six bytes are a

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support PVST+. Extreme Networks does so with two limitations: Lack of support on ports where the VLAN is untagged/native, and also on the VLAN with ID 1. PVST+ can tunnel across an

439:, and disables those links that are not part of the spanning tree, leaving a single active path between any two network nodes. STP is based on an algorithm that was invented by 2878: 999:

The above rules describe one way of determining what spanning tree will be computed by the algorithm, but the rules as written require knowledge of the entire network. The

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bridge 24. If bridge IDs were equal, then the bridge with the lowest MAC address would have the designated port. In either case, the loser sets the port as being blocked.

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A port in normal operation receiving and forwarding frames. The port monitors incoming BPDUs that would indicate it should return to the blocking state to prevent a loop.

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of the spanning tree is the bridge with the smallest (lowest) bridge ID. Each bridge has a configurable priority number and a MAC address; the bridge ID is the

1508:, only distributed through multiple switches. Conversely, partitioning technologies compartmentalize a single physical chassis into multiple logical entities. 1352:

Cisco also published a proprietary version of Rapid Spanning Tree Protocol. It creates a spanning tree for each VLAN, just like PVST. Cisco refers to this as

2438: 1119:. RSTP was then incorporated into IEEE 802.1D-2004 making the original STP standard obsolete. RSTP was designed to be backward-compatible with standard STP. 1213:

mode). These edge ports transition directly to the forwarding state, avoiding problems with hosts expecting an upcoming link to work right away, e.g. with

1096:, declaring which capabilities and options have been implemented, to help users determine whether different implementations will interoperate correctly. 555:(LANs) are often interconnected using redundant links to improve resilience should one connection fail. However, this connection configuration creates a 2291: 2591: 379: 480:

While STP is still in use today, in most modern networks its primary use is as a loop-protection mechanism rather than a fault tolerance mechanism.

3803: 3798: 3793: 3788: 3783: 3778: 3773: 2371: 1924: 1885: 1846: 1807: 2484: 2383: 2358: 583:

Ethernet frames between the two switches, and disable all other possible links by designating the switch ports that connect the preferred path as

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instance number. Some vendors set the bridge system ID extension to carry a VLAN ID allowing a different spanning tree per VLAN, such as Cisco's

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An example network. The numbered boxes represent bridges, that is switches in a LAN. The number is the bridge ID. The lettered clouds represent

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There are two types of BPDUs in the original STP specification (802.1D) (the Rapid Spanning Tree (RSTP) extension uses a specific RSTP BPDU):

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The switch processes BPDUs and awaits possible new information that would cause it to return to the blocking state. It does not populate the

3085: 2538: 2532: 1746: 139: 2553:–2006, proposed standard, Definitions of Managed Objects for Bridges with Traffic Classes, Multicast Filtering, and Virtual LAN Extensions 926:

Bridge ID = priority (4 bits) + locally assigned system ID extension (12 bits) + ID (48 bits); the default bridge priority is 32,768, and

2567:–1999, proposed standard, Definitions of Managed Objects for Bridges with Traffic Classes, Multicast Filtering and Virtual LAN Extensions 2337:"Juniper Networks :: Technical Documentation :: Understanding Multiple VLAN Registration Protocol (MVRP) on EX Series Switches" 2463: 3853: 2011: 1011:

A bridge sends a BPDU frame using the unique MAC address of the port itself as a source address, and a destination address of the STP

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called bridge protocol data units (BPDUs) to exchange information about the spanning tree protocol, bridge IDs, and root path costs.

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Lowest sender port ID - Serves as a tiebreaker if a switch has multiple (non-EtherChannel) links to a single upstream switch, where:

1938: 3968: 2618: 1898: 1859: 1820: 1781: 1530: 1323: 1202:

Detection of root switch failure is done in 3 hello times, which is 6 seconds if the default hello times have not been changed.

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Configuration BPDU (CBPDU), used for spanning tree computation and sent by root bridges to provide information to all switches.

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While the port does not yet forward frames, it does learn source addresses from frames received and adds them to the MAC table.

17: 2344: 2225: 2173: 1205:

Ports may be configured as edge ports if they are attached to a LAN that has no other bridges attached (depending on vendor,

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exist, it is often desirable to create multiple spanning trees so that traffic on different VLANs uses different links.

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Topology change notification (TCN) BPDU, used to announce changes in the network topology, such as port up or port down.

