Explore the premier mobile app development companies in the UK that stay on top of industry trends, and use advanced tools and high-end custom development to deliver innovative, engaging and high-performance apps for a variety of operating systems. Filter by cost, reviews and team size to find the most suitable team for your goals and budget.
- Home
- Mobile App Development Companies
- United Kingdom
Best United Kingdom Mobile App Developers
Every agency featured on DesignRush is vetted for expertise and client satisfaction to support your decision-making. Some listings may be sponsored.
Build The Future
We blend cutting-edge technology with beautiful design in unique ways to build the future...
Top Services:
- Web Development
- WordPress Website Design
- Web Design
- eCommerce Development
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $105/hr
- Minimal Budget
- $25,000 - $50,000
Digital Innovation Experts
At 10up, we think that where design and engineering knowledge intersect is where digital innovation frequently occurs...
Top Services:
- Web Development
- Web Design
- UI/UX Design
- Creative Services
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 100 - 249
- Average Hourly Rate
- $199/hr
- Minimal Budget
- $50,000 & Up
Your Digital Innovator
DigitSense helps companies create amazing digital products focusing on user experience, scalability, and user acquisition. From web and mobile app design and development to digital marketing, we do it all! Transform your digital presence with DigitSense - crafting exceptional digital products prioritizing...
Top Services:
- Web Design
- Web Development
- eCommerce Development
- Software Development
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $55/hr
- Minimal Budget
- $10,000 - $25,000
Resources for the BOLD
Whether you're an individual, start-up, or established business, we offer a range of IT solutions to fit your needs and take your business to the next level...
Top Services:
- Digital Marketing
- Web Development
- Social Media Marketing
- WordPress Website Design
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $25/hr
- Minimal Budget
- Under $1,000
Transform AI Experiments Into Workflows
&above is an AI product agency that helps scale-ups and enterprises turn AI experiments into a new way of working. With a problem-first, design-led approach, we design and build agentic products and AI operating systems that people actually use every day - not pilots that stall...
Top Services:
- AI Development
- Software Development
- Engineering
- UI/UX Design
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $100/hr
- Minimal Budget
- $50,000 & Up
Innovative Thinking
We are a Manchester based Agency with a focus on Design, Development and Marketing. You will have a dedicated team on hand, devoted to making your business a success. We have the ideas that can bring your brand to life, creating campaigns that are beautiful, engaging and effective...
Top Services:
- Web Design
- Branding
- SEO
- Email Marketing
- Mobile App Development
- Show more
- Location
- Manchester, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $150/hr
- Minimal Budget
- $1,000 - $10,000
Smart Digital Solutions, Powered by Practical AI
We're 383. We get the worlds biggest companies fit for the future, helping them to compete in an era of changing customers, competitors and technology...
Top Services:
- Design Services
- Graphic Design
- Product Design
- UI/UX Design
- Web Design
- Show more
- Location
- Birmingham, United Kingdom
- Number of Employees
- Under 49
Solved turns complex computing problems into practical solutions with IT strategies, app development, digital engineering, agile expertise, data analytics, cybersecurity, and other managed IT services. With innovative services and affordable prices, Solved works with clients all over the globe...
Top Services:
- UI/UX Design
- Software Development
- Web Development
- IoT
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $100/hr
- Minimal Budget
- $25,000 - $50,000
Better Service
eDesk Solutions is Leading IT Company Which is Providing Web Designing, Graphics, Mobile Application Development IOS Android & Hybrid, Agile Software...
Top Services:
- Web Development
- Graphic Design
- Digital Marketing
- Cybersecurity
- Mobile App Development
- Show more
- Location
- Luton, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $10/hr
- Minimal Budget
- Under $1,000
Right Place, Right Time, Right Experts
With ECO & Tech you can always expect a high-quality product and unique approach, followed by all-inclusive technical support and always with on-time and on-budget guarantee!...
Top Services:
- Web Development
- Managed Services
- eCommerce Development
- UI/UX Design
- Software Development
- Show more
- Location
- Newbury, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $25/hr
- Minimal Budget
- Under $1,000
Digital transformation and mobile solutions.
Digital Republic empowers businesses by harnessing the potential of web and mobile applications, cloud commerce, AI, and machine learning technologies. Our comprehensive approach ensures that our clients stay ahead in the digital landscape, driving innovation and achieving sustainable growth...
