convent ional traffic-engineering practices of ISPs, and this consist ing of a 32-bit IP address and a mask length(e.g. ght well explain why Internet ce has not 1.2.3 724). An AS employs an intradomain rout ing pro occurred vet. Howe ver, it is cruci ake these guidelines tocol (such as OSPF or Is-Is)to determine how to reach xplicit since BGP itself does no ain rout ing policies each customer prefix, and employs an interdomain rout ing m e convergence. Based on our results, we propose protocol (BGP) to advert ise the reachability of these pre outing registry that requires each As to disclos fixes to neighboring ASes. BGP is a dist ance-vector protocol relationship with each of its ne igh rat her than that constructs pat hs by successi vely propagat ing advertise the entire set of rout ing policies. ments bet s of routers t hat are configured as BGP peers [18: 19]. Each advertisement The remainder of the paper is structured as follows. S prefix and includes the list of the A Ses along the path(the tion 2 presents an overview of interdomain routing and di As path). Upon receiving an adver tisement, a BGP speaker cusses pre vious work on BGP protocol dynamics. Then, See must decide whe ther or not to use this path and, if the path on 3 presents a formal model of BGP that includes ASes is chosen, whet her or not to propagate the adver tisement with multiple BGP speakers, both interior BGP (BGP)and to neighboring A Ses (after adding its own AS number to exterior BGP(e BGP), and additional BGP at tributes. We the As path). A BGP speaker withdraws an adver tisement de fine the ty pes of relationships between ASes and describe when the prefix is no longer reachable with this route, which the hierarchical structure of the As ph in Secti on 4. In leads to a sequence of wit drawals by upstream ASes that ection 5, we present our policy guidelines and formally are using this path prove that adherence to these guidelines guarantees conver- ence for all possible init ial states. We show how to The simplest dist ance-vec tor protocol would employ shortest mit addit ional flexibility in choosing bet ween routes through path routing. BGP allows a much wider range of policie customers and routes through peers by making realistic as- based on how the routers are configured. An As can favor sumpt ions about peer-to-peer relationships. Then, Section 6 one path over anot her by assigning a local preference. BGP discusses the rob usiness of our guide lines to changes in net also allows an As to send a hint to a neighbor on the prefer work topolo nd relationships between ence that should be gi ven to a route by using the communit ASes. We describe how to apply our me thodolo gy to ne at tribute. An as can control how traffic enters its network ypes of relat ionships that can arise