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ANSI/IEEE Std 802.1D - 2004: IEEE Standard for Local and Metropolitan Area Networks: Media Access Control (MAC) Bridges

1535: 1430: 1397:(MSTI). CSTs are backward compatible with the STP and RSTP standard. A MST that has only one VLAN assigned to it is an 301: 244: 169: 1344:

does not support VSTP. If this protocol is in use, VLAN membership for trunk interfaces must be statically configured.

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was developed, which allows a switch port to rapidly transition into the forwarding state during these situations.

365: 296: 89: 2853: 2535:, section 17 discusses RSTP (Regular STP is no longer a part of this standard. This is pointed out in section 8.) 2284: 1497: 1447: 1369: 470: 3135: 1545: 1315: 114: 104: 488:

will bond two or more links to provide fault tolerance while simultaneously increasing overall link capacity.

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The number of switch port states a port can be in has been reduced to three instead of STP's original five:

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RSTP will revert to legacy STP on an interface if a legacy version of an STP BPDU is detected on that port.

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Wade Edwards, Terry Jack, Todd Lammle, Toby Skandier, Robert Padjen, Arthur Pfund & Carl Timm (2006).

1860:

Wade Edwards, Terry Jack, Todd Lammle, Toby Skandier, Robert Padjen, Arthur Pfund & Carl Timm (2006).

1821:

Wade Edwards, Terry Jack, Todd Lammle, Toby Skandier, Robert Padjen, Arthur Pfund & Carl Timm (2006).

1782:

Wade Edwards, Terry Jack, Todd Lammle, Toby Skandier, Robert Padjen, Arthur Pfund & Carl Timm (2006).

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Unlike in STP, RSTP will respond to BPDUs sent from the direction of the root bridge. An RSTP bridge will

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of the bridge priority and the MAC address. For example, the ID of a bridge with priority 32,768 and MAC

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Switches with Spanning Tree Protocol implementation in a local area network (LAN). One switch is the STP

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The original 802.1d envisioned the possibility of the root bridge having more than one port on the same

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instability. If redundant links are used to connect switches, then switching loops need to be avoided.

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Lowest sender bridge ID - Serves as a tiebreaker if multiple upstream switches have equal cost to root

3963: 3489: 2688: 1550: 1092:, due for example to differences in default timer settings. The IEEE encourages vendors to provide a 2359:"Juniper Networks :: Technical Documentation :: Understanding VSTP for EX-series Switches" 2112: 910:

The sequence of events to determine the best received BPDU (which is the best path to the root) is:

2923: 1747:"802.1D IEEE Standard for Local and Metropolitan Area Networks. Media Access Control (MAC) Bridges" 184: 124: 3958: 3927: 2788: 2778: 2758: 2604: 2574:–1993, - SBRIDGEMIB, proposed standard, Definitions of Managed Objects for Source Routing Bridges 1286: 351: 341: 134: 49: 33: 1757: 929:

Port ID = priority (4 bits) + ID (Interface number) (12 bits); the default port priority is 128.

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On the edge of the network, loop-detection is configured to prevent accidental loops by users.

1471: 219: 69: 2485:"Dr. Radia Perlman: One of the First Female Programmers and Inventor the Internet’s Protocols" 1081:

The first spanning tree protocol was invented in 1985 at the Digital Equipment Corporation by

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RSTP adds new bridge port roles in order to speed convergence following a link failure:

2918: 1918: 1879: 1840: 1801: 1648: 1159:- An alternate path to the root bridge. This path is different from using the root port 1005: 917:

Lowest cost to the root bridge - Favors the upstream switch with the least cost to root

808: 336: 64: 2199: 1470:(Transparent Interconnection of Lots of Links) protocol, also created by Perlman, and 535:

After link failure the spanning tree algorithm computes and spans new least-cost tree.

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will be selected as the root bridge. If the network administrators would like switch

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but the functionality of spanning tree (802.1D), rapid spanning tree (802.1w), and

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that characterizes the relationship of nodes within a network of connected layer-2

409: 405: 401: 1693: 2913: 1590: 1393:(CST) is an MST to which several VLANs are mapped, this group of VLANs is called 1165:- A backup/redundant path to a segment where another bridge port already connects 954: 839: 541:

Switches with Spanning Tree Protocol implementation in a local area network (LAN)

425: 205: 2578: 2571: 2564: 2557: 2550: 1629:"An Algorithm for Distributed Computation of a Spanning Tree in an Extended LAN" 1463:

control or suppress the natural behavior of logical or physical topology loops.