Top Services:
- Digital Strategy
- Software Development
- Digital Services
- eCommerce Development
- Mobile App Development
- Show more
- Location
- Chichester, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $75/hr
- Minimal Budget
- $10,000 - $25,000
Pushing the Boundaries of Digital Signage at Scale
STRATACACHE is accelerating the shift of digital retail transformation by having a full scope of technology under one roof. Our retail solutions allow us to be partners in creating an in-store evolution, fitting into your existing ecosystem by connecting different technologies to truly drive a frictionless...
Top Services:
- IT Services
- Managed Services
- Video Production
- Software Development
- Web Design
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 1000 & Up
We are a dedicated WordPress Agency and experts in digital marketing
We are a specialist web building agency working with WordPress and Blockchain technologies...
Top Services:
- Web Development
- Web Design
- eCommerce Development
- Digital Marketing
- CRO
- Show more
- Location
- Leatherhead, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $70/hr
- Minimal Budget
- $1,000 - $10,000
If Your Business Matters, Your Process Matters
At BP3, we transform your complex challenges into streamlined success stories through AI and Automation...
Top Services:
- Business Consulting
- UI/UX Design
- AI Development
- IoT
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 100 - 249
We Meet & Exceed Your Aspirations
Vecro Tech is a Glasgow-based digital agency that leverages its industry insights and technical knowledge to design contemporary websites. Our mission is to help businesses across central Scotland create eye-catching, fully responsive sites tailored specifically for them; enhance the visibility of your brand...
Top Services:
- Digital Marketing
- SEO
- PPC
- Web Design
- Web Development
- Show more
- Location
- Glasgow, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $99/hr
- Minimal Budget
- $1,000 - $10,000
Corporation Pop - Creating Deeply Engaging Interactive Experiences
We create deeply engaging interactive experiences that connect you with your customers...
Top Services:
- UI/UX Design
- Web Development
- Web Design
- VR/AR
- Mobile App Development
- Show more
- Location
- Manchester, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $75/hr
- Minimal Budget
- $25,000 - $50,000
A next-gen firm offering complete, seamless, result-driven, cost-effective services and solutionsA next-gen firm offering complete, seamless, result-driven, cost-effective services and solutions
We can help lead your organization with advanced IT strategies and creative solutions through top-notch IT consulting services...
Top Services:
- Web Design
- eCommerce Development
- Web Development
- Digital Marketing
- Mobile App Development
- Show more
- Location
- Croydon, United Kingdom
- Number of Employees
- Under 49
- Minimal Budget
- $1,000 - $10,000
Creating Impactful Solutions for Brands Like Yours.
NaughtyDuk is a digital studio that specializes in creating impactful solutions for brands like yours. Founded in 2023 by the digital specialist Jack Vanstone...
Top Services:
- Web Design
- Web Development
- Digital Services
- Digital Strategy
- Digital Marketing
- Show more
- Location
- Manchester, United Kingdom
- Number of Employees
- Under 49
Make The World Digitize.
SysStaff stands as a premier custom software development company in London, setting industry benchmarks with its innovative solutions and unwavering commitment to excellence. Renowned for its cutting-edge technologies, the company transforms business visions into reality, crafting bespoke software that...
Top Services:
- Digital Services
- Web Development
- eCommerce Development
- Digital Marketing
- IT Services
- Show more
- Location
- Gloucester, United Kingdom
- Number of Employees
- 100 - 249
- Average Hourly Rate
- $20/hr
- Minimal Budget
- $1,000 - $10,000
Where Technology Meets Imagination.
Devlinko specializes in providing customized web design, development, SEO, and digital marketing solutions, equipping businesses with the tools and strategies necessary to thrive online. With a focus on delivering measurable results and driving growth, we are committed to partnering with our clients to...
Top Services:
- Web Design
- eCommerce Development
- WordPress Website Design
- Web Development
- Mobile App Development
- Show more
- Location
- Burton upon Trent, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $25/hr
- Minimal Budget
- $1,000 - $10,000
Creating Website Design & Development That Converts!
Pure Website Design creates visually appealing and effective websites and apps. Based in the US and UK, we can help you build an online presence that attracts, engages and supports your business goal...
Top Services:
- Web Design
- UI/UX Design
- eCommerce Development
- Web Development
- WordPress Website Design
- Show more
- Location
- High Street, United Kingdom
- Number of Employees
- 100 - 249
- Average Hourly Rate
- $10/hr
- Minimal Budget
- $1,000 - $10,000
Digital Solutions, Engineered for Growth
Artonezero is a web design and development agency specializing in building bespoke digital solutions. With expertise in UX design, web development, and digital strategy, the agency helps businesses enhance their online presence and drive engagement through innovative and scalable platforms...
