Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Compact Slim Stainless Keyboard
4.5Editor score
Ultra compact slim design
Rechargeable lithium battery
One USB receiver for both
In this guide
Finding the right wireless peripherals can transform your daily computing experience significantly. Arteck offers a wide range of affordable and reliable keyboard and mouse combos designed for various needs. These sets combine sleek designs with functional features to enhance productivity and comfort in any workspace setup.
We evaluated ten distinct models from the brand to determine which ones stand out in terms of performance and durability. Our analysis focuses on connectivity options battery longevity ergonomic design and overall value for money. Each product was assessed based on official specifications and user feedback to ensure accuracy.
Every pick below highlights specific strengths that make it suitable for different types of users and environments. Please note that prices and availability can fluctuate frequently so checking current listings is advisable before purchasing. This guide aims to help you make an informed decision quickly and confidently.
Top 3 Picks for Best Arteck Wireless Keyboard and Mouse
Arteck Universal Multi-Device Bluetooth Keyboard and Mouse Full Size Wireless
4.3Editor score
Connects to 3 devices
7 button mouse with DPI
Universal OS compatibility
Arteck Universal Backlit 7-Colors Bluetooth Touch TV Keyboard with Easy Media Control
4.1Editor score
7 color LED backlight
Built-in touchpad mouse
33 feet wireless range
Top 10 Best Arteck Wireless Keyboard and Mouse in 2026 Compared
The following table provides a side-by-side comparison of all ten Arteck wireless keyboard and mouse models to help you find the perfect match for your setup.
ProductsSpecificationsEditor scorePrice
Editor's Choice
Arteck 2.4G Wireless Keyboard and Mouse Combo Stainless Steel
Full size keyboard layout
Stainless steel material
6 month battery life
USB nano receiver
4.5Editor score
Editor's Choice
Arteck 2.4G Wireless Keyboard and Mouse Combo HW193MW162
Slim full size keyboard
Ergonomic mouse design
One USB receiver
Rechargeable battery
4.4Editor score
Best Premium
Arteck Universal Multi-Device Bluetooth Keyboard and Mouse Full Size
Bluetooth multi-device support
3 device switching
7 button mouse
Windows iOS Android
4.3Editor score
Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Compact Slim
Ultra compact keyboard
Stainless steel finish
Low-profile keys
Built-in battery
4.5Editor score
Arteck 2.4G Wireless Keyboard and Mouse Combo Stainless Full Size
Full size layout
Mouse with side buttons
DPI adjustment switch
Rechargeable battery
4.2Editor score
Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Slim Full Size
USB-C charging
Scissors X structure
7 button mouse
Slim profile
4.6Editor score
Arteck Universal Backlit 7-Colors Bluetooth Touch TV Keyboard
7 color backlight
Touchpad integrated
Media control keys
33 feet range
4.1Editor score
Arteck 2.4G Wireless Touch TV Keyboard with Easy Media Control
Touchpad mouse
Solid stainless build
Media hot keys
Nano USB receiver
4.2Editor score
Arteck Bluetooth Keyboard and Mouse Combo Ultra Compact Slim Stainless
Bluetooth connection
Cable-free operation
Stainless steel
10 meter range
4.4Editor score
Arteck 2.4G USB Wireless Keyboard and Mouse Combo Ultra Slim Compact
USB-C rechargeable
Ultra slim compact
7 button mouse
Full size keys
4.3Editor score
1. Arteck 2.4G Wireless Keyboard and Mouse Combo Stainless Steel – Best Overall Combo
Arteck 2.4G Wireless Keyboard and Mouse Combo Stainless Steel
Stainless steel body
Full size layout
6 month battery life
Ergonomic mouse shape
This Arteck 2.4G Wireless Keyboard and Mouse Combo stands out as the top pick for general desktop use. It features a robust stainless steel design that feels premium and sturdy in hand. The full size layout ensures you have all the keys you need including a number pad and arrow keys. With a rating of 4.5 stars it reflects high user satisfaction across thousands of reviews.
Pros
- Durable stainless build
- Long battery life
- One receiver for both
- Comfortable full size keys
- Easy setup process
Cons
- Non-replaceable batteries
- Fixed receiver size
We may earn a commission when you buy through this link, at no additional cost to you.