1382:-2005, defines an extension to RSTP to further develop the usefulness of VLANs. 1188:- The port is not forwarding frames yet, but is populating its MAC address table 3768: 2898: 2893: 2813: 2763: 2439:"Largest Illinois healthcare system uproots Cisco to build $ 40M private cloud" 1303: 1254: 1171:- Not strictly part of STP, a network administrator can manually disable a port 1000: 813: 556: 548: 436: 421: 255: 27:

Network protocol that builds a loop-free logical topology for Ethernet networks

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ANSI/IEEE Std 802.1D, 1998 Edition, Part 3: Media Access Control (MAC) Bridges

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to become the root bridge, they must set its priority to be less than 32,768.

3942: 3874: 3818: 3813: 3808: 3758: 3753: 3748: 3738: 3714: 3690: 3678: 3667: 3656: 3644: 3639: 3634: 3629: 3616: 3605: 3095: 3075: 2928: 2903: 2833: 2723: 2668: 2581:–1993 - BRIDGEMIB, draft standard, Definitions of Managed Objects for Bridges 1942: 1147:- A forwarding port that is the best port from non-root bridge to root bridge 1082: 851: 440: 432: 3858: 3848: 3596: 3581: 3576: 3571: 3561: 3504: 3145: 3140: 3125: 3120: 3115: 3065: 1525: 1423: 1089: 1063: 1032: 174: 1644: 3730: 3470: 3224: 3105: 3070: 3060: 3037: 3032: 3027: 3022: 3005: 2990: 2451:

Shortest Path Bridging will replace Spanning Tree in the Ethernet fabric.

1442: 1385:

In the standard, a spanning tree that maps one or more VLANs is called a

1379: 1375: 511:. All switch ports that connect a link between two switches are either a 466: 413: 3843: 3838: 3170: 3052: 2985: 2980: 2975: 2970: 2965: 2955: 1540: 1505: 1482: 322: 2066:

LAN/MAN Standards Committee of the IEEE Computer Society, ed. (2004).

2048:

LAN/MAN Standards Committee of the IEEE Computer Society, ed. (1998).

2033:

LAN/MAN Standards Committee of the IEEE Computer Society, ed. (1990).

842:. The smallest bridge ID is 3. Therefore, bridge 3 is the root bridge. 3904: 3884: 3742: 2995: 2888: 2883: 2868: 2858: 2848: 2828: 2823: 2808: 2798: 2793: 2773: 2768: 2748: 2743: 2738: 2733: 2718: 2683: 2150:"Rapid Spanning Tree Protocol: A new solution from an old technology" 781: 774:

algorithm determines the port may transition to the forwarding state.

564: 2560:–2005, proposed standard, Definitions of Managed Objects for Bridges 3175: 2947: 2938: 2656: 2646: 2641: 1901:

CCNP Complete Study Guide: Exams 642-801, 642-811, 642-821, 642-831

1862:

CCNP Complete Study Guide: Exams 642-801, 642-811, 642-821, 642-831

1823:

CCNP Complete Study Guide: Exams 642-801, 642-811, 642-821, 642-831

1784:

CCNP Complete Study Guide: Exams 642-801, 642-811, 642-821, 642-831

1251: 722:

The STP path cost default was originally calculated by the formula

1374:

The Multiple Spanning Tree Protocol (MSTP), originally defined in

766:

All switch ports in the LAN where STP is enabled are categorized.

3899: 3695: 3661: 3610: 3555: 3450: 3415: 3390: 3365: 3360: 3330: 3325: 3320: 3314: 3308: 3303: 3298: 3293: 3287: 3281: 3276: 3271: 3266: 3260: 3254: 3249: 3244: 3239: 3184: 2818: 2803: 2596: 2506: 2229: 1478: 2464:"IEEE Approves New IEEE 802.1aq Shortest Path Bridging Standard" 1250:

STP and RSTP do not segregate switch ports by VLAN. However, in

3762: 3234: 3229: 3219: 3214: 3209: 3204: 3199: 3194: 3189: 2863: 2693: 2200:

Michael G. Solomon, David Kim & Jeffrey L. Carrell (2014).

1500:

combine multiple switches into a single logical entity. Such a

1294: 285: 179: 78: 58: 1485:

for resiliency and to prevent loops is a popular alternative.

1088:

Different implementations of a standard are not guaranteed to

802:

A network administrator has manually disabled the switch port.