Top Services:
- Digital Services
- Web Design
- Web Development
- Content Marketing
- Digital Marketing
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
Creating Brands That Leads.
Founded in 2018, We do this best is an AI-powered solutions provider specializing in website development, app development, digital marketing, and brand growth...
Top Services:
- Digital Marketing
- Branding
- Web Development
- Social Media Marketing
- PPC
- Show more
- Location
- Axminster, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $50/hr
- Minimal Budget
- Under $1,000
Tailored For Your Business Needs
SpireLabs is a UK-based software development agency specialising in bespoke solutions for service-based businesses. We design, develop, and deliver custom web platforms, client portals, and internal tools tailored to your unique needs. Whether you're streamlining operations or launching a new idea, our expert...
Top Services:
- Web Design
- Web Development
- Software Development
- SEO
- UI/UX Design
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $50/hr
- Minimal Budget
- $1,000 - $10,000
Empowering Your Business Growth With Precision
Staydify Growth Systems is a division of the UK-based HiringBooster Group, focused on driving technology-enabled business growth. The company specializes in delivering advanced custom software development and precision IT staffing services, leveraging its global footprint across the UK, USA, India, and other...
Top Services:
- Software Development
- IT Services
- Web Design
- Web Development
- Mobile App Development
- Show more
- Location
- Manchester, United Kingdom
- Number of Employees
- 100 - 249
- Average Hourly Rate
- $10/hr
- Minimal Budget
- Under $1,000
Your Trusted IT Support Partner
We deliver scalable IT, digital, and marketing solutions for businesses across the UK. From managed IT support and cybersecurity to web & app development, UI/UX design, and digital marketing, we provide proactive, flexible services trusted across healthcare, education, finance, logistics, and construction...
Top Services:
- IT Services
- Managed Services
- Cybersecurity
- UI/UX Design
- Web Development
- Show more
- Location
- Crawley, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $20/hr
- Minimal Budget
- $1,000 - $10,000
Code That Compounds Growth That Lasts
Devlixor Technologies is a high-velocity digital engineering firm dedicated to transforming complex technical challenges into market-leading growth engines. Specializing in Next.js architecture and AI-driven automation via n8n, we build scalable digital backbones for brands across the USA, UK, and APAC...
Top Services:
- Web Development
- SEO
- Web Design
- Digital Marketing
- Mobile App Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 100 - 249
- Average Hourly Rate
- $60/hr
- Minimal Budget
- $1,000 - $10,000
Digitizing Expressions
Pure Designers started in 2001 with 2 friends and from that day we have finished multiple projects world-wide, We designed and developed more than 5000 websites and applications, Currently we are working on Artificial Intelligence and recently we have launched a chatbot for SEO that help you optimize your...
Top Services:
- AI Development
- Mobile App Development
- UI/UX Design
- DevOps Consulting
- Cloud Consulting
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 50 - 99
- Average Hourly Rate
- $20/hr
- Minimal Budget
- $1,000 - $10,000
- Portfolios Count
- 1 Project Listed
AI That Transforms Businesses
Mindera Software Craft specializes in crafting robust IoT solutions through high-performance, scalable software systems. From product development and performance testing to technology consultancy, we provide end-to-end services tailored to your needs...
Top Services:
- Software Development
- Software Testing
- IoT
- DevOps Consulting
- UI/UX Design
- Show more
- Location
- Leicester, United Kingdom
- Number of Employees
- 250 - 499
- Average Hourly Rate
- $50/hr
- Minimal Budget
- $50,000 & Up
Award-winning web production that develops creative and strategic projects.
Provides both creative wow-websites, and business corporate ones...
Top Services:
- Web Design
- UI/UX Design
- eCommerce Development
- WordPress Website Design
- VR/AR
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 50 - 99
- Average Hourly Rate
- $48/hr
- Minimal Budget
- $25,000 - $50,000
Digital Story Telling
All inclusive social media services to tell your story online.Byter is a Digital Marketing and Social Media Agency that can help your business get noticed by the right people.It doesn’t matter where you are, or the shape and size of your business, we can transform the way you communicate and make sure...
Top Services:
- Social Media Marketing
- Video Marketing
- PPC
- SEO
- Digital Marketing
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $15/hr
- Minimal Budget
- Under $1,000
A strategic brand consultancy.
