Slippage

Slippage is the difference between the expected price of a cryptocurrency trade when it is initiated and the actual price at which the trade is ultimately executed on the blockchain or exchange. In the volatile and often illiquid markets characteristic of cryptocurrency trading, slippage can be positive (the trader receives a better price than expected) or negative (the trader receives a worse price than expected), though the term is most commonly used to describe unfavorable price deviations that result in the trader paying more for purchases or receiving less for sales than anticipated.

Slippage occurs in both centralized exchanges (CEXs) and decentralized exchanges (DEXs), but its causes and mechanisms differ significantly between the two environments. On centralized exchanges, slippage arises primarily from order book dynamics — when a market order consumes multiple price levels of liquidity before being fully filled, or when price movements occur between order placement and execution. On decentralized exchanges that use automated market maker (AMM) models, slippage is a mathematical certainty that stems from the constant product formula (x * y = k) or similar bonding curve mechanisms that define how token prices change as trades consume liquidity from a pool.

In AMM-based DEXs like Uniswap, SushiSwap, Curve, and PancakeSwap, every trade shifts the ratio of tokens in a liquidity pool, which inherently changes the price. The larger the trade relative to the pool’s total liquidity, the greater the price impact — and therefore the greater the slippage. For example, swapping $100 of ETH for USDC in a pool with $100 million in liquidity would cause negligible slippage, but the same swap in a pool with only $10,000 in liquidity could result in several percent of slippage, meaning the trader receives significantly fewer USDC than the displayed spot price would suggest.

Slippage is one of the most important concepts for any cryptocurrency trader to understand because it directly affects the profitability of trades, the viability of arbitrage strategies, the cost of entering or exiting DeFi positions, and the vulnerability of transactions to front-running and sandwich attacks by MEV (Maximal Extractable Value) bots. Slippage tolerance settings — which define the maximum acceptable deviation from the expected price — are a standard feature of every DEX interface, and setting them correctly is critical for both trade execution and protection against manipulation.

Origin & History

1990s: The concept of slippage originated in traditional financial markets, where it referred to the difference between the expected fill price and actual fill price of stock, futures, or forex orders. The term was widely used by institutional traders and market makers on Wall Street long before cryptocurrency existed.

2009-2013: Early Bitcoin trading on platforms like Mt. Gox experienced extreme slippage due to thin order books and nascent market infrastructure. A single large market order could move the Bitcoin price by several percentage points, and the concept of “moving the market” with a single trade was a routine experience for early crypto traders.

2017: The ICO boom brought thousands of new tokens with extremely low liquidity to centralized exchanges. Slippage became a major concern for traders attempting to buy or sell obscure ERC-20 tokens on exchanges like EtherDelta, where the decentralized order book model resulted in frequent and significant price deviations.

November 2018: Uniswap V1 launched on Ethereum mainnet, introducing the constant product AMM model (x * y = k) to decentralized trading. This design made slippage a mathematical function of trade size relative to pool depth, transforming slippage from an unpredictable market phenomenon into a calculable, deterministic outcome. Uniswap’s interface displayed “price impact” alongside every swap, educating an entire generation of DeFi users about slippage mechanics.

2020 (DeFi Summer): The explosion of decentralized finance brought slippage into mainstream crypto consciousness. Yield farming and liquidity mining created enormous demand for token swaps, but many new pools had shallow liquidity. Traders routinely experienced 5-10% slippage on popular farming tokens, and the need for slippage tolerance settings became a fundamental part of the DeFi user experience. The term “slippage tolerance” entered the standard crypto vocabulary.

January 2020: Curve Finance launched with a specialized AMM formula (StableSwap invariant) designed specifically to minimize slippage for stablecoin-to-stablecoin swaps. By concentrating liquidity around a 1:1 price ratio, Curve achieved slippage rates 100-1000x lower than Uniswap for same-peg asset pairs, demonstrating that AMM design could dramatically mitigate the slippage problem.

May 2021: Uniswap V3 launched with concentrated liquidity, allowing liquidity providers to allocate capital to specific price ranges rather than across the entire price curve. This innovation significantly reduced slippage for trades within active price ranges by concentrating more liquidity where it was most needed.

