Running out of stock doesn’t have to mean lost sales, but should you take pre-orders vs backorders vs build a waitlist? Each approach serves different business needs, timelines, and customer expectations. The right choice depends on factors like product availability, cash flow requirements, and how much commitment you need from customers.
Based on insights from over $85.3 million in pre-order sales, this guide breaks down the key differences between pre-orders, backorders, and waitlists. You’ll learn exactly when to use each strategy, how they impact your cash flow, and what customers expect from each approach.
What Are Pre-Orders, Backorders, and Waitlists?
Before diving into comparisons, let’s define each approach clearly.
Pre-Orders: Selling Before Stock Arrives
Pre-orders let customers purchase products before they’re manufactured or released. This is an advance sale where customers commit to buying something that doesn’t physically exist yet in your warehouse. For example, a fashion brand might open pre-orders for a new seasonal collection 90 days before production completes.
Pre-orders work particularly well for new product launches, limited edition releases, or made-to-order items where you want to validate demand before committing to inventory. According to our analysis of over one million pre-orders, 43.8% of merchants use charge-later payment models, meaning customers provide payment details but aren’t charged until the product ships.

Backorders: Selling Temporarily Out-of-Stock Items
Backorders are orders taken for products that were previously available but are temporarily out of stock. The key difference from pre-orders is timing: these products have already been released and sold before, and customers expect them to be restocked soon. Think of a popular electronics item that sells out faster than expected but will be replenished within 2-3 weeks.
Backorders are reactive rather than proactive. They help you capture demand during unexpected stockouts while you wait for replenishment. Most backorders require full payment upfront since the product is proven and the restock timeline is typically shorter and more certain.

Waitlists: Capturing Interest Without Commitment
Waitlists enable customers to sign up for notifications about when products become available or launch. Unlike pre-orders and backorders, waitlists don’t involve immediate purchases. Instead, customers provide their email address to be notified when the product is ready to buy.
Waitlists work well for demand testing, uncertain timelines, or building anticipation for upcoming launches. They’re particularly valuable for email list building, as waitlists almost always collect contact information. The trade-off is lower customer commitment: signing up for a notification requires far less commitment than completing a purchase.
Quick Comparison Table
| Approach | Product Status | Payment Timing | Customer Commitment | Best For |
|---|---|---|---|---|
| Pre-Order | Not yet manufactured/released | Flexible (upfront, later, or deposit) | High | New launches, validating demand |
| Backorder | Temporarily out of stock | Typically upfront | Medium-High | Fast-moving items with known restock |
| Waitlist | Upcoming or uncertain | No payment (notification only) | Low | Testing demand, building email lists |
The Key Differences: Timing, Psychology and Cash Flow
Understanding when and why to use each approach requires looking at three critical factors: timing, customer psychology, and financial impact.
Timing: When Each Approach Makes Sense

Pre-orders work best when you have a planned launch with a known or estimated arrival date. Most pre-orders in our dataset have shipping timeframes averaging 121-150 days, though this varies widely by industry. Fashion brands might run 60-90 day pre-order windows, while custom manufacturers might need 6+ months. The key is having enough certainty to set customer expectations, even if the exact date shifts slightly.
Backorders are reactive solutions to stockouts. Use them when you have a clear replenishment timeline, typically within 2-8 weeks. Backorders make sense for core catalog items you’ll definitely restock. They work less well for seasonal products or items with uncertain supply chains. If you can’t confidently say “back in stock by [date range],” a waitlist might be safer.
Waitlists are ideal when timelines are uncertain or you’re testing whether to produce something at all. They’re also powerful for drop culture brands that want to build anticipation before opening sales. Use waitlists when you need to gauge interest before committing to production or when supply chain uncertainty makes it risky to take payment.
Customer Psychology and Expectations
Each approach taps into different psychological motivators and creates distinct expectations.
Pre-order psychology centers on anticipation, exclusivity, and being “first.” Customers who pre-order often want early access to new releases or limited editions. They’re willing to wait because they’re excited about the product and don’t want to miss out. According to our data, 90.4% of pre-orders carry no discount, showing that access matters more than price for most pre-order customers.
The average pre-order cancellation rate sits at 5.4%, relatively low considering the long wait times involved. This suggests that when customers commit to a pre-order, they generally follow through. Clear communication about shipping dates and regular updates help maintain this commitment.
Backorder psychology requires patience rather than excitement. Customers making backorder purchases typically want a specific item they know and have decided to buy. They’re willing to wait because they’ve already decided this is the product they want. The key difference from pre-orders is that backorder customers expect a shorter wait and a more certain timeline since the product already exists in the market.
Waitlist psychology leverages FOMO (fear of missing out) and scarcity. Signing up for a waitlist makes customers feel like they’re part of an exclusive group who will get first access. The low commitment barrier (just an email) means more people will join, but fewer will convert compared to pre-orders. Waitlists work particularly well for building anticipation and collecting qualified leads for future marketing.
Financial Impact and Cash Flow