LBD Studio is a strategic brand consultancy that focuses on visual identity and design systems. With a small team of award-winning creatives, we collaborate with business owners to build value and drive growth...
Top Services:
- Package Design
- Branding
- Digital Services
- WordPress Website Design
- Web Design
- Show more
- Location
- Edinburgh, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $75/hr
- Minimal Budget
- $1,000 - $10,000
Scale Faster With Product Design Subscription.
We offer comprehensive product design services, covering UI/UX design and all aspects of product marketing, available for a fixed monthly rate, providing a convenient one-stop solution...
Top Services:
- Branding
- Product Design
- Web Design
- Logo Design
- Graphic Design
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
MAKE IT PERECT
KGN Technologies is value in "quality", not "quantity". We specialized in Magento, Shopify, Woo-Commerce, WordPress. Whether if you are planning a new store or redesign your website, we will make it happen. We are a white label agency with a highly qualified in-house developer...
Top Services:
- eCommerce Development
- Web Development
- WordPress Website Design
- Web Design
- UI/UX Design
- Show more
- Location
- Leicester, United Kingdom
- Number of Employees
- 50 - 99
- Average Hourly Rate
- $15/hr
Simple Solutions to Complex Problems
The DV Factory is a premier consultancy specialising in providing industry experts and holistic project and application development teams for the delivery of initiatives in the VOT/OO, Performance Marketing & Data Automation spaces...
Top Services:
- Cloud Consulting
- Managed Services
- DevOps Consulting
- IT Services
- Business Consulting
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $75/hr
- Minimal Budget
- $1,000 - $10,000
Creative Digital Agency London.
AndAgain has an Integrating strategic insights, creative ingenuity, and cutting-edge technology, we specialize in the development of digital products, websites, apps, and campaigns that not only enhance our clients' online presence but also elevate the image of our agency partners...
Top Services:
- Creative Services
- UI/UX Design
- Product Design
- Web Design
- Web Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $150/hr
- Minimal Budget
- $50,000 & Up
Shopify & Shopify Plus Specialists with 25+ Years of Ecommerce Expertise
Dewsign was founded in 1999 by Darren Williams.This was back in the time before Shopify existed, before SaaS ecommerce was even a concept.We have spent more than 25 years doing the hard work of digital commerce: not in theory, but in production - running real businesses...
Top Services:
- Web Design
- Digital Strategy
- Branding
- Logo Design
- UI/UX Design
- Show more
- Location
- Falmouth, United Kingdom
- Number of Employees
- Under 49
Simplifying Your Journey To The Internet World.
At OnlinXP, we believe in the transformative power of the digital world. Since our inception in 2016, we have been on a mission to empower businesses, entrepreneurs, and individuals to thrive in the ever-evolving online landscape. Headquartered in the bustling metropolis of New Delhi, India, our team of...
Top Services:
- Digital Services
- Web Design
- UI/UX Design
- eCommerce Development
- Web Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $15/hr
- Minimal Budget
- Under $1,000
- Portfolios Count
- 1 Project Listed
Naked Ideas® was founded in 2003 as a response to how other agencies routinely over complicate simple brand problems. We set out to prove that digital and brand campaigns can be tackled in a more intelligent way.Our team work with you to really understand your key messaging and to uncover the central ideas...
Top Services:
- Web Design
- eCommerce Development
- Web Development
- Package Design
- Branding
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $130/hr
We Bring Ideas to Life
At the heart of Lucky Duck there is a simple idea; empower businesses, big or small, to drive forward and disrupt the technology industry.We've seen what's out there and we think it can be done better. Be it design, development, or digital strategy - we're here to grow your business...
Top Services:
- WordPress Website Design
- eCommerce Development
- Web Design
- UI/UX Design
- Web Development
- Show more
- Location
- Leeds, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $115/hr
- Minimal Budget
- $10,000 - $25,000
Were a digital creative agency, built to amplify the purpose of charities
Were a digital creative agency, built to amplify the purpose of charities...
Top Services:
- Web Design
- UI/UX Design
- Branding
- Web Development
- WordPress Website Design
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $140/hr
- Minimal Budget
- $50,000 & Up
Tuned for the Modern Web
At Element Softworks, we fashion custom-made digital solutions to help our clients reach their objectives. From meticulously crafted components by meticulous methodology and the cutting-edge tech that defines the modern web, it's both quick and precise. We design with an eye toward creating a lasting brand...