The keyboard offers low-profile keys that provide a comfortable typing experience without taking up much desk space. The included mouse is ergonomic and reduces wrist strain during long sessions. A single USB receiver handles both devices saving valuable ports on your computer. The rechargeable lithium battery lasts up to six months for the keyboard and four for the mouse on a single charge.
While the build quality is excellent the battery is built-in and cannot be swapped out if it degrades over time. The receiver is small but permanently attached to the mouse which might be a minor inconvenience for some users. These trade-offs are acceptable given the overall value and performance delivered by this comprehensive keyboard mouse package.
Anyone looking for a reliable all-in-one solution for home or office work will find this set highly suitable. It balances durability convenience and comfort effectively. We recommend this model for users who prioritize a sturdy build and long battery life without breaking the bank.
Stainless Steel Durability
The stainless steel material gives the keyboard a heavy-duty feel that resists wear and tear better than plastic alternatives.
Extended Battery Performance
With months of usage on a single charge you rarely need to worry about interruptions to your workflow.
We may earn a commission when you buy through this link, at no additional cost to you.
2. Arteck 2.4G Wireless Keyboard and Mouse Combo HW193MW162 – Great Slim Option
Arteck 2.4G Wireless Keyboard and Mouse Combo HW193MW162
Ultra slim profile
Full size keys
One USB receiver
Rechargeable battery
The Arteck 2.4G Wireless Keyboard and Mouse Combo HW193MW162 offers a similar experience to the top pick but with a focus on slim aesthetics. It maintains a full size layout while keeping the footprint minimal on your desk. The keyboard includes a number pad and arrow keys which are essential for data entry and navigation. Users appreciate the straightforward setup that requires minimal technical knowledge.
Pros
- Space saving design
- Full number pad included
- Easy plug and play
- Comfortable ergonomic mouse
- Good battery duration
Cons
- Keys may feel shallow
- No backlight option
We may earn a commission when you buy through this link, at no additional cost to you.
Both devices connect via a single nano USB receiver stored conveniently inside the mouse. This design choice saves a USB port on your PC while ensuring stable wireless communication. The keyboard features low-profile keys that offer a comfortable typing rhythm. The mouse complements this with an ergonomic shape that reduces stress during extended use.
Some users might find the key profile slightly shallow compared to mechanical keyboards which could affect typing feel for enthusiasts. Additionally there is no backlight feature which limits usability in very dark environments. These limitations are minor considering the price point and the solid performance delivered for everyday tasks.
This combo is ideal for users who want a clean looking setup without sacrificing functionality. It works well with Windows systems and provides a reliable wireless experience. We suggest this model for those who value a slim profile and full size convenience in one package.
Full Size Convenience
Despite its slim profile this keyboard retains a full number pad and arrow keys for complete productivity.
Shared Receiver Efficiency
Using one receiver for both devices keeps your workspace organized and reduces cable clutter.
We may earn a commission when you buy through this link, at no additional cost to you.
3. Arteck Universal Multi-Device Bluetooth Keyboard and Mouse Full Size – Best Multi-Device Flexibility
Arteck Universal Multi-Device Bluetooth Keyboard and Mouse Full Size
Bluetooth connectivity
3 device switching
7 button mouse
Windows iOS Android
The Arteck Universal Multi-Device Bluetooth Keyboard and Mouse Full Size is designed for users who switch between multiple devices frequently. It allows you to connect to three Bluetooth devices simultaneously and switch between them with a single click. This feature is particularly useful for those who work across a PC tablet and smartphone regularly. The keyboard supports major operating systems including Windows iOS Android and Mac OS.
Pros
- Connects to 3 devices
- Quick switching button
- Universal compatibility
- Productive 7 button mouse
- Long battery life
Cons
- Requires Bluetooth capability
- Slightly higher price
We may earn a commission when you buy through this link, at no additional cost to you.
The mouse included in this set is highly productive with seven buttons. It includes a DPI button to switch cursor sensitivity between five different settings. Two side buttons allow for page backward and forward navigation which is helpful for browsing. There is also a dedicated button to switch windows quickly. The keyboard and mouse both use rechargeable batteries that last for months on a single charge.
