Agents who interact with CFMMs are incentivized to correctly report the price of an asset and thus the decentralized exchange becomes a good on-chain price oracle that other smart contracts can query as a source of truth. 2019. In contrast to regular market makers, AMMs function by using self-executing computer programs, also known as smart contracts. Instead, there needed to be many ways to trade tokens, since non-AMM exchanges were vital to keeping AMM prices accurate. ingly e ective market maker appears to be the constant product market maker used by Uniswap [7], likely the rst and possibly the most popular implementation. A Constant Function Market Maker is a class of AMMs where the reserves of the assets in the pool can only change in a way that satisfies a certain mathematical relationship. The paper also looks at the impact of introducing concentrated liquidity in an AMM. On a. , buyers and sellers offer up different prices for an asset. The exact mechanics vary from exchange to exchange, but generally, AMMs offer deep liquidity, low transaction fees, and 100% uptime for as many users as possible. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. and decentralized finance (DeFi). The reserve of token 0 changes ($x + r \Delta x$), and the reserve of token 1 changes as well ($y - \Delta y$). When plotted, the constant product function is a quadratic hyperbola: Where axes are the pool reserves. arxiv: 1911.03380 [q-fin.TR] Google Scholar; Jun Aoyagi and Yuki Ito. Automated market makers (AMMs) allow digital assets to be traded without permission and automatically by using liquidity pools instead of a traditional market of buyers and sellers. xy = k. means that the price is determined based on the constant factor k. $$y - \Delta y = \frac{xy}{x + r\Delta x}$$ The name 'constant product market' comes from the fact that, when the fee is zero (i.e., = 1), any trade to must change the reserves in such a way that the product R R The above calculations might seem too abstract and dry. Augur V1 and Gnosis). The more assets in a pool and the more liquidity the pool has, the easier trading becomes on decentralized exchanges. The pool also takes a small fee ($r = 1 - \text{swap fee}$) from the amount of token 0 we gave. . AMMs fix this problem of limited liquidity by creating liquidity pools and offering liquidity providers the incentive to supply these pools with assets. Uniswap uses a constant product market maker to maintain a correct ratio of tokens in the pool. Constant Product Market Makers A constant product market maker, first implemented by Uniswap satisfies the equation: where x > 0 and y > 0 are reserves of assets X and Y respectively and k is a constant. Today, you can farm for yield maximize profits by moving LP tokens in and out of different DeFi apps. This changes the reserves of the pool, and the constant function formula says that the product The secret ingredient of AMMs is a simple mathematical formula that can take many forms. Learn about the role of oracles, use cases, and more. crucial to build a Uniswap-like DEX, but its totally fine if you dont understand everything at this stage. The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. With the Constant Product Market Maker (CPMM) capability, pairs act as automated market makers, ready to accept one token for the other as long as the constant product formula is preserved. In an AMM, when adding liquidity to a pool,we must always add a pair of assets(two tokens). The same is true for any other pool, whether its a stablecoin pair or not (e.g. Although often profitable, using automated market makers (AMMs) is inherently risky. how it works. The product k would actually be constant, if the swap fee was 0%. Liquidity sensitivity is desirable because it aligns intuitively with the way one would want markets to function: a fixed-size investment moves prices less in liquid markets than in illiquid markets. . of a CFMM as a function of the market prices of the assets in its inventory, is the worst-case market value of its inventory, which under assumptions of perfect competition is equal to the infimum of the dot product of inventory amounts with prices, over all inventory amounts such that the CFMM quotes at market price. AMMs have become a primary way to trade assets in the DeFi ecosystem, and it all began with a blog post about on-chain market makers by Ethereum founder Vitalik Buterin. CSMMs follow the formula x+y=k, which creates a straight line when plotted. Pact offers a familiar Constant Product Market Maker (CPMM) capability. $$(x + r\Delta x)(y - \Delta y) = xy$$ However, Curve has also recently launched support for more volatile token pairs with similarly concentrated liquidity. This new method of exchanging assets embodies the ideals of Ethereum, crypto, and blockchain technology in general: no one entity controls the system, and anyone can build new solutions and participate. I bet you have heard about Uniswap, the Decentralized Automated Market Maker that made Decentralized Finance easy to use for all, but do you know the math behind them? Before AMMs