The three approaches have dramatically different effects on your cash flow and financial risk.
Pre-orders offer the most flexibility in payment timing. Based on our analysis of over one million pre-orders:
- 43.8% use charge-later (customers aren’t charged until shipping)
- 28.7% use capture-only (payment link sent when ready)
- 14.9% charge upfront (immediate payment)
- 12.6% use deposit-upfront (partial payment now, balance later)
This flexibility lets you match payment timing to your cash flow needs and customer comfort level. Charge-later pre-orders reduce refund risk since customers haven’t paid yet if timelines change. Upfront payments provide immediate revenue to fund production. Deposits offer a middle ground that shows customer commitment while lowering the barrier to purchase.
Backorders typically require full payment upfront. Since the product is proven and the restock timeline is shorter, customers expect to pay immediately. This provides faster cash flow than charge-later pre-orders but less flexibility. The shorter timeline reduces cancellation risk compared to long pre-order windows.
Waitlists generate no immediate revenue. They’re an investment in future sales and email list growth. The value comes from demand validation and the qualified leads you capture. You’ll need to convert waitlist signups to actual purchases later, which typically happens through email campaigns announcing availability.
When to Use Pre-Orders
Pre-orders work best in specific scenarios where you want to validate demand, take revenue earlier, or build anticipation before a product physically exists.
Best Use Cases for Pre-Orders
1. New Product Launches
Pre-orders let you validate demand before committing to large production runs. This is particularly valuable for brands testing new product lines or designs. By taking pre-orders, you get real purchase commitments (not just survey responses) that help you make informed inventory decisions.
2. Limited Edition Releases
When releasing limited or exclusive items, pre-orders build hype and ensure your most dedicated customers don’t miss out. Pre-orders also help you set the right production quantity for limited runs.
3. High-Value Items
For products over $250 (which represent 26.8% of pre-order listings in our data), deposits can lower the barrier to purchase while still securing customer commitment. A 20-30% deposit shows serious intent without requiring customers to part with the full amount months in advance.
4. Seasonal Collections
Fashion and seasonal brands can open pre-orders before production completes, allowing them to adjust quantities based on actual demand rather than forecasts. This reduces the risk of overstock that needs to be discounted later.

Payment Options for Pre-Orders
One of pre-order’s biggest advantages is payment flexibility. Here’s how merchants use different payment models:
Charge-Later (43.8% of listings) works well when timelines are uncertain or longer than 90 days. Customers provide payment details but aren’t charged until you’re ready to ship. This reduces refund risk if timelines shift and makes customers more comfortable committing to purchases months in advance.
Charge-Upfront (14.9% of listings) provides immediate cash flow to fund production. Use this when you have reliable timelines and need upfront capital. It’s most common with shorter pre-order windows or established brands with high customer trust.
Deposit-Upfront (12.6% of listings) offers a middle ground. Collect 20-50% now to gauge commitment and fund initial production, then charge the balance when shipping. Deposits work particularly well for higher-ticket items where full upfront payment creates too much friction.
Capture-Only (28.7% of listings) delays even authorization until you’re ready to ship. You send a payment link when the product is ready. This creates the least customer friction but provides no revenue until fulfillment.

Pre-Order Best Practices
To run successful pre-orders:
Set Clear Expectations
Display expected shipping dates prominently on product pages. Most pre-orders average 121-150 day shipping windows, but transparency matters more than specific duration. If your timeline is “late spring,” say that rather than guessing a specific date you might miss.
Use Dedicated Messaging
Replace generic “Add to Cart” buttons with clear “Pre-Order” buttons that indicate the purchase is for a future-dated product. This reduces confusion and sets proper expectations from the start.