2021-2022: MEV (Maximal Extractable Value) and sandwich attacks became a major slippage-related concern. MEV bots on Ethereum began routinely front-running DEX trades by detecting pending swaps in the mempool, executing a buy before the victim’s transaction, and then selling after — extracting value by exploiting the victim’s slippage tolerance setting. This led to the development of private transaction pools and MEV protection services like Flashbots and MEV Blocker.

2023-2026: DEX aggregators like 1inch, Paraswap, and CowSwap became the primary tools for minimizing slippage by splitting trades across multiple liquidity sources. Intent-based trading systems emerged, where users specify desired outcomes (e.g., “swap 1 ETH for at least 2,500 USDC”) and solvers compete to find the best execution path, often achieving better prices than direct AMM swaps. Slippage optimization became a core competency of DeFi infrastructure.

“In DeFi, the price you see is not the price you get. Understanding slippage is the difference between a profitable trade and an expensive lesson.”
Hayden Adams, Creator of Uniswap

In Simple Terms

  1. Imagine you walk into a currency exchange at the airport and see a rate of 1 EUR = 1.10 USD on the display board. But by the time the teller processes your transaction, the rate has shifted to 1 EUR = 1.08 USD. You expected $110 for your 100 euros but received $108. That $2 difference is slippage.
  2. Think of slippage like buying concert tickets. You see a price of $50 each, but by the time you click “buy” and complete the purchase, the price has jumped to $55 because other buyers grabbed the $50 tickets first. The $5 difference between what you expected to pay and what you actually paid is slippage.
  3. Picture a swimming pool. If you gently pour a bucket of water into an Olympic-sized pool, the water level barely changes (low slippage). But pour that same bucket into a kiddie pool, and the water level rises dramatically (high slippage). The “pool” is the liquidity, and the “bucket” is your trade size. Bigger trades relative to available liquidity cause more slippage.
  4. Slippage is like the gap between the listed price and actual cost of buying something at a busy auction. You might plan to bid $100 for an item, but if many other people want it too, you end up paying $120 to actually win it. The more demand and the less supply, the bigger the gap.
  5. Consider ordering food at a restaurant with a dynamic menu. You see a steak listed at $30, but by the time the waiter puts your order in, the kitchen has raised the price to $32 because ingredients are running low. That price difference is slippage — the market moved before your order was fulfilled.

Important: Slippage is not always negative. If the market moves in your favor between order placement and execution, you may receive a better price than expected (positive slippage). However, on most DEXs, the AMM formula guarantees some negative slippage on every trade because each swap shifts the pool ratio. Setting an appropriate slippage tolerance is essential — too low and your transaction may fail to execute, too high and you expose yourself to sandwich attacks and excessive price impact.

Key Technical Features

AMM Price Impact Formula

  • In Uniswap V2’s constant product model (x  y = k), the output amount for a swap is calculated as: output = (y  input) / (x + input), where x and y are the pool reserves
  • This formula inherently produces less output than the spot price would suggest, because the trade itself moves the price during execution
  • The “price impact” displayed on DEX interfaces is the percentage difference between the spot price and the effective execution price, which is a direct measure of slippage
  • Larger trades relative to pool reserves produce exponentially greater price impact

How Slippage Occurs on a DEX

  1. A trader initiates a swap (e.g., 10 ETH for USDC) on a DEX like Uniswap and the interface displays an estimated output based on the current pool reserves
  2. The transaction is broadcast to the blockchain mempool, where it waits to be included in a block
  3. While the transaction is pending, other transactions may execute first, changing the pool’s reserve ratios and shifting the price
  4. MEV bots scanning the mempool may front-run the transaction by executing their own swap first, further moving the price against the trader
  5. When the trader’s transaction is finally executed, the pool reserves are different from when the quote was generated, resulting in a different output amount
  6. If the actual output falls within the trader’s slippage tolerance setting, the swap completes; if it exceeds the tolerance, the transaction reverts and the trader pays only the gas fee
  7. After the trader’s swap executes, any MEV bot that front-ran the trade may execute a back-run, selling its position at the now-shifted price, completing a sandwich attack

Slippage Tolerance Settings

  • Slippage tolerance defines the maximum percentage deviation from the quoted price that a trader will accept
  • Common settings range from 0.1% (for stablecoin pairs with deep liquidity) to 5% or higher (for volatile, low-liquidity tokens)
  • Setting tolerance too low causes frequent transaction failures (reverts), wasting gas fees
  • Setting tolerance too high exposes the trader to sandwich attacks, where MEV bots extract value up to the full tolerance amount
  • Some DEXs offer “auto” slippage settings that dynamically adjust based on recent pool volatility and trade size