Top Services:
- Web Design
- Web Development
- UI/UX Design
- Logo Design
- Graphic Design
- Show more
- Location
- Colchester, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $99/hr
- Minimal Budget
- $1,000 - $10,000
A Result-Oriented Website Design and Development Specialists
A creative, technical, full-service website design and development company that creates stunning, alluring, and reasonably priced works of art for both small and large businesses...
Top Services:
- Branding
- Video Production
- Logo Design
- Web Design
- Web Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $49/hr
- Minimal Budget
- $1,000 - $10,000
Websites and Digital Platforms Designed for Whats Next
Yellow Peach is a digital design and development agency specialising in WordPress development, digital platforms, and custom web applications. We are based in Frome, UK, near Bristol and Bath...
Top Services:
- Web Design
- WordPress Website Design
- Web Development
- Design Services
- Branding
- Show more
- Location
- Frome, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $99/hr
- Minimal Budget
- $10,000 - $25,000
Get Slam Dunk Results For Your Business.
We Combine Decades of Experience to Deliver You Powerful, Intelligent Data-Driven Marketing, Branding, Design and Web Development...
Top Services:
- Graphic Design
- Logo Design
- Web Design
- eCommerce Development
- WordPress Website Design
- Show more
- Location
- Haywards Heath, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $80/hr
- Minimal Budget
- $1,000 - $10,000
Digital Solutions Provider.
At GSS Tech Solutions, were redefining IT services with a commitment to excellence, reliability, and innovation. Each project reflects our dedication to quality, timeliness, and consistent performance. By continuously evolving our technology and enhancing client value, our passionate team thrives on embracing...
Top Services:
- Web Development
- eCommerce Development
- Digital Marketing
- SEO
- Software Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 50 - 99
- Average Hourly Rate
- $25/hr
- Minimal Budget
- $1,000 - $10,000
World-Class Solutions Tailored for Your Business Success.
We are a forward thinking company dedicated to delivering innovative web development , app development, custom applications and digital marketing solutions. Partner with our IT experts to elevate your digital presence and empower your business with cutting-edge strategies for seamless growth and success...
Top Services:
- Web Development
- Web Design
- WordPress Website Design
- eCommerce Development
- Blockchain
- Show more
- Location
- Nottingham, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $95/hr
- Minimal Budget
- $1,000 - $10,000
Reimagined With AI
Net Solutions is a global digital product development and experience engineering company with over 26 years of expertise. We design, build, and modernize digital platforms using AI, agile engineering, and design thinking to help businesses accelerate digital growth...
Top Services:
- eCommerce Development
- Web Development
- Web Design
- UI/UX Design
- AI Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- 250 - 499
- Minimal Budget
- $25,000 - $50,000
Digital Design With A Pulse
We handle strategy, branding, UX design, web development and mobile app design under one roof. No outsourcing, no handoffs between teams. The same people who research your users are the ones designing and building your product. We work best with startups, scale-ups and progressive teams who need a partner...
Top Services:
- Product Design
- Branding
- Web Design
- UI/UX Design
- Web Development
- Show more
- Location
- Gillingham, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $70/hr
- Minimal Budget
- Under $1,000
Accelerate Your AI Transformation
Vahue is an AI transformation consultancy and engineering company that helps startups and scaling enterprises become AI-native through team augmentation, workforce training, and enterprise AI systems. The company combines AI-native engineering talent, practical upskilling programs, and custom AI solutions to...
Top Services:
- AI Development
- Staff Augmentation
- Software Development
- SEO
- Web Development
- Show more
- Location
- London, United Kingdom
- Number of Employees
- Under 49
- Average Hourly Rate
- $50/hr
- Minimal Budget
- $10,000 - $25,000
Related Services
Mobile App Development Companies by City
Popular Services
About The Author and Expert Reviewer
Selina Garcia has authored 500+ articles and edited 50+ published books in economics, law, and history. Her unique blend of experiences allows her to approach content creation from a well-rounded perspective. Currently, Selina applies her expertise to producing insightful articles on IT, software, and applications for DesignRush.
Sergio is a technology leader with over six years of experience managing global teams and delivering projects across fintech, sportstech, and B2B platforms. At DesignRush, he drove product growth and development execution, building tools that speed up processes by 95% and cut costs by 35% while maintaining full uptime.



















