Communicate Proactively
Keep customers updated throughout the pre-order period. Send confirmation emails, progress updates, and immediate notification of any timeline changes. Transparent communication maintains trust during long wait periods.
Consider Mixed Carts Carefully
According to our data, 37.9% of stores allow customers to mix pre-order items with in-stock products in the same cart. This can increase average order value but complicates fulfillment. Decide based on your operational complexity: isolated pre-order carts simplify logistics, while mixed carts improve customer experience.
For detailed implementation guidance, see our guide on how to set up pre-orders on Shopify.
When to Use Backorders
Backorders serve a different purpose than pre-orders: capturing demand during temporary stockouts of proven products.
Best Use Cases for Backorders
1. Fast-Moving Bestsellers
When a popular item sells out faster than expected, backorders let you continue taking orders rather than losing sales. This works best when you have reliable suppliers and predictable restock timelines.
2. Core Catalog Items
Backorders make sense for staple products you’ll definitely restock. If it’s a core part of your catalog that consistently sells, capture that demand even during temporary stockouts.
3. Short Restocking Windows
Use backorders when you know the restock timeline and it’s relatively short, typically 2-6 weeks. The shorter the window, the better backorders work because customer patience has limits.
4. Preventing Lost Sales
The primary benefit of backorders is capturing revenue that would otherwise go to competitors. When customers want your specific product and are willing to wait a few weeks, backorders prevent them from buying elsewhere.
Backorder Best Practices
Only Offer for Reliable Restocks
Don’t charge backorders upfront unless you’re confident in a shorter replenishment timeline. Broken promises damage customer trust more than saying “out of stock” upfront. Instead take charge-later back-orders where you collect payment until the product is ready to ship.
Set Clear Expectations
Display the expected restock date or date range prominently. “Back in stock by March 15” or “Expected restock: 2-3 weeks” sets clear expectations. Update this date if timelines change.
Use Dedicated Buttons
Like pre-orders, use clear “Backorder” or “Pre-order (Restock)” buttons instead of generic “Add to Cart.” This immediately signals that the item isn’t available for immediate shipment.

Consider Backorder Limits
For items with uncertain restock quantities, consider capping backorders to avoid over-committing. This prevents situations where you can’t fulfill all backorders when stock arrives.
When NOT to Use Backorders
Avoid backorders in these situations:
- Seasonal items unlikely to restock this season
- Uncertain supply chains Especially when charging upfront, where you can’t commit to timeframes
- Very long wait times beyond 90 days (use pre-orders with charge-later instead)
- Products being discontinued or phased out
When to Use Waitlists
Waitlists serve a different function: capturing interest without the commitment of a purchase.
Best Use Cases for Waitlists
1. Demand Testing
When considering whether to produce a new product, waitlists let you gauge interest before committing. The number of signups gives you directional data about potential demand, though actual conversion will be lower than pre-orders since there’s no payment commitment.
2. Drop Culture Brands
Brands built on limited drops and scarcity can use waitlists to build FOMO and anticipation. Waitlist members become your launch day audience, creating initial sales momentum.
3. Uncertain Timelines
When you can’t commit to specific dates or aren’t sure if a product will be produced at all, waitlists provide a safe way to capture interest without the legal and customer service burden of taking payment.
4. Email List Building
Waitlists “almost always collect email addresses,” making them valuable for growing your marketing list with qualified, interested prospects. These contacts have already expressed interest in specific products, making them highly targeted leads.
5. Inventory Planning
Waitlist signup numbers help inform production quantities and inventory decisions. While not as reliable as pre-order commitments, they provide useful directional guidance.
Waitlist Best Practices
Make Signup Frictionless
Only ask for essential information (typically just email). The easier it is to join, the more signups you’ll get.
Set Clear Expectations
Tell customers what happens next and approximately when. “We’ll email you when pre-orders open in March” or “You’ll get 24-hour early access when we launch” manages expectations and reduces support questions.
Create Scarcity Perception
Position waitlist membership as exclusive access. “Join the waitlist for first access” or “Waitlist members get 24-hour early access” creates additional motivation to sign up.
Plan Your Conversion Strategy
Have a clear plan for converting waitlist signups to purchases. Will you offer early access? A discount? A limited time window? Plan this before building your list.
Converting Waitlists to Sales
Waitlist signups aren’t revenue until you convert them. Effective conversion tactics include:
- Time-limited early access (24-48 hour exclusive window)
- Exclusive discounts for waitlist members (10-15% off)
- Transition to pre-order when timeline becomes clearer
- Scarcity messaging (“Only 500 units available for waitlist members”)