Types of Slippage in Crypto Markets

  • Price Impact Slippage: The inherent slippage caused by the AMM formula as a trade consumes liquidity and moves the pool price. This is deterministic and calculable before execution.
  • Market Movement Slippage: Slippage caused by other transactions executing before yours, changing the pool reserves between quote time and execution time. This is non-deterministic and depends on network congestion and block timing.
  • MEV-Induced Slippage: Slippage caused by front-running bots that deliberately move the price against you before your transaction executes. This is adversarial and can be mitigated by private transaction pools and MEV protection services.
  • Cross-Chain Slippage: Additional slippage incurred when swapping assets across different blockchains via bridges or cross-chain aggregators, where price quotes may become stale during the bridging process.

Slippage Mitigation Techniques

  • DEX Aggregation: Platforms like 1inch and Paraswap split large trades across multiple liquidity pools and DEXs, reducing price impact on any single pool
  • Concentrated Liquidity (Uniswap V3): Liquidity providers concentrate capital in active price ranges, increasing effective liquidity depth and reducing slippage for trades within those ranges
  • Limit Orders on DEXs: Protocols like 1inch Limit Order and CowSwap allow traders to specify exact execution prices, eliminating slippage entirely at the cost of potential non-execution
  • Private Transaction Pools: Services like Flashbots Protect and MEV Blocker route transactions directly to block builders, bypassing the public mempool and eliminating front-running MEV slippage
  • Time-Weighted Average Price (TWAP) Orders: Breaking large trades into smaller chunks executed over time, reducing price impact on each individual execution

Advantages & Disadvantages

AdvantagesDisadvantages
Market Efficiency Signal: Slippage serves as a real-time indicator of market liquidity depth, helping traders assess the true cost of executing trades of various sizesProfit Erosion: Negative slippage directly reduces trading profits and can turn otherwise profitable arbitrage or trading strategies into losing positions
AMM Viability: The inherent slippage in AMM formulas is what makes automated market making mathematically viable — it compensates liquidity providers for the risk of impermanent lossExploitable by MEV Bots: High slippage tolerance settings are targeted by sandwich attack bots that extract value from traders, creating an adversarial trading environment
Predictability on DEXs: Unlike centralized exchanges where slippage is unpredictable, AMM slippage can be precisely calculated before execution using the pool’s bonding curve formulaBarrier to Large Trades: Institutional-sized trades on DEXs can incur prohibitive slippage, forcing large traders to either fragment orders or use OTC desks, limiting DEX utility
Incentivizes Liquidity Provision: High slippage in shallow pools creates incentives for liquidity providers to deploy capital, improving market depth over timeUser Confusion: Many retail DeFi users do not understand slippage mechanics, leading to unexpected losses and poor trading outcomes
Trade Failure Protection: Slippage tolerance settings provide a safety mechanism that automatically reverts transactions if prices move beyond acceptable bounds, protecting traders from extreme adverse movesGas Fee Waste: When trades fail due to tight slippage tolerance, traders still pay gas fees for the reverted transaction, creating a cost even on non-executed trades
Drives Innovation: The problem of slippage has driven significant innovation in DeFi, including concentrated liquidity, DEX aggregation, intent-based trading, and MEV protection infrastructureStablecoin Depeg Amplification: During stablecoin stress events, slippage in AMM pools can amplify depegging as large sell orders push prices further from the peg than fundamentals warrant
Transparent Pricing: Slippage on AMMs is transparent and calculable from on-chain data, unlike hidden costs in traditional finance or CEX dark poolsFront-Running Vulnerability: The public mempool on most blockchains means pending trades are visible, allowing adversarial actors to profit from anticipated slippage

Risk Management

Trade Sizing Risk

  • Always check the displayed “price impact” on a DEX interface before confirming a swap — price impacts above 1% warrant caution, and impacts above 5% indicate serious liquidity constraints
  • Split large trades into multiple smaller transactions executed over time to reduce cumulative slippage
  • Use DEX aggregators (1inch, Paraswap, CowSwap) that automatically route trades across multiple pools to minimize price impact
  • For very large trades ($100K+), consider OTC desks or institutional liquidity providers that offer fixed-price execution