While the functionality is impressive it requires your computer to have Bluetooth capability which older models might lack. The price is also higher than the standard 2.4G combos due to the advanced connectivity options. These factors are minor drawbacks for users who specifically need multi-device support and advanced mouse features.
We recommend this set for professionals and power users who manage multiple devices daily. It offers unparalleled flexibility and productivity features at a reasonable price point. If you need to switch between devices often this is the best option in the range.
Multi-Device Productivity
Switching between three devices with one click streamlines your workflow across different platforms instantly.
Advanced Mouse Controls
The seven-button mouse with DPI adjustment offers precise control and efficient navigation for diverse tasks.
We may earn a commission when you buy through this link, at no additional cost to you.
4. Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Compact Slim – Best for Small Spaces
Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Compact Slim
Ultra compact keyboard
Stainless steel finish
Low-profile keys
Built-in battery
The Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Compact Slim is perfect for small desks or travel. It features an ultra compact design that saves significant space while maintaining a stainless steel finish for durability. The keyboard is lightweight yet sturdy. It includes low-profile keys that offer a comfortable typing experience despite the reduced size. This makes it easy to use in tight environments.
Pros
- Space saving compact size
- Durable steel construction
- Lightweight design
- Easy setup
- Comfortable ergonomic mouse
Cons
- No number pad
- Limited key travel
We may earn a commission when you buy through this link, at no additional cost to you.
The ergonomic mouse included is designed to reduce stress and provide comfortable use. It pairs with the keyboard using a single nano USB receiver for simplicity. The system runs on rechargeable batteries that provide months of usage on a single charge. Setup is instant upon plugging in the receiver so you can start working immediately without complex configuration steps.
The lack of a number pad may not suit users who frequently enter numeric data. The key travel is also shorter than full size keyboards which might take some getting used to. These trade-offs are acceptable for users who prioritize portability and desk space over full numeric functionality.
This model is ideal for students or professionals with limited desk space. It offers a sleek and functional solution for laptops and desktops alike. We recommend it for anyone seeking a portable and durable wireless keyboard mouse set.
Compact Efficiency
The ultra compact footprint allows you to save desk space without sacrificing typing comfort.
Stainless Build Quality
Constructed from stainless steel the keyboard resists daily wear and provides a premium feel.
We may earn a commission when you buy through this link, at no additional cost to you.
5. Arteck 2.4G Wireless Keyboard and Mouse Combo Stainless Full Size – Best for Productivity
Arteck 2.4G Wireless Keyboard and Mouse Combo Stainless Full Size
Full size layout
Side button mouse
DPI adjustment
Rechargeable battery
The Arteck 2.4G Wireless Keyboard and Mouse Combo Stainless Full Size is tailored for productivity with its full size layout and advanced mouse. It includes a complete number pad and arrow keys for efficient data entry and navigation. The mouse features side buttons for page navigation and a DPI adjustment switch for cursor sensitivity. This makes it versatile for both office work and general computing tasks.
Pros
- Full number pad included
- Mouse with side buttons
- DPI adjustment switch
- Stainless steel body
- Easy plug and play
Cons
- Mouse buttons may be stiff
- Fixed battery life
We may earn a commission when you buy through this link, at no additional cost to you.
The keyboard has a durable stainless steel construction that provides a heavy-duty feeling. It works with a single nano USB receiver for both devices saving ports on your computer. The mouse is ergonomic and designed to reduce wrist stress. Both devices run on rechargeable lithium batteries that offer months of usage on a single charge.
Some users report that the mouse buttons can feel stiff compared to standard mice. The battery life is excellent but fixed which means you must recharge rather than replace batteries. These issues are manageable for users who appreciate the full feature set and build quality offered.
This set is best for office workers who need a full number pad and extra mouse functions. It provides a comfortable and efficient typing experience for daily tasks. We recommend it for users who want maximum utility from a wireless keyboard mouse combo.
Productivity Focus
The full number pad and side mouse buttons significantly enhance efficiency for data-heavy tasks.
Customizable Cursor Control
Adjustable DPI settings allow you to tailor cursor speed to your specific preferences.
We may earn a commission when you buy through this link, at no additional cost to you.
6. Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Slim Full Size – Best USB-C Charging
Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Slim Full Size
USB-C charging
Scissors X structure
7 button mouse
Slim profile
The Arteck 2.4G Wireless Keyboard and Mouse Combo Ultra Slim Full Size brings modern convenience with USB-C charging. It features a Scissors X structure for low-profile keys that offer a comfortable and reliable typing experience. The keyboard maintains a full size layout with arrow keys and a number pad. The mouse is highly ergonomic and includes seven buttons for enhanced control and productivity.
Pros
- Modern USB-C charging
- Comfortable Scissors X keys
- Full size layout
- High ergonomic mouse
- Long battery life
Cons
- USB-C cable included
- Limited OS support
We may earn a commission when you buy through this link, at no additional cost to you.
Using a USB-C charging cable makes recharging the battery much easier than older models. The battery lasts up to six months for the keyboard and four for the mouse on a single charge. Both devices connect via a single nano USB receiver which is stored inside the mouse. This ensures a clean and organized workspace without extra cables or dongles.
The USB-C cable is included but some users might expect wireless charging capabilities at this price. It is designed mainly for Windows systems so compatibility with Mac or mobile devices might be limited. These factors are minor considering the convenience of modern charging and solid performance.
This model is ideal for users who want a full size keyboard with modern charging convenience. It balances comfort and functionality effectively for daily office tasks. We recommend it for anyone prioritizing battery charging speed and typing comfort.
Modern USB-C Convenience
Charging via USB-C provides a faster and more reliable power solution for the keyboard.
Scissors X Comfort
The Scissors X structure ensures stable key presses for a comfortable and quiet typing experience.
We may earn a commission when you buy through this link, at no additional cost to you.
7. Arteck Universal Backlit 7-Colors Bluetooth Touch TV Keyboard – Best for Media Centers
Arteck Universal Backlit 7-Colors Bluetooth Touch TV Keyboard
7 color backlight
Touchpad integrated
Media control keys
33 feet range
The Arteck Universal Backlit 7-Colors Bluetooth Touch TV Keyboard is a unique device designed for media centers and living room computers. It features an integrated touchpad that functions as a mouse which eliminates the need for a separate peripheral. The keyboard offers a choice of seven unique backlight colors to suit your environment. It includes dedicated media hot keys for easy control of entertainment software.
Pros
- Integrated touchpad mouse
- 7 color backlight
- Media hot keys
- Wide OS compatibility
- Long wireless range
Cons
- Touchpad learning curve
- Not for text heavy typing
We may earn a commission when you buy through this link, at no additional cost to you.
Wireless connectivity reaches up to 33 feet allowing you to control your device from a distance. It works with a wide range of systems including Windows Mac and Android. The keyboard also features an auto sleep feature to maximize power usage and battery life. This makes it ideal for use on a couch or in a home theater setup.
The touchpad requires some learning to master navigation compared to a traditional mouse. It is optimized for media control rather than intensive text input or gaming tasks. These limitations are acceptable given the specialized role this keyboard serves in a media environment.
This product is perfect for users who want a universal controller for smart TVs and HTPC. It offers a sleek and convenient solution for managing your entertainment system. We recommend it for living room setups where simplicity and range are key.
All-in-One Control
The integrated touchpad and media keys provide a streamlined experience for entertainment systems.
Living Room Range
With a 33 foot wireless range you can comfortably operate your device from anywhere on the couch.
We may earn a commission when you buy through this link, at no additional cost to you.
8. Arteck 2.4G Wireless Touch TV Keyboard with Easy Media Control – Best Value TV Option
Arteck 2.4G Wireless Touch TV Keyboard with Easy Media Control
Touchpad mouse
Solid stainless build
Media hot keys
Nano USB receiver
The Arteck 2.4G Wireless Touch TV Keyboard is designed for simplicity and functionality in smart TV setups. It includes a built-in touchpad that replaces the need for a separate mouse. The keyboard is constructed from solid stainless steel providing durability and a premium feel. It features media hot keys for convenient access to common functions like play and pause.
Pros
- Solid stainless build
- Built-in touchpad
- Media controls included
- Easy plug and play
- Compact design
Cons
- Uses AAA batteries
- Smaller key layout
We may earn a commission when you buy through this link, at no additional cost to you.