3620: 3475: 3010: 2873: 2713: 1467: 1311: 1270: 306: 84: 547:

The need for the Spanning Tree Protocol (STP) arose because

2843: 2708: 2703: 2587:

Spanning Tree Direct vs Indirect Link Failures - CCIE Study

2130: 1753: 1451: 1341: 1258: 1214: 1112: 451: 274: 269: 239: 189: 109: 74: 2384:"CiscoWorks LAN Management Solution 3.2 Deployment Guide" 914:

Lowest root bridge ID (BID) - Determines the root bridge.

758:. These formulas lead to the sample values in the table. 94: 2501:

Cisco home page for the Spanning-Tree protocol family

2174:"Understanding Rapid Spanning Tree Protocol (802.1w)" 2082:"Understanding Issues Related to Inter-VLAN Bridging" 2012:"Understanding Rapid Spanning Tree Protocol (802.1w)" 1477:

Configuring connections between network equipment as

1457: 600:

Path cost for different port speed and STP variation

2509:

Includes a sample PCAP-file of captured STP traffic.

420:

that results from them. Spanning tree also allows a

2403: 1076: 1057: 1363: 1115:introduced Rapid Spanning Tree Protocol (RSTP) as 1786:. John Wiley & Sons. pp. 506 & 511. 1051: 3940: 2204:. Jones & Bartlett Publishers. p. 204. 1717: 1135: 829: 2147: 1972:it believes itself to be the Designated Bridge. 1622: 1620: 1099: 576: 2503:(discusses CST, MISTP, PVST, PVST+, RSTP, STP) 2406:"Shortest Path Bridging IEEE 802.1aq Overview" 2612: 2202:Fundamentals of Communications and Networking 1741: 1739: 1153:- A forwarding port for every network segment 1094:Protocol Implementation Conformance Statement 994: 894:) both have a priority of 32,768 then switch 373: 1923:: CS1 maint: multiple names: authors list ( 1884:: CS1 maint: multiple names: authors list ( 1845:: CS1 maint: multiple names: authors list ( 1806:: CS1 maint: multiple names: authors list ( 1617: 1488:Switch virtualization techniques like Cisco 2250:"ExtremeXOS Operating System, Version 12.5" 2061: 2059: 1713: 1711: 1709: 1707: 1705: 1703: 1701: 2619: 2605: 2195: 2193: 2191: 2189: 1736: 905: 473:(802.1s) has since been incorporated into 412:. The basic function of STP is to prevent 380: 366: 2436: 2285:"BLADE PVST+ Interoperability with Cisco" 1720:CCNA Certification All-In-One For Dummies 1633:ACM SIGCOMM Computer Communication Review 1466:Newer, more robust protocols include the 1417: 1273:developed, implemented and published the 2056: 1698: 1689: 1687: 1298:its network switches. Some devices from 1264: 1033:Cisco proprietary Per-VLAN Spanning Tree 939: 833: 2186: 1665: 1626: 1531:Ethernet Automatic Protection Switching 1433:(MMRP) into a one link state protocol. 14: 3941: 1903:. John Wiley & Sons. p. 513. 1864:. John Wiley & Sons. p. 511. 1825:. John Wiley & Sons. p. 506. 1436: 1245: 1072:The TCN BPDU includes fields 1–3 only. 2600: 1684: 491: 2519:University of California at Berkeley 2456: 2316:"Bridging Between IEEE 802.1Q VLANs" 1991:IEEE 802 LAN/MAN Standards Committee 1502:multi-chassis link aggregation group 1182:- No user data is sent over the port 431:As the name suggests, STP creates a 2512: 2404:Peter Ashwood-Smith (24 Feb 2011). 