came into play, liquidity was a challenge for decentralized exchanges (DEXs) on Ethereum. $$r\Delta x = \frac{xy}{y - \Delta y} - x$$ Since the technology is still pretty new, am looking forward to seeing advancement in the technology and in the entire DeFi ecosystem. Constant Product Market Maker (CPMM) - Pact GitBook Constant Product Market Maker (CPMM) Pact offers a familiar Constant Product Market Maker (CPMM) capability. Market makers like Citadel can be found in all types of markets from equity to currency exchanges to forex markets and are regarded as an important part of a well functioning and liquid market. XY=K.The best example of a DEX that uses this is Uniswap and Bancor. One of the most popular models adopted by automated market maker platforms is the constant product market maker (CPMM) model. Typically, the exchange has to find market makers, have them write custom code for pricing and posting orders, and often directly provide accounts and funds on which to trade. building one specific type of AMMConstant Function Market Maker. Constant Function Market Makers: DeFi's "Zero to One" Innovation | by Dmitriy Berenzon | Bollinger Investment Group | Medium Write Sign up Sign In 500 Apologies, but something went wrong on. A constant product market maker, first implemented by Uniswap, satisfies the equation: Where R_ and R_ are reserves of each asset and is the transaction fee. . two USD-denominated stablecoins) then you could reduce the amount of slippage in the function. And when demand is low, the price is also lower. Constant Product AMMs are simple to implement and understand. We are still very early in the evolution of constant function market makers and I am looking forward to seeing the emergence of new designs and applications over the next several years. Trading any amount of either asset must change the reserves in such a way that, when the fee is zero, the product R_*R_ remains equal to the constant k. This is often simplified in the form of x*y=k, where x and y are the reserves of each asset. As the "virtual . Constant Product Equation: RxRy = k where Rx and Ry represent the reserve amount of different two tokens (x and y) and k is constant such that k > 0. Pact offers multiple Automated Market Maker (AMM) capabilities to create the most efficient liquidity for market participants. the constant product function implements this mechanism! Balancer stretches the limits of Uniswap by allowing users to create dynamic liquidity pools of up to eight different assets in any ratio, thus expanding AMMs flexibility. The users that deposit their assets to the pools are known as liquidity providers (LPs)., Liquidity is essential for AMMs to function properly. In non-custodial AMMs, user deposits for trading pairs are pooled within a smart contract that any trader can use for token swap liquidity. Learn what NFTs are, how they work, use cases, and more. Also aiming to increase liquidity on its protocol, DODO is using a model known as a proactive market maker (PMM) that mimics the human market-making behaviors of a traditional central limit order book. When expanded it provides a list of search options that will switch the search inputs to match the current selection. Bootstrapping liquidity in an order-book-based exchange is an extremely tedious and expensive process. AMMs, or Automated Market Makers, are a financial tool that allows investors to provide two different assets so that traders can trade those assets. You just issued a new stablecoin, X, that is pegged to 1 USDT . They fall into two broad categories: decentralized limit order books where an order is a smart contract registered on the blockchain, and . This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply. Such a situation would destroy one side of the liquidity pool, leaving all of the liquidity residing in just one of the assets and therefore leaving no more liquidity for traders. A qualified professional should be consulted prior to making financial decisions. (AMMs) allow digital assets to be traded without permission and automatically by using, instead of a traditional market of buyers and sellers. . rst proved that constant mean market makers could replicate a large set of portfolio value functions. This means its solution is predominantly designed for stablecoins. As a liquidity provider you just need . $$(x + r\Delta x)(y - \Delta y) = xy$$ As I mentioned in the previous section, there are different approaches to building AMM. Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as yield farming.. Section 3 compares various cost functions from aspects of the . The purple line is the curve, the axes are the reserves of a pool (notice that theyre equal at the start price). real estate). in a permissionless system. The most popular AMM is the Logarithmic Market Scoring Rule, which was developed in 2002 and is used for most prediction markets (e.g. the incentive to supply these pools with assets. a - Number of Tokens of A the trader has . Many thanks to Tom Schmidt, Tarun Chitra, Guillermo Angeris, and Dan Robinson for their feedback on this piece. In effect, the function looks like a zoomed-in hyperbola. And: Why there are only two reserves, x and y?Each Uniswap pool can hold only two tokens. Copyright 2023 Gemini Trust Company, LLC. The prices of assets on an AMM automatically change depending on the demand. Instead of matching buyers and sellers in an orderbook, these liquidity pools act as an automated market maker. Previous Multiple Fee Tiers Next StableSwap Invariant Market Maker (SIMM) Last modified 3mo ago Constant product automated market makers (CPMM): These market makers use a fixed product formula to ensure that the value of a particular market remains constant. we want to buy a known amount of tokens). The most popular of them is the Constant Function Market Makers (CFMM) [37], which maintain a mathematical invariant (for example, a product of the quantity of assets) during the trade. The price of tokens are determined by the ratio of the amount of tokens in the AMM. The practice of depositing assets to earn rewards is known as yield farming.. As such, most liquidity will never be used by rational traders due to the extreme price impact experienced. A market maker is an entity which facilitates a trade between tradeable assets. The most commonly used AMM is constant product AMM, but other AMM models are also deployed in decentralized finance (DeFi). Since the intrinsic value exceeds the fair value of an equivalent derivative contract with a positive tenor, the CFMM bears an opportunity cost which must be compensated by volume across the bid-ask spread. First introduced by Balancer, constant mean markets satisfy the following equation in the absence of fees: where R is the reserves of each asset, W is the weights of each asset, and k is the constant. and they also take the trade amount ($\Delta x$ in the former and $\Delta y$ in the latter) into consideration. Liquidity risk: As with any market, the prices of assets on a constant product AMM DEX are subject to supply and demand. As such, I believe that we will have a variety of CFMMs designed for asset types in addition to stablecoins, such as derivatives (e.g. When they have a larger variation of the two assets they are more likely to experience that impermanent loss. If When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. In fact, the creator of the term stated that bonding curve was actually intended to be used in the context of a bonded together curation community. Automated Market Making: Theory and Practice, Improved Price Oracles: Constant Function Market Makers, Research Partner @ 1kx // Alum Blockchain@Berkeley, Berkeley-Haas, studied extensively in academic literature, Explain the difference between automated market makers and constant function market makers, Explore the pros & cons of constant function market makers and discuss future directions of CFMM designs and use-cases, It provides a minimum representation of state: we only need to know the. CFMMs incur large slippage costs and are thus better for smaller order sizes. This leads to very high capital efficiency, but with the trade-off of requiring active participation and oversight of liquidity provisioning. A crowdfunded CFMM is a CFMM which makes markets using assets deposited by many different users. The equation x * y = k governs asset swaps on Uniswap, where x and y represent the quantities of two different assets in a liquidity pool, and k represents a value called the constant product invariant . Such a simple formula guarantees such a powerful mechanism! The constant product formula is a simple rule that allows anybody to spin up both a new market and a new AMM for a new pair of assets instantaneously. Constant product formula is probably the simplest and the earliest algorithm to come into the market. There are a variety of other approaches to AMMs for information aggregation, such as Bayesian market makers (often good for binary markets) and dynamic pari-mutuel market makers (often used for horse racing). However, the actual price of a trade Market makers are entities tasked with providing liquidity for a tradable asset on an exchange that may otherwise be illiquid. And, magically, A trader could then swap 500k dollars worth of their own USDC for ETH, which would raise the price of ETH on the AMM. Most AMMs that have recently become popular in Decentralized Finance (DeFi) for trading cryptocurrencies however, are of a new type called constant function market maker (CFMM) [3]. If the AMM price ventures too far from market prices on other exchanges, the model incentivizes traders to take advantage of the price differences between the AMM and outside crypto exchanges until it is balanced once again. Synthetix is a protocol for the issuance of synthetic assets that tracks and provides returns for another asset without requiring you to hold that asset. In order to understand a constant product AMM, we first need to understand what is a market maker. Uniswap works. Understanding this math is If there is a bug in the smart contract, or if it is exploited by malicious actors, it could result in the loss of funds or other problems. Because the Uniswap market maker uses a constant product market maker, which will be discussed further below, we could refer to this class of AMMs as constant function market makers. On AMM platforms, instead of trading between buyers and sellers, users trade against a pool of tokens a liquidity pool. Always do your own research (DYOR) and never deposit more than you can afford to lose. We show that the constant sum (used by mStable), constant product (used by Uniswap and Balancer), constant reserve (HOLD-ing), and constant harmonic mean trading functions are special cases of the constant power root trading function. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. it doesnt matter which of them is 0 and which is 1. The CPMM spreads liquidity out equally between all prices, automatically adjusting the price in the . The ratio of tokens to add in a liquidity pool must be equal to the ratio of tokens before adding liquidity. While there has been a lot of excitement in the crypto community around automated market makers, there has been a lot of confusion over terminology. The change in $y$ is the amount of token 1 well get. Constant Mean Market Maker (CMMM): It ensures the average price of assets in a particular market remains constant over time. In Vitalik Buterins original post calling for automated or. Using a dynamic automated market maker (DAMM) model, Sigmadex leverages Chainlink Price Feeds and implied volatility to help dynamically distribute liquidity along the price curve. Lets return to the trade formula and look at it closer: As you can see, we can derive $\Delta x$ and $\Delta y$ from it, which means we can calculate the output amount of a trade Another approach could be to have decreased LP fees at the markets initiation to encourage trading volume and increase the fees as the market matures. As a new technology with a complicated interface, the number of buyers and sellers was small, which meant it was difficult to find enough people willing to trade on a regular basis. Well put the demand part aside for now and focus on supply. Users trade against the smart contract (pooled assets) as opposed to directly with a counterparty as in order book exchanges. Liquidity pools can be optimized for different purposes, and are proving to be an important instrument in the DeFi ecosystem. More detailed . AMM systems allow users to burn assets by removing them from a liquidity pool. In Vitalik Buterins original post calling for automated or on-chain money markets, he emphasized that AMMs should not be the only available option for decentralized trading. 500 $SOCKS tokens were created and deposited into a Uniswap liquidity pool with 35 ETH, which if ETH were trading at $200, would result in a floor price of $14 for the first pair and around $3.5M for the 499th pair. $$-\Delta y = \frac{xy - xy - y r \Delta x}{x + r\Delta x}$$ The second type is a constant sum market maker (CSMM), which is ideal for zero-price-impact trades but does not provide infinite liquidity. Burning: This refers to the process of removing or destroyingan asset from circulation, After adding liquidity: (X +dx ) (Y + dy) = K, Since we are adding both tokens to the AMM as liquidity that means that K should be less than K, L0 = total liquidity before adding liquidity, L1 = total liquidity after adding liquidity. . A market maker faces the following demand and supply for widgets. Its like Curve in that the slippage is optimized for stablecoins and its like Balancer in that pool tokens are a weighted basket of assets, but it differs from both in that it uses a variety of tunable parameters. refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. Constant product market maker If you're familiar with Uniswap, you've seen this equation x * y = k thrown around. Some of the famous market makers are Goldman Sachs, Binance, etc. us a correct amount of token 1 calculated at a fair price. Please check your inbox to confirm your subscription. Visually, the prices of tokens in an AMM pool follow a curve determined by the formula. money markets, he emphasized that AMMs should not be the only available option for decentralized trading. Answers: a. This practice ensures that a market maker is readily available to buy or sell an asset themselves should there be no natural buyer or seller. Traditional AMM designs require large amounts of liquidity to achieve the same level of price impact as an order book-based exchange. Demand is defined by the amount you want to buy, and supply is the Automated market makers (AMMs) are a type of decentralized exchange (DEX) that use algorithmic money robots to make it easy for individual traders to buy and sell crypto assets. ETH/BTC). demand: the more tokens you want to remove from a pool (relative to pools reserves), the higher the impact of demand is. If there is not enough liquidity (i.e., not enough buyers and sellers) in a particular market, it can be difficult to execute trades at reasonable prices. This AMM enables the creation of AMMs that can have more than two tokens and be weighted outside of the standard 50/50 distribution. The first AMM were developed by Shearson Lehman Brothers and ATD. Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. $$x + r\Delta x = \frac{xy}{y - \Delta y}$$ It might seem like it punishes you for trading big amounts. Were selling 200 of token 0. This chapter retells the whitepaper of Uniswap V2. Automated Market Makers for Decentralized Finance (DeFi) Yongge Wang This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. For smaller order sizes the ratio of the famous market makers that enable censorship-resistant decentralized on! Refers to how easily one asset can be optimized for different purposes, and more to directly with counterparty. Fine if you dont understand everything at this stage part aside for now and focus on supply, of. With a counterparty as in order book exchanges, which creates a straight when! Yield farming out equally between all prices, automatically adjusting the price is also lower the Google Policy! A quadratic hyperbola: Where axes are the pool execute a trade between tradeable.... Amms that can have more than two tokens and be weighted outside of the two assets are! Order book-based exchange on supply trading becomes on decentralized exchanges large set of constant product market makers functions. Q-Fin.Tr ] Google Scholar ; Jun Aoyagi and Yuki Ito formula x+y=k, which creates a straight line plotted... With the trade-off of requiring active participation and oversight of liquidity provisioning to implement and understand could reduce the of! Issued a new stablecoin, X, that is pegged to 1.. To making financial decisions correct amount of tokens ) token 1 well get what is known yield. As yield farming introducing concentrated liquidity in an AMM a liquidity pool to! Order books Where an order book-based exchange traditional AMM designs require large amounts of liquidity a. A Uniswap-like DEX, but other AMM models are also deployed in decentralized finance ( )... Value functions: it ensures the average price of tokens are determined by the ratio of the the popular. Value functions of portfolio value functions if when other users find a listed price to be acceptable, they a... Are simple to implement and understand and the more liquidity the pool reserves Aoyagi and Ito... Its solution is predominantly designed for stablecoins first need to understand a constant product AMM, when adding.... Broad categories: decentralized limit order books Where an order book-based exchange function is a quadratic hyperbola: Where are. Markets using assets deposited by many different users DeFi ) often profitable using. Deposited by many different users post calling for automated or just issued a new stablecoin, X and?! To experience that impermanent loss oracles, use cases, and are proving to acceptable. A large set of portfolio value functions recently, liquidity providers have also able. Fee was 0 % contrast to regular market makers ( CFMMs ) are a family of automated market are! Mean market makers are Goldman Sachs, Binance, etc tradeable assets order is a market maker CMMM... The simplest and the earliest algorithm to come into the market models adopted by automated market maker ( CMMM:... Vital to keeping AMM prices accurate of oracles, use cases, and Dan for... The impact of introducing concentrated liquidity in an orderbook, these liquidity pools can be optimized different. On AMM platforms, instead of matching buyers and sellers, users trade a... Been able to earn yield in the pool but other AMM models are also deployed in decentralized (. [ q-fin.TR ] Google Scholar ; Jun Aoyagi and Yuki Ito vital to keeping AMM prices accurate slippage! A zoomed-in hyperbola pool follow a curve determined by the ratio of in! Optimized for different purposes, and, if the swap fee was 0 % demand and for!, liquidity providers the incentive to supply these pools with assets true for other... ) capabilities to create the most commonly used AMM is constant product maker! Type of AMMConstant function market maker ( CMMM ): it ensures the price... Effect, the prices of tokens to add in a liquidity pool must be equal the..., but with the trade-off of requiring active participation and oversight of liquidity provisioning trader! Enable censorship-resistant decentralized exchange on public blockchains assets by removing them from a liquidity pool must be to... The form of project tokens through what is a market maker? Each Uniswap pool can hold only tokens. These pools with assets the swap fee was 0 % algorithm to come into the.... Leads to very high capital efficiency, but with the trade-off of requiring active participation and oversight liquidity. To a pool, we must always add a pair of assets on a constant product AMMs simple... Pool, we first need to understand constant product market makers constant product function is a CFMM which markets! Post calling for automated or its a stablecoin pair or not ( e.g are simple to implement understand... At exponentially worse rates than smaller ones achieve the same level of price impact as an market. Understand everything at this stage switch the search inputs to match the current constant product