MEV and Sandwich Attack Risk

  • Use private transaction submission services like Flashbots Protect or MEV Blocker to prevent front-running bots from seeing your pending transactions
  • Avoid setting slippage tolerance higher than necessary — a 10% tolerance on a popular token pair is an open invitation for sandwich attacks
  • Consider intent-based DEXs like CowSwap, which batch orders and execute them off-chain, eliminating mempool-based MEV entirely
  • Monitor your transaction history for signs of sandwich attacks using tools like EigenPhi or Flashbots Explorer

Slippage Tolerance Configuration Risk

  • For stablecoin-to-stablecoin swaps (USDC/USDT, DAI/USDC): use 0.1-0.5% tolerance
  • For major token pairs (ETH/USDC, BTC/WETH): use 0.5-1% tolerance
  • For mid-cap or volatile tokens: use 1-3% tolerance, with MEV protection enabled
  • For micro-cap or newly launched tokens: slippage may need to be 5-15%, but always use private transaction routing
  • Never set slippage tolerance to “auto” without understanding what maximum the interface may select

Cross-Chain Slippage Risk

  • Cross-chain swaps via bridges introduce additional slippage from stale price quotes during the bridging window
  • Mitigation: use cross-chain aggregators that provide guaranteed minimum outputs, or bridge stablecoins and swap on the destination chain to separate bridging risk from slippage risk
  • Be aware that bridge liquidity pools can have significant depth constraints on smaller chains

Volatility-Driven Slippage Risk

  • During high-volatility events (token launches, liquidation cascades, major news), slippage can spike dramatically as liquidity providers withdraw or pools become imbalanced
  • Mitigation: avoid trading during extreme volatility unless necessary; use limit orders that will only execute at acceptable prices
  • Set transaction deadlines (most DEXs allow specifying a time limit) to prevent old transactions from executing at stale prices after network congestion clears

Cultural Relevance

Slippage has become one of the most widely discussed topics in cryptocurrency trading culture, spawning countless memes, cautionary tales, and educational content. The phrase “I got rekt by slippage” is a common refrain in crypto communities, often shared alongside screenshots of trades where the executed price differed dramatically from expectations. This shared experience has created a collective awareness of slippage that drives demand for better DEX infrastructure and MEV protection.

The concept of “slippage tolerance” has become a cultural touchstone in DeFi. New users often learn about slippage the hard way — either by setting tolerance too low and having transactions fail repeatedly (wasting gas), or by setting it too high and falling victim to sandwich attacks. The DeFi community has responded with extensive educational resources, and the question “what slippage should I set?” is one of the most frequently asked in Discord servers and Reddit forums.

MEV and sandwich attacks — which are fundamentally about exploiting slippage — have become one of the most contentious topics in blockchain culture. The emergence of Flashbots and the broader MEV ecosystem has created a philosophical divide: some view MEV extraction as a natural and efficient market mechanism, while others see it as a predatory tax on regular users. This debate touches on fundamental questions about fairness, decentralization, and who benefits from blockchain infrastructure.

In trading culture, slippage awareness separates experienced traders from novices. Professional DeFi traders meticulously plan their execution strategies — using aggregators, private mempools, TWAP orders, and limit orders — to minimize slippage. The ability to execute large trades with minimal slippage is considered a core competency, and sophisticated slippage management strategies are widely shared in trading communities.

The stablecoin trading community, particularly around Curve Finance, has developed a subculture centered on ultra-low slippage. “Curve Wars” — the competition for governance control of Curve’s CRV emissions — are fundamentally about directing liquidity to specific pools to reduce slippage for particular stablecoin pairs. This demonstrates how slippage considerations can drive governance behavior and ecosystem-wide capital allocation decisions.