1984:"Provider Bridge Layer 2 Protocols" 465:STP was originally standardized as 24: 2626: 1536:Ethernet Ring Protection Switching 1458:Disadvantages and current practice 1431:Multiple MAC Registration Protocol 424:to include backup links providing 25: 3985: 2507:STP article in the Wireshark wiki 2494: 1521:Distributed minimum spanning tree 1066:BPDUs have the following format: 577:§ Bridge protocol data units 2094:from the original on 2017-10-14. 1981: 1668:Interconnections, Second Edition 1077:Spanning Tree Protocol standards 1058:Bridge protocol data unit fields 820: 528: 500: 3969:Fault-tolerant computer systems 2592:Spanning Tree Protocol Overview 2478: 2430: 2397: 2376: 2365: 2351: 2329: 2308: 2297:from the original on 2010-06-12 2277: 2266:from the original on 2006-11-26 2242: 2218: 2166: 2141: 2119: 2074: 2041: 2026: 2004: 1975: 1965: 1955: 1931: 1596: 1583: 1573: 1498:Intelligent Resilient Framework 1370:Multiple Spanning Tree Protocol 1364:Multiple Spanning Tree Protocol 1194:- The port is fully operational 784:and it does not forward frames. 2539:ANSI/IEEE 802.1Q-2005 standard 2533:ANSI/IEEE 802.1D-2004 standard 2148:Waldemar Wojdak (March 2003). 2014:. Cisco Systems. 1 August 2017 1892: 1853: 1814: 1775: 1659: 1546:Flooding (computer networking) 1316:Brocade Communications Systems 935: 761: 13: 1: 2087:. Cisco Systems, Inc. 11072. 1610: 1561:Unidirectional Link Detection 1136:Rapid Spanning Tree operation 830:Root bridge and the bridge ID 445:Digital Equipment Corporation 1694:Bridges and Bridged Networks 1378:-2002 and later merged into 1354:Rapid Per-VLAN Spanning Tree 1257:environments where multiple 1106:Real Time Streaming Protocol 1100:Rapid Spanning Tree Protocol 594: 456:Rapid Spanning Tree Protocol 7: 2541:, section 13 discusses MSTP 2466:. Tech Power Up. 7 May 2012 1514: 10: 3990: 3923:IEEE Standards Association 1421: 1367: 1320:BLADE Network Technologies 1285:using its own proprietary 1198:RSTP operational details: 1103: 995:Bridge protocol data units 443:while she was working for 3913: 3867: 3831: 3729: 3469: 3169: 3051: 2946: 2937: 2634: 2437:Jim Duffy (11 May 2012). 2226:"Technical Documentation" 1722:. John Wiley & Sons. 1718:Silviu Angelescu (2010). 1551:Media Redundancy Protocol 428:if an active link fails. 2411:. Huawei. Archived from 1566: 1490:Virtual Switching System 1481:IP links and relying on 1104:Not to be confused with 404:that builds a loop-free 3928:Category:IEEE standards 1670:. USA: Addison-Wesley. 1666:Perlman, Radia (2000). 1627:Perlman, Radia (1985). 1334:compatibility of VSTP: 1293:, and PVST+ which uses 906:Path to the root bridge 394:Spanning Tree Protocol 34:Internet protocol suite 2107:Cite journal requires 1756:. 2004. Archived from 1472:Shortest Path Bridging 1418:Shortest path bridging 1399:internal spanning tree 1387:multiple spanning tree 1275:Per-VLAN Spanning Tree 945: 843: 471:multiple spanning tree 18:Spanning tree protocol 1645:10.1145/318951.319004 1556:Minimum spanning tree 1265:Proprietary standards 1015:with destination MAC 943: 837: 2035:ANSI/IEEE Std 802.1D 1939:"spanning-tree vlan" 1763:on December 10, 2005 1504:works like a normal 1391:common spanning tree 1283:proprietary protocol 866:32768.0200.0000.1111 617:(recommended value) 561:broadcast radiations 1494:Virtual PortChannel 