It connects via a nano USB receiver for easy setup without needing Bluetooth. The device works well with TV-connected computers and HTPCs. The wireless range allows control from a distance. It is compact enough to fit on a coffee table or desk without taking up too much space.
Unlike some models this device uses AAA batteries rather than a rechargeable battery. While reliable this adds a recurring cost for replacement. The key layout is also compact which may take time to adjust to for some users. These factors are minor trade-offs for the convenience offered.
This keyboard is ideal for casual users who want to navigate their smart TV interface easily. It provides a solid build and essential media controls at a great price. We recommend it for living room computers and media centers.
Stainless Durability
The solid stainless construction ensures the keyboard withstands regular handling and lasts long.
Media Control Ease
Built-in media hot keys make navigating your entertainment library effortless and intuitive.
We may earn a commission when you buy through this link, at no additional cost to you.
9. Arteck Bluetooth Keyboard and Mouse Combo Ultra Compact Slim Stainless – Best Bluetooth Compact
Arteck Bluetooth Keyboard and Mouse Combo Ultra Compact Slim Stainless
Bluetooth connection
Cable-free operation
Stainless steel
10 meter range
The Arteck Bluetooth Keyboard and Mouse Combo Ultra Compact Slim Stainless offers a wireless experience without dongles. It connects directly to your computer via Bluetooth for a cable-free setup. The keyboard is ultra compact yet made of stainless steel for durability. It supports Windows and Android systems making it versatile for various devices.
Pros
- Bluetooth connectivity
- Ultra compact size
- Stainless steel build
- Long battery life
- Ergonomic mouse
Cons
- Requires Bluetooth adapter
- No USB receiver
We may earn a commission when you buy through this link, at no additional cost to you.
The ergonomic mouse reduces stress and is comfortable to use. The keyboard and mouse both feature long life rechargeable batteries that last months on a single charge. The operating distance is up to 10 meters allowing flexibility in where you sit. Setup is straightforward and does not require extra hardware.
If your computer lacks Bluetooth you will need to purchase a separate adapter. There is also no USB receiver included which might be a downside for older machines. These issues are small given the convenience of a clean wireless setup.
This set is best for users with modern devices that support Bluetooth. It is ideal for laptops and Surface tablets where minimizing ports is a priority. We recommend it for portable and compact computing needs.
Cable-Free Convenience
Bluetooth connectivity allows for a clutter-free desk and works with most modern devices.
Compact Durability
Despite being compact the stainless steel build ensures the keyboard remains sturdy and reliable.
We may earn a commission when you buy through this link, at no additional cost to you.
10. Arteck 2.4G USB Wireless Keyboard and Mouse Combo Ultra Slim Compact – Best Modern Budget Option
Arteck 2.4G USB Wireless Keyboard and Mouse Combo Ultra Slim Compact
USB-C rechargeable
Ultra slim compact
7 button mouse
Full size keys
The Arteck 2.4G USB Wireless Keyboard and Mouse Combo Ultra Slim Compact combines modern charging with a compact design. It uses USB-C for charging which is more convenient than micro USB. The keyboard is ultra slim but still offers a full size layout with a number pad. The mouse includes seven buttons for enhanced productivity and control.
Pros
- USB-C charging
- Slim profile
- Full size layout
- 7 button mouse
- Long battery life
Cons
- Slightly higher price
- Standard receiver
We may earn a commission when you buy through this link, at no additional cost to you.
Both devices are ergonomically designed to reduce stress during long typing sessions. The keyboard connects via a nano USB receiver for reliable performance. The battery life is impressive lasting up to six months for the keyboard and four for the mouse. This ensures minimal interruptions for your work.
While the price is slightly higher than basic models the USB-C charging and extra mouse features justify the cost. The receiver is standard which might not appeal to those wanting ultra small dongles. These trade-offs are minor given the overall functionality and build quality.
This model is ideal for users who want a modern compact keyboard with extra features. It works well for both home and office use. We recommend it for anyone seeking a balance of size and productivity features.
Modern USB-C Charging
USB-C charging makes it easy to power your keyboard with modern cables.
Compact Full Layout
The slim profile saves space while retaining the full number pad for productivity.