between ASes, and how by assigning a different multiple erit discriminator(MED) n As pair can transition to a new relationship while pre- value to the advertisements it sends on each link to a neigh- serving BGP stabilit 7 concludes the paper with boring As. Ot her wise, the neighboring As would select the a discussion of future research direct ions link based on its own intradomain rout ing protocol. An AS 2. INTERDOMAIN ROUTING forming As prepending, which inflates the length of the AS pat h by listing an As number multiple times. Processing an ternet architect ure [11] and the use of BGP for interdom air advertisement involves three steps import policies that outing [18; 19]. We also decide which routes to consider, path selection that decide protocol dynamics of BGP. which route to use, and export policies that decide whet her and what)t vermis t hat are 2.1 Internet architecture detail in se 3 The Internet consists of a large collection of hosts intercon- nected by networks of links and routers. The Internet 2.2 Protocol Dynamics divided into thousands of dist inct regions of ad minist rat lexit y of the Internet rout- control, referred to as aut derstanding BGP ples range from college campuses and corporate net works to protocol dynamics. Previous work consists of measurement o, Se Internet Service Providers(ISPs). An AS has its ov based st udies of BGP protocol traffic and theoret ical analy lters and routing policies, and connects to other ASes to sis of BGP convergence properties. Extensi ve traces of Bo exchange traffic with remote hosts. A router t ypically has update messages have been used to characterize the struc very detailed knowledge of the topology within its AS, and ture(and growth)of the Internet tond\: 13: 14; 15]. In ge points(IXPs)or ch on bGP convergence has focused on dedicated point-to-point links. Public exchange points typ termining what combinat cally consist of a shared medium, such as a FDDI ring or ar group of A Ses to continually advertise and withdraw routes TM switch, that interconnects routers from several differ to a given prefix [6;8; 9; 10; 20]. BGP conve nt ASes. Physical connectivity at the IXP does not neces lems would not arise if every As selects shortest-path routes sarily imply that every pair of ASes exchanges traffic with However, ASes can have conflicting local policies when they ach other as pairs ne got iate cont ractual ts that tribute to fa route with control the exchange of traffic. These relationships include non-minimal AS path. This can result in route oscillat ion, Section 4 to its neighbors, whic eighbors to change their de en,these A Ses withdraw thei ous route and Each As has responsibility for carrying traffic to and from advertise new ones, and the process repeats a set of customer ip addr ternet