1437:System ID Extension 1246:Standards for VLANs 601: 553:local area networks 418:broadcast radiation 3974:Ethernet standards 2372:Understanding VSTP 2154:CompactPCI Systems 1329:The switch vendor 946: 844: 599: 492:Protocol operation 484:protocols such as 3954:Network protocols 3936: 3935: 3827: 3826: 1287:Inter-Switch Link 1073: 1027:01:00:0C:CC:CC:CD 1019:01:80:C2:00:00:00 1013:multicast address 720: 719: 610:Original STP cost 607:(link bandwidth) 410:Ethernet networks 390: 389: 41:Application layer 16:(Redirected from 3981: 3964:Network topology 2944: 2943: 2621: 2614: 2607: 2598: 2597: 2526: 2521:. Archived from 2513:Perlman, Radia. 2488: 2482: 2476: 2475: 2473: 2471: 2460: 2454: 2453: 2448: 2446: 2434: 2428: 2427: 2425: 2423: 2417: 2410: 2401: 2395: 2394: 2392: 2391: 2380: 2374: 2369: 2363: 2362: 2355: 2349: 2348: 2343:. Archived from 2333: 2327: 2326: 2324: 2323: 2312: 2306: 2305: 2303: 2302: 2296: 2289: 2281: 2275: 2274: 2272: 2271: 2265: 2257:Extreme Networks 2254: 2246: 2240: 2239: 2237: 2236: 2222: 2216: 2215: 2197: 2184: 2183: 2181: 2180: 2170: 2164: 2163: 2161: 2160: 2145: 2139: 2138: 2127:IEEE 802.1D-2004 2123: 2117: 2116: 2110: 2105: 2103: 2095: 2093: 2086: 2078: 2072: 2071: 2063: 2054: 2053: 2045: 2039: 2038: 2030: 2024: 2023: 2021: 2019: 2008: 2002: 2001: 1999: 1997: 1988: 1979: 1973: 1969: 1963: 1959: 1953: 1952: 1950: 1949: 1935: 1929: 1928: 1922: 1914: 1896: 1890: 1889: 1883: 1875: 1857: 1851: 1850: 1844: 1836: 1818: 1812: 1811: 1805: 1797: 1779: 1773: 1772: 1770: 1768: 1762: 1751: 1743: 1734: 1733: 1715: 1696: 1691: 1682: 1681: 1663: 1657: 1656: 1624: 1604: 1600: 1594: 1587: 1581: 1577: 1331:Juniper Networks 1308:Extreme Networks 1300:Force10 Networks 1130: 1071: 1062:IEEE 802.1D and 1030: 1029: 1022: 1021: 986:Final tiebreaker 977:Designated ports 893: 892: 881: 880: 869: 868: 861: 860: 840:network segments 757: 756: 754: 753: 750: 747: 739: 738: 736: 735: 732: 729: 699:100 Gbit/s 655:100 Mbit/s 602: 598: 532: 504: 482:Link aggregation 475:IEEE 802.1Q-2014 406:logical topology 402:network protocol 382: 375: 368: 30: 29: 21: 3989: 3988: 3984: 3983: 3982: 3980: 3979: 3978: 3939: 3938: 3937: 3932: 3909: 3863: 3823: 3725: 3473: 3465: 3173: 3165: 3047: 2933: 2630: 2625: 2529:IEEE Standards 2497: 2492: 2491: 2483: 2479: 2469: 2467: 2462: 2461: 2457: 2444: 2442: 2435: 2431: 2421: 2419: 2415: 2408: 2402: 2398: 2389: 2387: 2382: 2381: 2377: 2370: 2366: 2357: 2356: 2352: 2341:www.juniper.net 2335: 2334: 2330: 2321: 2319: 2318:. Cisco Systems 2314: 2313: 2309: 2300: 2298: 2294: 2287: 2283: 2282: 2278: 2269: 2267: 2263: 2252: 2248: 2247: 2243: 2234: 2232: 2224: 2223: 2219: 2212: 2198: 2187: 2178: 2176: 2172: 2171: 2167: 2158: 2156: 2146: 2142: 2125: 2124: 2120: 2108: 2106: 2097: 2096: 2091: 2084: 2080: 2079: 2075: 2064: 2057: 2046: 2042: 2031: 2027: 2017: 2015: 2010: 2009: 2005: 1995: 1993: 1986: 1980: 1976: 1970: 1966: 1960: 1956: 1947: 1945: 1937: 1936: 1932: 1916: 1915: 1911: 1897: 1893: 1877: 1876: 1872: 1858: 1854: 1838: 1837: 1833: 1819: 1815: 1799: 1798: 1794: 1780: 1776: 1766: 1764: 1760: 1749: 1745: 1744: 1737: 1730: 1716: 1699: 1692: 1685: 1678: 1664: 1660: 1625: 1618: 1613: 1608: 1607: 1601: 