Real-World Examples

  1. Uniswap Large Swap Price Impact (2021)
  • Scenario: During the peak of DeFi Summer’s successor wave in 2021, a trader attempted to swap 500 ETH (approximately $2 million at the time) for a mid-cap DeFi governance token on Uniswap V2, where the token’s primary liquidity pool had only $5 million in total value locked.
  • Implementation: The constant product formula meant that the trade would consume a significant portion of the pool’s reserves. Uniswap’s interface displayed a price impact warning of approximately 18%, meaning the trader would receive roughly 18% fewer tokens than the displayed spot price suggested. Despite this warning, the trader proceeded with the swap in a single transaction.
  • Outcome: The trader received approximately $1.64 million worth of tokens for their $2 million in ETH — a loss of $360,000 to slippage. Arbitrage bots immediately pounced on the resulting price discrepancy, rebalancing the pool price with trades on centralized exchanges. The incident was widely shared as a cautionary example of why large trades should be split across multiple execution venues.
  1. Sandwich Attack on Ethereum Mainnet (2023)
  • Scenario: A DeFi user submitted a transaction to swap 50 ETH for a popular meme token on Uniswap V3 with a slippage tolerance of 5%. The transaction was submitted to the public Ethereum mempool.
  • Implementation: An MEV bot detected the pending transaction and executed a front-run buy of the meme token (pushing the price up), allowed the victim’s swap to execute at the inflated price (consuming most of the 5% slippage tolerance), and then immediately sold the tokens back (a back-run) at the higher post-swap price. The entire sandwich took place within a single Ethereum block.
  • Outcome: The MEV bot extracted approximately 4.8% of the victim’s trade value — nearly the entire slippage tolerance — as profit. The victim received significantly fewer meme tokens than expected. This type of attack became so common in 2022-2023 that private transaction submission services like Flashbots Protect became essential tools for any DeFi trader executing swaps above a few hundred dollars.
  1. Curve Finance Stablecoin Efficiency (2022)
  • Scenario: A DeFi protocol needed to swap $10 million of USDC to USDT to rebalance its treasury reserves. The treasury manager compared execution options across Uniswap V3 (standard AMM), Curve Finance (StableSwap), and a centralized exchange.
  • Implementation: On Uniswap V3, the estimated slippage for a $10 million USDC-to-USDT swap was approximately 0.15% ($15,000 in slippage cost). On Curve’s 3pool, the same swap showed an estimated slippage of only 0.01% ($1,000 in slippage cost), thanks to Curve’s StableSwap invariant that concentrates liquidity around the 1:1 peg. The centralized exchange quoted approximately 0.05% ($5,000) including maker/taker fees.
  • Outcome: The treasury manager executed the swap on Curve Finance, saving $14,000 compared to Uniswap and $4,000 compared to the centralized exchange. This example demonstrates how specialized AMM designs can dramatically reduce slippage for same-peg asset pairs, and why Curve became the dominant venue for stablecoin trading in DeFi.
  1. DEX Aggregator Slippage Optimization (2024)
  • Scenario: A trader wanted to sell 200,000 ARB tokens (approximately $300,000) on Arbitrum. Direct execution on a single Uniswap V3 pool showed a price impact of 2.3%, while the 1inch aggregator offered a route splitting the trade across multiple pools.
  • Implementation: The 1inch routing algorithm split the 200,000 ARB sell order across four different liquidity sources: 40% through Uniswap V3’s deepest ARB/ETH pool, 25% through Camelot DEX’s ARB/USDC pool, 20% through SushiSwap’s ARB/WETH pool, and 15% through a Balancer weighted pool. Each partial execution experienced minimal price impact because the trade size was small relative to each individual pool’s liquidity.
  • Outcome: The aggregated execution achieved an effective slippage of only 0.4%, compared to the 2.3% that would have occurred on a single pool — saving the trader approximately $5,700. The example illustrates how DEX aggregation has become essential infrastructure for reducing slippage on trades above a few thousand dollars.

Comparison Table

FeatureSlippage (AMM DEXs)Spread (CEX Order Books)Fixed-Price OTC Trading
Price DeterminationBonding curve formula based on pool reservesBid-ask spread set by limit orders from market makersNegotiated fixed price between counterparties
PredictabilityDeterministic and calculable from on-chain pool data before executionVariable, depends on order book depth and market conditions at execution timeFully predictable once price is agreed upon
Size SensitivityHighly sensitive — slippage scales exponentially with trade size relative to pool depthModerately sensitive — large orders walk through multiple order book levelsSize-insensitive once agreed — execution price is guaranteed regardless of trade size
MEV/Front-Running RiskHigh on public mempools — trades visible to MEV bots before executionLower — centralized matching engines process orders without mempool exposureNone — private bilateral execution with no public order visibility
Minimum Trade CostGas fee + slippage (can be near-zero for small trades in deep pools)Maker/taker fee (typically 0.01-0.3%) + minimal spread on liquid pairsNegotiated fee or premium (typically 0.1-1% over market price)
Liquidity SourcePassive liquidity providers in AMM pools; depth varies widely by tokenActive market makers posting limit orders; deep for major pairsInstitutional counterparties, OTC desks, dedicated dealers
Best ForSmall-to-medium swaps, DeFi composability, permissionless accessFrequent trading, tight spreads on major pairs, advanced order typesLarge institutional trades, privacy, guaranteed execution price