routing infrast ructure depends on the aggregation Previous research has studied route convergence under of IP addresses in contiguous blocks, called prefires, each assumpt ion of global know ledge of the to polo gy and rout ing✍ ✆ ✓ ✚ ✄ ✓ ✡ ✙ ✆ ✓ ✠ ✎ ✡ ✝ ✠ ✭ ✍ ✩ ✄ ✓ ✜ ✙ ✓ ✄ ✄ ✝ ✙ ✓ ✜ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✄ ✒ ✆ ✛ ✫ ✗ ✌ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✙ ✒ ✕ ✙ ✜ ✂ ✡ ☛ ✄ ✎ ✎ ✄ ✪ ✘ ✎ ✠ ✙ ✓ ☛ ✂ ☞ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✙ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✂ ✠ ✒ ✓ ✆ ✡ ✆ ✍ ✍ ✔ ✝ ✝ ✄ ✞ ☞ ✄ ✡ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✙ ✡ ✙ ✒ ✍ ✝ ✔ ✍ ✙ ✠ ✎ ✡ ✆ ✕ ✠ ✵ ✄ ✡ ✂ ✄ ✒ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✒ ✙ ✓ ✍ ✄ ☎ ✟ ✌ ✙ ✡ ✒ ✄ ✎ ✛ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✍ ✆ ✓ ✒ ✡ ✝ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✆ ✄ ✓ ✒ ✔ ✝ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✣ ☎ ✠ ✒ ✄ ✞ ✆ ✓ ✆ ✔ ✝ ✝ ✄ ✒ ✔ ✎ ✡ ✒ ✥ ☛ ✄ ✘ ✝ ✆ ✘ ✆ ✒ ✄ ✠ ✒ ✙ ✕ ✘ ✎ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✡ ✂ ✠ ✡ ✝ ✄ ✧ ✔ ✙ ✝ ✄ ✒ ✄ ✠ ✍ ✂ ✖ ✗ ✡ ✆ ✞ ✙ ✒ ✍ ✎ ✆ ✒ ✄ ✆ ✓ ✎ ☞ ✙ ✡ ✒ ￾ ✁ ✂ ✄ ☎ ✆ ✝ ✞ ✟ ✠ ✆ ✡ ☛ ✙ ✡ ✂ ✄ ✠ ✍ ✂ ✆ ✛ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✥ ✝ ✠ ✡ ✂ ✄ ✝ ✡ ✂ ✠ ✓ ✡ ✂ ✄ ✄ ✓ ✡ ✙ ✝ ✄ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✁ ✂ ✄ ✝ ✄ ✕ ✠ ✙ ✓ ✞ ✄ ✝ ✆ ✛ ✡ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ✙ ✒ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✞ ✠ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✒ ✣ ✗ ✄ ✍ ✩ ✡ ✙ ✆ ✓ ❃ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✓ ✆ ✚ ✄ ✝ ✚ ✙ ✄ ☛ ✆ ✛ ✙ ✓ ✡ ✄ ✝ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✠ ✓ ✞ ✞ ✙ ✒ ✩ ✍ ✔ ✒ ✒ ✄ ✒ ✘ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ☛ ✆ ✝ ✵ ✆ ✓ ☎ ✟ ✌ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✒ ✣ ✁ ✂ ✄ ✓ ✥ ✗ ✄ ✍ ✩ ✡ ✙ ✆ ✓ ✾ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✛ ✆ ✝ ✕ ✠ ✎ ✕ ✆ ✞ ✄ ✎ ✆ ✛ ☎ ✟ ✌ ✡ ✂ ✠ ✡ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✖ ✗ ✄ ✒ ☛ ✙ ✡ ✂ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✥ ✢ ✆ ✡ ✂ ✙ ✓ ✡ ✄ ✝ ✙ ✆ ✝ ☎ ✟ ✌ ✏ ✙ ☎ ✟ ✌ ✑ ✠ ✓ ✞ ✄ ✪ ✡ ✄ ✝ ✙ ✆ ✝ ☎ ✟ ✌ ✏ ✄ ☎ ✟ ✌ ✑ ✥ ✠ ✓ ✞ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ☎ ✟ ✌ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✒ ✣ ✱ ✄ ✞ ✄ ✮ ✓ ✄ ✡ ✂ ✄ ✡ ☞ ✘ ✄ ✒ ✆ ✛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✠ ✓ ✞ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✄ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✜ ✝ ✠ ✘ ✂ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ☛ ✣ ✫ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✺ ✥ ☛ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✆ ✔ ✝ ✘ ✆ ✎ ✙ ✍ ☞ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✠ ✓ ✞ ✛ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✠ ✞ ✂ ✄ ✝ ✄ ✓ ✍ ✄ ✡ ✆ ✡ ✂ ✄ ✒ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✜ ✔ ✠ ✝ ✠ ✓ ✡ ✄ ✄ ✒ ✍ ✆ ✓ ✚ ✄ ✝ ✩ ✜ ✄ ✓ ✍ ✄ ✛ ✆ ✝ ✠ ✎ ✎ ✘ ✆ ✒ ✒ ✙ ✢ ✎ ✄ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✒ ✣ ✱ ✄ ✒ ✂ ✆ ☛ ✂ ✆ ☛ ✡ ✆ ✘ ✄ ✝ ✩ ✕ ✙ ✡ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ✦ ✄ ✪ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✍ ✂ ✆ ✆ ✒ ✙ ✓ ✜ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✘ ✄ ✄ ✝ ✒ ✢ ☞ ✕ ✠ ✵ ✙ ✓ ✜ ✝ ✄ ✠ ✎ ✙ ✒ ✡ ✙ ✍ ✠ ✒ ✩ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✒ ✠ ✢ ✆ ✔ ✡ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✣ ✁ ✂ ✄ ✓ ✥ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ❅ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✄ ✒ ✡ ✂ ✄ ✝ ✆ ✢ ✔ ✒ ✡ ✓ ✄ ✒ ✒ ✆ ✛ ✆ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✓ ✓ ✄ ✡ ✩ ☛ ✆ ✝ ✵ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✥ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ✠ ✓ ✞ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✣ ✱ ✄ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✄ ✂ ✆ ☛ ✡ ✆ ✠ ✘ ✘ ✎ ☞ ✆ ✔ ✝ ✕ ✄ ✡ ✂ ✆ ✞ ✆ ✎ ✆ ✜ ☞ ✡ ✆ ✓ ✄ ☛ ✡ ☞ ✘ ✄ ✒ ✆ ✛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✡ ✂ ✠ ✡ ✍ ✠ ✓ ✠ ✝ ✙ ✒ ✄ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✥ ✠ ✓ ✞ ✂ ✆ ☛ ✠ ✓ ✖ ✗ ✘ ✠ ✙ ✝ ✍ ✠ ✓ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✡ ✆ ✠ ✓ ✄ ☛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✂ ✙ ✎ ✄ ✘ ✝ ✄ ✩ ✒ ✄ ✝ ✚ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✹ ✍ ✆ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✡ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ☛ ✙ ✡ ✂ ✠ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✙ ✆ ✓ ✆ ✛ ✛ ✔ ✡ ✔ ✝ ✄ ✝ ✄ ✒ ✄ ✠ ✝ ✍ ✂ ✞ ✙ ✝ ✄ ✍ ✡ ✙ ✆ ✓ ✒ ✣ 2. INTERDOMAIN ROUTING ✫ ✓ ✡ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✢ ✠ ✍ ✵ ✜ ✝ ✆ ✔ ✓ ✞ ✕ ✠ ✡ ✄ ✝ ✙ ✠ ✎ ✆ ✓ ✡ ✂ ✄ ✫ ✓ ✩ ✡ ✄ ✝ ✓ ✄ ✡ ✠ ✝ ✍ ✂ ✙ ✡ ✄ ✍ ✡ ✔ ✝ ✄ ✿ ✽ ✽ ❁ ✠ ✓ ✞ ✡ ✂ ✄ ✔ ✒ ✄ ✆ ✛ ☎ ✟ ✌ ✛ ✆ ✝ ✙ ✓ ✡ ✄ ✝ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✿ ✽ ✼ ❀ ✽ ✸ ❁ ✣ ✱ ✄ ✠ ✎ ✒ ✆ ✒ ✔ ✕ ✕ ✠ ✝ ✙ ✲ ✄ ✘ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ☛ ✆ ✝ ✵ ✆ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✒ ✆ ✛ ☎ ✟ ✌ ✣ 2.1 Internet Architecture ✁ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✠ ✎ ✠ ✝ ✜ ✄ ✍ ✆ ✎ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✆ ✛ ✂ ✆ ✒ ✡ ✒ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✩ ✓ ✄ ✍ ✡ ✄ ✞ ✢ ☞ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✒ ✆ ✛ ✎ ✙ ✓ ✵ ✒ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✣ ✁ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✙ ✒ ✞ ✙ ✚ ✙ ✞ ✄ ✞ ✙ ✓ ✡ ✆ ✡ ✂ ✆ ✔ ✒ ✠ ✓ ✞ ✒ ✆ ✛ ✞ ✙ ✒ ✡ ✙ ✓ ✍ ✡ ✝ ✄ ✜ ✙ ✆ ✓ ✒ ✆ ✛ ✠ ✞ ✕ ✙ ✓ ✙ ✒ ✡ ✝ ✠ ✡ ✙ ✚ ✄ ✍ ✆ ✓ ✡ ✝ ✆ ✎ ✥ ✝ ✄ ✛ ✄ ✝ ✝ ✄ ✞ ✡ ✆ ✠ ✒ ✄ ☞ ☎ ✝ ✞ ✝ ✌ ✝ ☞ ✟ ✟ ✍ ✟ ☎ ✁ ✌ ✟ ✏ ✖ ✗ ✄ ✒ ✑ ✣ ✻ ✪ ✠ ✕ ✩ ✘ ✎ ✄ ✒ ✝ ✠ ✓ ✜ ✄ ✛ ✝ ✆ ✕ ✍ ✆ ✎ ✎ ✄ ✜ ✄ ✍ ✠ ✕ ✘ ✔ ✒ ✄ ✒ ✠ ✓ ✞ ✍ ✆ ✝ ✘ ✆ ✝ ✠ ✡ ✄ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✒ ✡ ✆ ✎ ✠ ✝ ✜ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✗ ✄ ✝ ✚ ✙ ✍ ✄ ✌ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✏ ✫ ✗ ✌ ✒ ✑ ✣ ✖ ✓ ✖ ✗ ✂ ✠ ✒ ✙ ✡ ✒ ✆ ☛ ✓ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ✠ ✓ ✞ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✒ ✡ ✆ ✆ ✡ ✂ ✄ ✝ ✖ ✗ ✄ ✒ ✡ ✆ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✝ ✠ ✭ ✍ ☛ ✙ ✡ ✂ ✝ ✄ ✕ ✆ ✡ ✄ ✂ ✆ ✒ ✡ ✒ ✣ ✖ ✝ ✆ ✔ ✡ ✄ ✝ ✡ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✂ ✠ ✒ ✚ ✄ ✝ ☞ ✞ ✄ ✡ ✠ ✙ ✎ ✄ ✞ ✵ ✓ ✆ ☛ ✎ ✄ ✞ ✜ ✄ ✆ ✛ ✡ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ☛ ✙ ✡ ✂ ✙ ✓ ✙ ✡ ✒ ✖ ✗ ✥ ✠ ✓ ✞ ✎ ✙ ✕ ✙ ✡ ✄ ✞ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✠ ✢ ✆ ✔ ✡ ✆ ✡ ✂ ✄ ✝ ✖ ✗ ✄ ✒ ✣ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✠ ✡ ✘ ✔ ✢ ✎ ✙ ✍ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✘ ✆ ✙ ✓ ✡ ✒ ✏ ✫ ✎ ✌ ✒ ✑ ✆ ✝ ✞ ✄ ✞ ✙ ✍ ✠ ✡ ✄ ✞ ✘ ✆ ✙ ✓ ✡ ✩ ✡ ✆ ✩ ✘ ✆ ✙ ✓ ✡ ✎ ✙ ✓ ✵ ✒ ✣ ✌ ✔ ✢ ✎ ✙ ✍ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✘ ✆ ✙ ✓ ✡ ✒ ✡ ☞ ✘ ✙ ✩ ✍ ✠ ✎ ✎ ☞ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✆ ✛ ✠ ✒ ✂ ✠ ✝ ✄ ✞ ✕ ✄ ✞ ✙ ✔ ✕ ✥ ✒ ✔ ✍ ✂ ✠ ✒ ✠ ✯ ✰ ✰ ✫ ✝ ✙ ✓ ✜ ✆ ✝ ✠ ✓ ✖ ✁ ✏ ✒ ☛ ✙ ✡ ✍ ✂ ✥ ✡ ✂ ✠ ✡ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✛ ✝ ✆ ✕ ✒ ✄ ✚ ✄ ✝ ✠ ✎ ✞ ✙ ✳ ✄ ✝ ✩ ✄ ✓ ✡ ✖ ✗ ✄ ✒ ✣ ✌ ✂ ☞ ✒ ✙ ✍ ✠ ✎ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✚ ✙ ✡ ☞ ✠ ✡ ✡ ✂ ✄ ✫ ✎ ✌ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✓ ✄ ✍ ✄ ✒ ✩ ✒ ✠ ✝ ✙ ✎ ☞ ✙ ✕ ✘ ✎ ☞ ✡ ✂ ✠ ✡ ✄ ✚ ✄ ✝ ☞ ✘ ✠ ✙ ✝ ✆ ✛ ✖ ✗ ✄ ✒ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✡ ✝ ✠ ✭ ✍ ☛ ✙ ✡ ✂ ✄ ✠ ✍ ✂ ✆ ✡ ✂ ✄ ✝ ✣ ✖ ✗ ✘ ✠ ✙ ✝ ✒ ✓ ✄ ✜ ✆ ✡ ✙ ✠ ✡ ✄ ✍ ✆ ✓ ✡ ✝ ✠ ✍ ✡ ✔ ✠ ✎ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✒ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✡ ✝ ✆ ✎ ✡ ✂ ✄ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✆ ✛ ✡ ✝ ✠ ✭ ✍ ✣ ✁ ✂ ✄ ✒ ✄ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✥ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✥ ✠ ✓ ✞ ✢ ✠ ✍ ✵ ✔ ✘ ✥ ✠ ✓ ✞ ✠ ✝ ✄ ✞ ✙ ✒ ✩ ✍ ✔ ✒ ✒ ✄ ✞ ✙ ✓ ✕ ✆ ✝ ✄ ✞ ✄ ✡ ✠ ✙ ✎ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ☛ ✣ ✻ ✠ ✍ ✂ ✖ ✗ ✂ ✠ ✒ ✝ ✄ ✒ ✘ ✆ ✓ ✒ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✛ ✆ ✝ ✍ ✠ ✝ ✝ ☞ ✙ ✓ ✜ ✡ ✝ ✠ ✭ ✍ ✡ ✆ ✠ ✓ ✞ ✛ ✝ ✆ ✕ ✠ ✒ ✄ ✡ ✆ ✛ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✫ ✌ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✄ ✒ ✣ ✁ ✂ ✄ ✒ ✍ ✠ ✎ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✩ ✡ ✄ ✝ ✓ ✄ ✡ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✛ ✝ ✠ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✞ ✄ ✘ ✄ ✓ ✞ ✒ ✆ ✓ ✡ ✂ ✄ ✠ ✜ ✜ ✝ ✄ ✜ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ✫ ✌ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✄ ✒ ✙ ✓ ✍ ✆ ✓ ✡ ✙ ✜ ✔ ✆ ✔ ✒ ✢ ✎ ✆ ✍ ✵ ✒ ✥ ✍ ✠ ✎ ✎ ✄ ✞ ✡ ￾ ✁ ✑ ✒ ✁ ✟ ✥ ✄ ✠ ✍ ✂ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✙ ✓ ✜ ✆ ✛ ✠ ✾ ❃ ✩ ✢ ✙ ✡ ✫ ✌ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✠ ✓ ✞ ✠ ✕ ✠ ✒ ✵ ✎ ✄ ✓ ✜ ✡ ✂ ✏ ✄ ✣ ✜ ✣ ✥ ✽ ✓ ❃ ✓ ✾ ✓ ❂ ✔ ❃ ☛ ✑ ✣ ✖ ✓ ✖ ✗ ✄ ✕ ✘ ✎ ✆ ☞ ✒ ✠ ✓ ✆ ✞ ☎ ￾ ✄ ✕ ✝ ✌ ✄ ✆ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✩ ✡ ✆ ✍ ✆ ✎ ✏ ✒ ✔ ✍ ✂ ✠ ✒ ★ ✗ ✌ ✯ ✆ ✝ ✫ ✗ ✩ ✫ ✗ ✑ ✡ ✆ ✞ ✄ ✡ ✄ ✝ ✕ ✙ ✓ ✄ ✂ ✆ ☛ ✡ ✆ ✝ ✄ ✠ ✍ ✂ ✄ ✠ ✍ ✂ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✘ ✝ ✄ ✮ ✪ ✥ ✠ ✓ ✞ ✄ ✕ ✘ ✎ ✆ ☞ ✒ ✠ ✓ ✆ ✞ ☎ ✁ ￾ ✕ ✝ ✌ ✄ ✆ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✏ ☎ ✟ ✌ ✑ ✡ ✆ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✡ ✂ ✄ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✒ ✄ ✘ ✝ ✄ ✩ ✮ ✪ ✄ ✒ ✡ ✆ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✣ ☎ ✟ ✌ ✙ ✒ ✠ ✞ ✙ ✒ ✡ ✠ ✓ ✍ ✄ ✩ ✚ ✄ ✍ ✡ ✆ ✝ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✒ ✘ ✠ ✡ ✂ ✒ ✢ ☞ ✒ ✔ ✍ ✍ ✄ ✒ ✒ ✙ ✚ ✄ ✎ ☞ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✙ ✓ ✜ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✩ ✕ ✄ ✓ ✡ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✘ ✠ ✙ ✝ ✒ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✠ ✝ ✄ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✄ ✞ ✠ ✒ ✖ ✗ ✘ ✡ ✁ ✁ ￾ ✟ ✿ ✽ ✼ ❀ ✽ ✸ ❁ ✣ ✻ ✠ ✍ ✂ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✍ ✆ ✓ ✍ ✄ ✝ ✓ ✒ ✠ ✘ ✠ ✝ ✡ ✙ ✍ ✔ ✎ ✠ ✝ ✘ ✝ ✄ ✮ ✪ ✠ ✓ ✞ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✡ ✂ ✄ ✎ ✙ ✒ ✡ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✠ ✎ ✆ ✓ ✜ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✏ ✡ ✂ ✄ ✙ ✚ ✡ ✄ ☎ ✠ ✑ ✣ ❆ ✘ ✆ ✓ ✝ ✄ ✍ ✄ ✙ ✚ ✙ ✓ ✜ ✠ ✓ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✥ ✠ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✕ ✔ ✒ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✆ ✝ ✓ ✆ ✡ ✡ ✆ ✔ ✒ ✄ ✡ ✂ ✙ ✒ ✘ ✠ ✡ ✂ ✠ ✓ ✞ ✥ ✙ ✛ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✙ ✒ ✍ ✂ ✆ ✒ ✄ ✓ ✥ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✆ ✝ ✓ ✆ ✡ ✡ ✆ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✄ ✡ ✂ ✄ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✡ ✆ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✏ ✠ ✛ ✡ ✄ ✝ ✠ ✞ ✞ ✙ ✓ ✜ ✙ ✡ ✒ ✆ ☛ ✓ ✖ ✗ ✓ ✔ ✕ ✢ ✄ ✝ ✡ ✆ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ✑ ✣ ✖ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✒ ✠ ✓ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ☛ ✂ ✄ ✓ ✡ ✂ ✄ ✘ ✝ ✄ ✮ ✪ ✙ ✒ ✓ ✆ ✎ ✆ ✓ ✜ ✄ ✝ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✎ ✄ ☛ ✙ ✡ ✂ ✡ ✂ ✙ ✒ ✝ ✆ ✔ ✡ ✄ ✥ ☛ ✂ ✙ ✍ ✂ ✎ ✄ ✠ ✞ ✒ ✡ ✆ ✠ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✆ ✛ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✠ ✎ ✒ ✢ ☞ ✔ ✘ ✒ ✡ ✝ ✄ ✠ ✕ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✠ ✝ ✄ ✔ ✒ ✙ ✓ ✜ ✡ ✂ ✙ ✒ ✘ ✠ ✡ ✂ ✣ ✁ ✂ ✄ ✒ ✙ ✕ ✘ ✎ ✄ ✒ ✡ ✞ ✙ ✒ ✡ ✠ ✓ ✍ ✄ ✩ ✚ ✄ ✍ ✡ ✆ ✝ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ☛ ✆ ✔ ✎ ✞ ✄ ✕ ✘ ✎ ✆ ☞ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✩ ✘ ✠ ✡ ✂ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✣ ☎ ✟ ✌ ✠ ✎ ✎ ✆ ☛ ✒ ✠ ✕ ✔ ✍ ✂ ☛ ✙ ✞ ✄ ✝ ✝ ✠ ✓ ✜ ✄ ✆ ✛ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ✂ ✆ ☛ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✠ ✝ ✄ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✄ ✞ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✛ ✠ ✚ ✆ ✝ ✆ ✓ ✄ ✘ ✠ ✡ ✂ ✆ ✚ ✄ ✝ ✠ ✓ ✆ ✡ ✂ ✄ ✝ ✢ ☞ ✠ ✒ ✒ ✙ ✜ ✓ ✙ ✓ ✜ ✠ ✂ ✝ ✛ ✄ ✂ ✡ ￾ ✁ ✜ ✁ ￾ ✁ ✞ ✛ ✁ ✣ ☎ ✟ ✌ ✠ ✎ ✒ ✆ ✠ ✎ ✎ ✆ ☛ ✒ ✠ ✓ ✖ ✗ ✡ ✆ ✒ ✄ ✓ ✞ ✠ ✂ ✙ ✓ ✡ ✡ ✆ ✠ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✆ ✓ ✡ ✂ ✄ ✘ ✝ ✄ ✛ ✄ ✝ ✩ ✄ ✓ ✍ ✄ ✡ ✂ ✠ ✡ ✒ ✂ ✆ ✔ ✎ ✞ ✢ ✄ ✜ ✙ ✚ ✄ ✓ ✡ ✆ ✠ ✝ ✆ ✔ ✡ ✄ ✢ ☞ ✔ ✒ ✙ ✓ ✜ ✡ ✂ ✄ ✛ ✝ ✌ ✌ ☞ ✞ ✆ ☎ ✍ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✍ ✆ ✓ ✡ ✝ ✆ ✎ ✂ ✆ ☛ ✡ ✝ ✠ ✭ ✍ ✄ ✓ ✡ ✄ ✝ ✒ ✙ ✡ ✒ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✢ ☞ ✠ ✒ ✒ ✙ ✜ ✓ ✙ ✓ ✜ ✠ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✌ ☞ ✂ ☎ ✆ ✡ ✂ ✁ ✁ ✒ ✆ ☎ ✕ ✆ ✟ ✛ ￾ ✆ ✌ ✆ ✞ ✄ ☎ ✝ ￾ ✏ ✏ ✻ ✰ ✑ ✚ ✠ ✎ ✔ ✄ ✡ ✆ ✡ ✂ ✄ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✒ ✙ ✡ ✒ ✄ ✓ ✞ ✒ ✆ ✓ ✄ ✠ ✍ ✂ ✎ ✙ ✓ ✵ ✡ ✆ ✠ ✓ ✄ ✙ ✜ ✂ ✩ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✣ ★ ✡ ✂ ✄ ✝ ☛ ✙ ✒ ✄ ✥ ✡ ✂ ✄ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ☛ ✆ ✔ ✎ ✞ ✒ ✄ ✎ ✄ ✍ ✡ ✡ ✂ ✄ ✎ ✙ ✓ ✵ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ✙ ✡ ✒ ✆ ☛ ✓ ✙ ✓ ✡ ✝ ✠ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✠ ✎ ✒ ✆ ✞ ✙ ✒ ✍ ✆ ✔ ✝ ✠ ✜ ✄ ✡ ✝ ✠ ✭ ✍ ✛ ✝ ✆ ✕ ✄ ✓ ✡ ✄ ✝ ✙ ✓ ✜ ✙ ✡ ✒ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✢ ☞ ✘ ✄ ✝ ✩ ✛ ✆ ✝ ✕ ✙ ✓ ✜ ✙ ✚ ✡ ￾ ✁ ✡ ✁ ✞ ✕ ✆ ✞ ✢ ✥ ☛ ✂ ✙ ✍ ✂ ✙ ✓ ✦ ✠ ✡ ✄ ✒ ✡ ✂ ✄ ✎ ✄ ✓ ✜ ✡ ✂ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ✢ ☞ ✎ ✙ ✒ ✡ ✙ ✓ ✜ ✠ ✓ ✖ ✗ ✓ ✔ ✕ ✢ ✄ ✝ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ✡ ✙ ✕ ✄ ✒ ✣ ✌ ✝ ✆ ✍ ✄ ✒ ✒ ✙ ✓ ✜ ✠ ✓ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✙ ✓ ✚ ✆ ✎ ✚ ✄ ✒ ✡ ✂ ✝ ✄ ✄ ✒ ✡ ✄ ✘ ✒ ✣ ✆ ✌ ✡ ✝ ￾ ☎ ✡ ✝ ✂ ✆ ✛ ✆ ✁ ✟ ✡ ✂ ✠ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ☛ ✂ ✙ ✍ ✂ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✥ ✡ ✄ ☎ ✠ ✟ ✁ ✂ ✁ ✛ ☎ ✆ ✝ ✞ ✡ ✂ ✠ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ✒ ☛ ✂ ✙ ✍ ✂ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✔ ✒ ✄ ✥ ✠ ✓ ✞ ✁ ✒ ✡ ✝ ￾ ☎ ✡ ✝ ✂ ✆ ✛ ✆ ✁ ✟ ✡ ✂ ✠ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✏ ✠ ✓ ✞ ☛ ✂ ✠ ✡ ✑ ✡ ✆ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✡ ✆ ✠ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✣ ✡ ✂ ✠ ✡ ✠ ✝ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✄ ✞ ✙ ✓ ✕ ✆ ✝ ✄ ✞ ✄ ✡ ✠ ✙ ✎ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✾ ✣ 2.2 Protocol Dynamics ✁ ✂ ✄ ✜ ✝ ✆ ☛ ✙ ✓ ✜ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✍ ✄ ✠ ✓ ✞ ✍ ✆ ✕ ✘ ✎ ✄ ✪ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✝ ✆ ✔ ✡ ✩ ✙ ✓ ✜ ✙ ✓ ✛ ✝ ✠ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✂ ✠ ✒ ✒ ✘ ✠ ✝ ✵ ✄ ✞ ✙ ✓ ✡ ✄ ✝ ✄ ✒ ✡ ✙ ✓ ✔ ✓ ✞ ✄ ✝ ✒ ✡ ✠ ✓ ✞ ✙ ✓ ✜ ☎ ✟ ✌ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✒ ✣ ✌ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ☛ ✆ ✝ ✵ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✕ ✄ ✠ ✒ ✔ ✝ ✄ ✕ ✄ ✓ ✡ ✩ ✢ ✠ ✒ ✄ ✞ ✒ ✡ ✔ ✞ ✙ ✄ ✒ ✆ ✛ ☎ ✟ ✌ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✡ ✝ ✠ ✭ ✍ ✠ ✓ ✞ ✡ ✂ ✄ ✆ ✝ ✄ ✡ ✙ ✍ ✠ ✎ ✠ ✓ ✠ ✎ ☞ ✩ ✒ ✙ ✒ ✆ ✛ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✣ ✻ ✪ ✡ ✄ ✓ ✒ ✙ ✚ ✄ ✡ ✝ ✠ ✍ ✄ ✒ ✆ ✛ ☎ ✟ ✌ ✔ ✘ ✞ ✠ ✡ ✄ ✕ ✄ ✒ ✒ ✠ ✜ ✄ ✒ ✂ ✠ ✚ ✄ ✢ ✄ ✄ ✓ ✔ ✒ ✄ ✞ ✡ ✆ ✍ ✂ ✠ ✝ ✠ ✍ ✡ ✄ ✝ ✙ ✲ ✄ ✡ ✂ ✄ ✒ ✡ ✝ ✔ ✍ ✩ ✡ ✔ ✝ ✄ ✏ ✠ ✓ ✞ ✜ ✝ ✆ ☛ ✡ ✂ ✑ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✥ ✠ ✒ ☛ ✄ ✎ ✎ ✠ ✒ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✄ ✒ ✿ ✹ ❀ ✽ ✾ ❀ ✽ ☛ ❀ ✽ ✺ ❁ ✣ ✫ ✓ ✍ ✆ ✓ ✡ ✝ ✠ ✒ ✡ ✥ ✝ ✄ ✒ ✄ ✠ ✝ ✍ ✂ ✆ ✓ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✂ ✠ ✒ ✛ ✆ ✍ ✔ ✒ ✄ ✞ ✆ ✓ ✞ ✄ ✩ ✡ ✄ ✝ ✕ ✙ ✓ ✙ ✓ ✜ ☛ ✂ ✠ ✡ ✍ ✆ ✕ ✢ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ☎ ✟ ✌ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ☛ ✆ ✔ ✎ ✞ ✍ ✠ ✔ ✒ ✄ ✠ ✜ ✝ ✆ ✔ ✘ ✆ ✛ ✖ ✗ ✄ ✒ ✡ ✆ ✍ ✆ ✓ ✡ ✙ ✓ ✔ ✠ ✎ ✎ ☞ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✠ ✓ ✞ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✠ ✜ ✙ ✚ ✄ ✓ ✘ ✝ ✄ ✮ ✪ ✿ ❅ ❀ ✼ ❀ ✸ ❀ ✽ ❂ ❀ ❃ ❂ ❁ ✣ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✩ ✎ ✄ ✕ ✒ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✠ ✝ ✙ ✒ ✄ ✙ ✛ ✄ ✚ ✄ ✝ ☞ ✖ ✗ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✩ ✘ ✠ ✡ ✂ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✖ ✗ ✄ ✒ ✍ ✠ ✓ ✂ ✠ ✚ ✄ ✍ ✆ ✓ ✦ ✙ ✍ ✡ ✙ ✓ ✜ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ☛ ✂ ✄ ✓ ✡ ✂ ✄ ☞ ✔ ✒ ✄ ✡ ✂ ✄ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✡ ✆ ✛ ✠ ✚ ✆ ✝ ✠ ✝ ✆ ✔ ✡ ✄ ☛ ✙ ✡ ✂ ✠ ✓ ✆ ✓ ✩ ✕ ✙ ✓ ✙ ✕ ✠ ✎ ✖ ✗ ✘ ✠ ✡ ✂ ✣ ✁ ✂ ✙ ✒ ✍ ✠ ✓ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✝ ✆ ✔ ✡ ✄ ✆ ✒ ✍ ✙ ✎ ✎ ✠ ✡ ✙ ✆ ✓ ✥ ☛ ✂ ✄ ✝ ✄ ✠ ✓ ✖ ✗ ✕ ✠ ✵ ✄ ✒ ✠ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ✠ ✓ ✞ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✒ ✠ ✓ ✄ ☛ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✥ ☛ ✂ ✙ ✍ ✂ ✍ ✠ ✔ ✒ ✄ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✂ ✄ ✙ ✝ ✞ ✄ ✩ ✍ ✙ ✒ ✙ ✆ ✓ ✒ ❀ ✡ ✂ ✄ ✓ ✥ ✡ ✂ ✄ ✒ ✄ ✖ ✗ ✄ ✒ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✡ ✂ ✄ ✙ ✝ ✘ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ✝ ✆ ✔ ✡ ✄ ✠ ✓ ✞ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✓ ✄ ☛ ✆ ✓ ✄ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✝ ✄ ✘ ✄ ✠ ✡ ✒ ✣ ✌ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ✝ ✄ ✒ ✄ ✠ ✝ ✍ ✂ ✂ ✠ ✒ ✒ ✡ ✔ ✞ ✙ ✄ ✞ ✝ ✆ ✔ ✡ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✔ ✓ ✞ ✄ ✝ ✡ ✂ ✄ ✠ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✆ ✛ ✜ ✎ ✆ ✢ ✠ ✎ ✵ ✓ ✆ ☛ ✎ ✄ ✞ ✜ ✄ ✆ ✛ ✡ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