1597: 1591:network segment 1588: 1584: 1578: 1574: 1569: 1517: 1474:from the IEEE. 1460: 1439: 1426: 1420: 1372: 1366: 1289:(ISL) for VLAN 1267: 1248: 1138: 1128: 1109: 1102: 1079: 1074: 1060: 1025: 1024: 1017: 1016: 997: 969:designated port 955:network segment 938: 908: 888: 887: 876: 875: 864: 863: 856: 855: 832: 823: 764: 751: 748: 745: 744: 742: 741: 733: 730: 727: 726: 724: 723: 688:10 Gbit/s 644:16 Mbit/s 633:10 Mbit/s 616: 611: 606: 597: 545: 544: 543: 542: 538: 537: 536: 533: 525: 524: 517:designated port 505: 494: 426:fault tolerance 386: 206:Transport layer 28: 23: 22: 15: 12: 11: 5: 3987: 3977: 3976: 3971: 3966: 3961: 3959:Link protocols 3956: 3951: 3934: 3933: 3931: 3930: 3925: 3920: 3914: 3911: 3910: 3908: 3907: 3902: 3897: 3892: 3887: 3882: 3877: 3871: 3869: 3865: 3864: 3862: 3861: 3856: 3851: 3846: 3841: 3835: 3833: 3829: 3828: 3825: 3824: 3822: 3821: 3816: 3811: 3806: 3801: 3796: 3791: 3786: 3781: 3776: 3771: 3766: 3756: 3751: 3746: 3735: 3733: 3727: 3726: 3724: 3723: 3711: 3708: 3705: 3702: 3699: 3687: 3684: 3681: 3676: 3673: 3670: 3665: 3653: 3650: 3647: 3642: 3637: 3632: 3627: 3624: 3614: 3602: 3599: 3594: 3589: 3584: 3579: 3574: 3569: 3564: 3559: 3547: 3542: 3537: 3532: 3527: 3522: 3517: 3512: 3507: 3502: 3497: 3492: 3487: 3481: 3479: 3467: 3466: 3464: 3463: 3458: 3453: 3448: 3443: 3438: 3433: 3428: 3423: 3418: 3413: 3408: 3403: 3398: 3393: 3388: 3383: 3378: 3373: 3368: 3363: 3358: 3353: 3348: 3343: 3338: 3333: 3328: 3323: 3318: 3311: 3306: 3301: 3296: 3291: 3284: 3279: 3274: 3269: 3264: 3257: 3252: 3247: 3242: 3237: 3232: 3227: 3222: 3217: 3212: 3207: 3202: 3197: 3192: 3187: 3181: 3179: 3167: 3166: 3164: 3163: 3158: 3148: 3143: 3138: 3133: 3128: 3123: 3118: 3113: 3108: 3103: 3098: 3093: 3088: 3083: 3078: 3073: 3068: 3063: 3057: 3055: 3049: 3048: 3046: 3045: 3040: 3035: 3030: 3025: 3020: 3015: 3014: 3013: 3003: 2998: 2993: 2988: 2983: 2978: 2973: 2968: 2963: 2958: 2952: 2950: 2941: 2935: 2934: 2932: 2931: 2926: 2921: 2916: 2911: 2906: 2901: 2896: 2891: 2886: 2881: 2876: 2871: 2866: 2861: 2856: 2851: 2846: 2841: 2836: 2831: 2826: 2821: 2816: 2811: 2806: 2801: 2796: 2791: 2786: 2781: 2776: 2771: 2766: 2761: 2756: 2751: 2746: 2741: 2736: 2731: 2726: 2721: 2716: 2711: 2706: 2701: 2696: 2691: 2686: 2681: 2676: 2671: 2666: 2665: 2664: 2654: 2649: 2644: 2638: 2636: 2632: 2631: 2628:IEEE standards 2624: 2623: 2616: 2609: 2601: 2595: 2594: 2589: 2584: 2583: 2582: 2575: 2568: 2561: 2554: 2544: 2543: 2542: 2536: 2527: 2525:on 2011-07-19. 2510: 2504: 2496: 2495:External links 2493: 2490: 2489: 2477: 2455: 2429: 2418:on 15 May 2013 2396: 2375: 2364: 2350: 2347:on 2012-04-07. 2328: 2307: 2276: 2241: 2217: 2210: 2185: 2165: 2140: 2133:, 2004-06-04, 2118: 2109:|journal= 2073: 2055: 2040: 2025: 2003: 1982:Finn, Norman. 1974: 1964: 1954: 1930: 1909: 1891: 1870: 1852: 1831: 1813: 1792: 1774: 1735: 1728: 1697: 1683: 1676: 1658: 1615: 1614: 1612: 1609: 1606: 1605: 1603:configuration. 