FAQ

What is a good slippage tolerance to set on a DEX?

The optimal slippage tolerance depends on the asset pair and market conditions. For stablecoin pairs (USDC/USDT, DAI/USDC), 0.1-0.5% is typically sufficient. For major token pairs (ETH/USDC, WBTC/ETH), 0.5-1% works in normal conditions. For volatile or low-liquidity tokens, 1-5% may be necessary, though you should use MEV protection (Flashbots Protect, MEV Blocker) whenever setting tolerance above 1% to avoid sandwich attacks. If you find yourself needing more than 5%, consider splitting the trade into smaller portions or using a DEX aggregator.

What is the difference between slippage and price impact?

Price impact is a subset of slippage. Price impact refers specifically to the price change caused by your trade moving the AMM bonding curve, and it can be calculated precisely before execution based on the pool reserves. Slippage is the broader term encompassing price impact plus any additional price deviation caused by other transactions executing between your quote and your trade (market movement), front-running bots, and network congestion. On DEXs, price impact is the primary component of slippage, but market movement and MEV can add additional unpredictable deviation.

How do sandwich attacks exploit slippage?

A sandwich attack works in three steps: (1) A bot detects your pending swap in the mempool and front-runs it by buying the same token, pushing the price up. (2) Your swap executes at the inflated price, using up some or all of your slippage tolerance. (3) The bot immediately sells the tokens at the higher post-swap price, pocketing the difference. The bot’s profit is limited by your slippage tolerance setting — this is why setting an unnecessarily high tolerance is dangerous. Using private transaction pools (Flashbots Protect) prevents bots from seeing your pending swap, eliminating this attack vector.

Why do some token swaps require very high slippage tolerance?

Tokens with very thin liquidity pools, anti-bot transfer taxes (common in meme tokens), or deflationary token mechanisms (where a percentage of each transfer is burned or redistributed) may require high slippage tolerance. Some tokens impose a built-in transfer tax of 5-10% on every transaction, which appears as “slippage” even though it is actually a tax taken by the token contract. Always research whether a token has transfer taxes before interpreting high slippage requirements, and be cautious of tokens requiring extreme slippage as this can indicate honeypot scams.

Can slippage be positive (in my favor)?

Yes, positive slippage occurs when you receive a better price than expected. This can happen when the market moves in your favor between quote time and execution, or when a DEX aggregator finds a more optimal route than initially quoted. However, positive slippage is relatively rare on DEXs because AMM price impact always works against the trader. Positive slippage is more common on centralized exchanges during volatile conditions or when using limit orders that execute at better-than-specified prices.

How do DEX aggregators reduce slippage?

DEX aggregators like 1inch, Paraswap, and CowSwap reduce slippage by splitting a single large trade into multiple smaller trades routed across different liquidity pools and exchanges. Instead of consuming deep into one pool’s reserves (causing high price impact), the aggregator distributes the trade so that each pool only absorbs a small portion. The algorithm considers pool depths, gas costs, and routing fees to find the combination that yields the best net output for the trader. For medium-to-large trades, aggregation can reduce slippage by 50-80% compared to single-pool execution.

What is the relationship between slippage and liquidity?

Slippage and liquidity are inversely related — deeper liquidity means less slippage for a given trade size. On AMM-based DEXs, the price impact formula means that a trade consuming 1% of a pool’s reserves produces roughly the same percentage slippage regardless of the pool’s absolute size. Therefore, a $1,000 trade in a $100,000 pool experiences similar slippage to a $100,000 trade in a $10 million pool. This mathematical relationship is why liquidity depth is the single most important factor determining slippage on DEXs, and why protocols compete aggressively for liquidity through incentive programs.

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