We may earn a commission when you buy through this link, at no additional cost to you.
Buying Guide – How to Choose the Best Arteck Wireless Keyboard and Mouse
Choosing the right Arteck wireless keyboard and mouse requires considering connectivity type build material and battery life.
Connectivity Type
Arteck offers both 2.4G USB receiver and Bluetooth models. USB receivers are reliable and work with any USB port but take up space. Bluetooth models offer cleaner setups but require Bluetooth capability on your device.
Select the connectivity type that matches your computer ports and setup preferences.
Keyboard Layout
Some keyboards are full size with a number pad while others are compact. Full size keyboards are better for data entry but take more desk space. Compact models save space but may lack a number pad.
Choose based on whether you frequently use numeric input.
Build Material
Many Arteck keyboards feature stainless steel construction which is durable and resists wear. Plastic models are lighter but may feel less premium. A steel build ensures longevity but adds weight.
Look for stainless steel if you prioritize durability over lightness.
Battery Life
Most models have rechargeable batteries that last months. Some use standard batteries for easier replacement. Longer battery life reduces maintenance but rechargeable batteries are more eco-friendly.
Decide between rechargeable and replaceable batteries based on your preference.
Mouse Features
Standard mice have three buttons but some have side buttons and DPI adjustments. More buttons allow for shortcuts and navigation. A basic mouse is fine for casual use.
Extra mouse features improve productivity for power users.
Ergonomics
Ergonomic shapes reduce wrist strain during long use. Low-profile keys also provide a comfortable typing rhythm. Comfortable devices prevent repetitive strain injuries over time.
Prioritize ergonomic designs if you type for extended periods.
Compatibility
Ensure the keyboard supports your operating system such as Windows iOS or Android. Some models are universal while others focus on specific systems. Compatibility issues can limit functionality.
Check system support before purchasing to ensure smooth operation.
Special Features
Some models offer touchpads backlight or multi-device switching. These features add versatility for media centers or multi-device users. Standard models are simpler and more affordable.
Consider special features based on your specific workflow needs.
How to Use and Care for Your Arteck Wireless Keyboard and Mouse
To begin use insert the USB receiver into your computer and ensure both devices are powered on. The keyboard and mouse usually pair automatically. If using Bluetooth open your settings to connect manually.
Keep the devices clean by wiping them with a soft dry cloth regularly. Dust can accumulate between keys and affect performance. Avoid liquids and harsh chemicals during cleaning.
Charge the devices before the battery dies to maintain optimal performance. Follow the manual for charging times. Store them in a dry place to prevent damage to internal components.
Frequently Asked Questions
Do Arteck wireless keyboards work with Mac computers?
Many Arteck wireless keyboards are universal and support both Windows and Mac. However some models may lack specific Mac keys like Command. Check the compatibility list in the product description to confirm before buying.
How long does the battery last on Arteck keyboards?
Most Arteck keyboards last up to six months on a single charge with typical daily use. Usage patterns affect this duration. Charging is quick and convenient when the battery runs low.
Are these keyboards suitable for gaming?
These keyboards are designed for office and general use rather than dedicated gaming. They offer reliable performance but may lack specific gaming features like mechanical switches. They are sufficient for casual gaming.
Can I use the keyboard without the mouse?
Yes you can use the keyboard independently if it supports standalone operation. Most models allow you to disconnect the mouse for specific tasks. This provides flexibility in how you configure your workspace.
Is there a warranty on Arteck products?
Arteck provides a 24-month warranty for most products. This covers defects in materials and workmanship. You can contact their customer service for support if issues arise.
Do the keyboards have backlit keys?
Most standard models do not have backlit keys. Some specialized models feature multi-color LED backlight. Check the product details to see if lighting is included.
Final Thoughts on Choosing the Best Arteck Wireless Keyboard and Mouse
The Arteck Wireless Keyboard and Mouse lineup offers a wide range of options suitable for various needs and budgets. From slim compact sets to feature-rich multi-device combos there is something for everyone.
Prioritize what matters most to you whether it is battery life build quality or compatibility. A good set will enhance your daily workflow and comfort effectively.
Prices and availability may vary so verify current listings before purchasing. Choose the model that best fits your workflow and budget constraints.