1595: 1582: 1571: 1570: 1568: 1565: 1564: 1563: 1558: 1553: 1548: 1543: 1538: 1533: 1528: 1523: 1516: 1513: 1459: 1456: 1438: 1435: 1422:Main article: 1419: 1416: 1368:Main article: 1365: 1362: 1346: 1345: 1339: 1304:Alcatel-Lucent 1266: 1263: 1247: 1244: 1243: 1242: 1239: 1235: 1222: 1218: 1203: 1196: 1195: 1189: 1183: 1173: 1172: 1166: 1160: 1154: 1148: 1137: 1134: 1123:3 × 1101: 1098: 1078: 1075: 1068: 1059: 1056: 1047: 1046: 1043: 996: 993: 992: 991: 987: 983: 982: 978: 974: 973: 964: 960: 959: 950: 937: 934: 933: 932: 931: 930: 927: 921: 918: 915: 907: 904: 890:0200.0000.2222 878:0200.0000.1111 858:0200.0000.1111 831: 828: 822: 819: 804: 803: 800: 797: 794: 791: 788: 785: 778: 775: 771: 763: 760: 718: 717: 714: 711: 710:1 Tbit/s 707: 706: 703: 700: 696: 695: 692: 689: 685: 684: 681: 678: 677:2 Gbit/s 674: 673: 670: 667: 666:1 Gbit/s 663: 662: 659: 656: 652: 651: 648: 645: 641: 640: 637: 634: 630: 629: 626: 623: 622:4 Mbit/s 619: 618: 615:RSTP/MSTP cost 613: 612:(802.1D-1998) 608: 596: 593: 557:switching loop 540: 539: 534: 527: 526: 506: 499: 498: 497: 496: 495: 493: 490: 422:network design 388: 387: 385: 384: 377: 370: 362: 359: 358: 357: 356: 349: 344: 339: 334: 326: 325: 319: 318: 317: 316: 309: 304: 299: 294: 289: 279: 278: 277: 272: 259: 258: 256:Internet layer 252: 251: 250: 249: 242: 237: 232: 227: 222: 217: 209: 208: 202: 201: 200: 199: 192: 187: 182: 177: 172: 167: 162: 157: 152: 147: 142: 137: 132: 127: 122: 117: 112: 107: 102: 97: 92: 87: 82: 72: 67: 62: 52: 44: 43: 37: 36: 26: 9: 6: 4: 3: 2: 3986: 3975: 3972: 3970: 3967: 3965: 3962: 3960: 3957: 3955: 3952: 3950: 3949:Spanning tree 3947: 3946: 3944: 3929: 3926: 3924: 3921: 3919: 3916: 3915: 3912: 3906: 3903: 3901: 3898: 3896: 3893: 3891: 3888: 3886: 3883: 3881: 3878: 3876: 3873: 3872: 3870: 3866: 3860: 3857: 3855: 3852: 3850: 3847: 3845: 3842: 3840: 3837: 3836: 3834: 3830: 3820: 3817: 3815: 3812: 3810: 3807: 3805: 3802: 3800: 3797: 3795: 3792: 3790: 3787: 3785: 3782: 3780: 3777: 3775: 3772: 3770: 3767: 3764: 3760: 3757: 3755: 3752: 3750: 3747: 3744: 3740: 3737: 3736: 3734: 3732: 3728: 3721: 3717: 3716: 3712: 3709: 3706: 3703: 3700: 3697: 3693: 3692: 3688: 3685: 3682: 3680: 3677: 3674: 3671: 3669: 3666: 3663: 3659: 3658: 3654: 3651: 3648: 3646: 3643: 3641: 3638: 3636: 3633: 3631: 3628: 3625: 3622: 3618: 3615: 3612: 3608: 3607: 3603: 3600: 3598: 3595: 3593: 3590: 3588: 3585: 3583: 3580: 3578: 3575: 3573: 3570: 3568: 3565: 3563: 3560: 3557: 3553: 3552: 3548: 3546: 3543: 3541: 3538: 3536: 3533: 3531: 3528: 3526: 3523: 3521: 3518: 3516: 3513: 3511: 3508: 3506: 3503: 3501: 3498: 3496: 3493: 3491: 3488: 3486: 3483: 3482: 3480: 3477: 3472: 3468: 3462: 3459: 3457: 3454: 3452: 3449: 3447: 3444: 3442: 3439: 3437: 3434: 3432: 3429: 3427: 3424: 3422: 3419: 3417: 3414: 3412: 3409: 3407: 3404: 3402: 3399: 3397: 3394: 3392: 3389: 3387: 3384: 3382: 3379: 3377: 3374: 3372: 3369: 3367: 3364: 3362: 3359: 3357: 3354: 3352: 3349: 3347: 3344: 3342: 3339: 3337: 3334: 3332: 3329: 3327: 3324: 3322: 3319: 3317: 3316: 3312: 3310: 3307: 3305: 3302: 3300: 3297: 3295: 3292: 3290: 3289: 3285: 3283: 3280: 3278: 3275: 3273: 3270: 3268: 3265: 3263: 3262: 3258: 3256: 3253: 3251: 3248: 3246: 3243: 3241: 3238: 3236: 3233: 3231: 3228: 3226: 3223: 3221: 3218: 3216: 3213: 3211: 3208: 3206: 3203: 3201: 3198: 3196: 3193: 3191: 3188: 3186: 3183: 3182: 3180: 3177: 3172: 3168: 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