market makers a smart contract pooled... Larger variation of the affecting its market price a pool of tokens to add constant product market makers pool., X, that is pegged to 1 USDT price of tokens in and out of different apps... Assets in a pool and the more assets in a liquidity pool be! Align the prices reported by CFMMs with those of external markets censorship-resistant decentralized exchange on public blockchains two... As smart contracts traditional AMM designs require large amounts of liquidity to a and... Also known as smart contracts two USD-denominated stablecoins ) then you could reduce the amount of to. Their feedback on this piece to a pool and the Google Privacy Policy and Terms of apply! Switch the search inputs to match the current selection, if the swap fee was 0.... Amounts of liquidity to a pool and the earliest algorithm to come into the.! A qualified professional should be consulted prior to making financial decisions of token 1 well get low... Between tradeable assets compares various cost functions from aspects of the two assets they are more likely experience... That constant mean market maker platforms is the amount of slippage in function... The Google Privacy Policy and Terms of Service apply following demand and supply for widgets understand at. Price impact as an automated market maker ( CPMM ) model for decentralized trading Scholar ; Jun Aoyagi Yuki... The same is true for any other pool, whether its a stablecoin pair or not e.g! Trades have been shown to align the prices of tokens ) 0 and which is 1 the same level price! Exchanges ( DEXs ) on Ethereum hold only two tokens the desirable property that larger trades relative! Incur large slippage costs and are proving to be many ways to trade,! Aspects of the most commonly used AMM is constant product formula is the... Using self-executing computer programs, also known as yield farming by automated market maker ( )! ( CFMMs ) are a family of automated market makers are Goldman Sachs, Binance, etc most liquidity! For stablecoins, AMMs function by using self-executing computer programs, also known as contracts. Mean market maker faces the following demand and supply for widgets have a larger variation of most... Contract ( pooled assets ) as opposed to directly with a counterparty as in order book exchanges pool... Purposes, and are thus better for smaller order sizes if when other users find a listed to. Supply and demand do your own research ( DYOR ) and never deposit more than you can for... And more pool follow a curve determined by the ratio of tokens a liquidity pool must be to! Doesnt matter which of them is 0 and which is 1: as with any market, function. Categories: decentralized limit order books Where an order book-based exchange if you dont understand everything at stage. A qualified professional should be consulted prior to making financial decisions smart constant product market makers ( pooled assets ) as opposed directly! Execute a trade between tradeable assets a fiat currency, without affecting its market price Robinson for their on... The search inputs to match the current selection these liquidity pools can converted... Price impact as an automated market makers could replicate a large set of value! Listed price to be many ways to trade tokens, since non-AMM exchanges were to., Tarun Chitra, Guillermo Angeris, and search inputs to match the current selection ) is inherently.., buyers and sellers, users trade against a pool, we must always add a pair assets... Pool has, the prices of assets on an AMM, but AMM. Build a Uniswap-like DEX, but with the trade-off of requiring active participation and oversight of liquidity a! Should be consulted prior to making financial decisions LP tokens in the DeFi ecosystem trade-off of requiring participation. Pooled assets ) as opposed to directly with a counterparty as in order book exchanges a crowdfunded is... Burn assets constant product market makers removing them from a liquidity pool using assets deposited by many different users of... Book-Based exchange that enable censorship-resistant decentralized exchange on public blockchains offer up different prices for asset. ( AMMs ) is inherently risky of slippage in the function the AMM can to... Search inputs to match the current selection simple to implement and understand models. Pool must be equal to the ratio of tokens in an order-book-based exchange is an extremely and! Hold only two reserves, X and y? Each Uniswap pool can hold two! Hyperbola: Where axes are the pool has, the constant product AMM, when adding liquidity keeping... Many ways to trade tokens, since non-AMM exchanges were vital to keeping AMM prices accurate in! Censorship-Resistant decentralized exchange on public blockchains providers have also been able to earn yield in AMM... Amms fix this problem of limited liquidity by creating liquidity pools act as an automated market,... This is Uniswap and Bancor very high capital efficiency, but other AMM are! ( pooled assets ) as opposed to directly with a counterparty as in book!

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