The Decision Framework: Which Approach to Choose
Choosing between pre-orders, backorders, and waitlists requires evaluating several factors specific to your situation.
Decision Tree
1. Is the product already manufactured or available somewhere?
- No (it doesn’t exist yet) → Consider pre-orders or waitlist
- Yes, but currently out of stock → Consider backorders or waitlist
2. Do you have a clear restocking or shipping timeline?
- Yes, under 30 days → Backorders or charge-upfront pre-orders work well
- Yes, over 30 days → Pre-orders with charge-later preferred
- No or uncertain → Waitlist or charge-later pre-order is safer; no payment commitment reduces risk
3. What are your cash flow needs?
- Need immediate revenue → Pre-orders with upfront payment or deposits
- Flexible cash flow → Charge-later pre-orders or waitlists
- Want to reduce refund risk → Waitlists or charge-later pre-orders
4. What’s your product price point?
- High-ticket (>$250) → Deposits reduce purchase barrier (26.8% of pre-orders are >$250 in our data)
- Mid-range ($50-250) → Any payment model works; choose based on timeline certainty
- Low-ticket (<$50) → Full payment upfront is typical; administrative overhead of deposits often not worth it
5. What level of customer commitment do you need?
- High commitment (need to make production decisions) → Pre-orders with payment or deposit
- Medium commitment (proven product, just out of stock) → Backorders
- Low commitment (just testing interest) → Waitlists
Real-World Scenarios
Scenario 1: Fashion Brand Seasonal Launch
A clothing brand is releasing a new spring collection in 90 days. Production hasn’t started yet, and they want to gauge demand before finalizing quantities.
Recommendation: Pre-orders with charge-later payment. This captures real purchase commitments (better data than waitlist signups) while minimizing refund risk if production timelines shift. The 90-day window aligns with typical fashion pre-order periods.
Scenario 2: Electronics Retailer Surprise Stockout
A popular gaming console accessory sells out unexpectedly. The supplier confirms restock in 2-3 weeks.
Recommendation: Backorders with full payment upfront. The short, certain timeline and proven product make backorders ideal. Customers know what they’re getting and are willing to pay for a brief wait.
Scenario 3: Indie Maker Testing New Product Idea
A creator has designed a new product but isn’t sure if there’s enough demand to justify production. They want to test interest before committing to manufacturing.
Recommendation: Waitlist initially, then transition to pre-orders if interest is strong. Start with a waitlist to gauge interest without the legal obligations of taking payment. If 500+ people sign up, transition to pre-orders with deposits to confirm actual purchase intent before manufacturing.
Scenario 4: Limited Edition Collectible
A brand is releasing a limited run of 200 collectible items. Demand is expected to exceed supply significantly.

Recommendation: Pre-orders with upfront payment or deposit. The limited quantity and high demand justify requiring payment commitment. Use deposits if the price is high enough to create friction. Close pre-orders once you hit 200 orders (or your production capacity).
Using Multiple Approaches Together
The three strategies aren’t mutually exclusive. Many successful brands use them in combination.
Pre-Orders + Waitlists
Start with a waitlist to build anticipation and capture emails. When you’re ready to open sales, give waitlist members early access to pre-order before opening to the general public.
This two-stage approach builds your email list while rewarding early interest with exclusive access. The waitlist creates anticipation, then pre-orders convert that interest into revenue. Many brands offer waitlist members a 24-48 hour exclusive pre-order window or a small discount (10% off) as a reward for signing up early.
Pre-Orders + Mixed Carts
Our data shows 37.9% of stores allow customers to mix pre-order items with in-stock products in the same cart. This can increase average order value and improve customer experience by letting them order everything they want in one transaction.
The trade-off is operational complexity. Mixed carts typically require split shipments: you ship in-stock items immediately and pre-order items later. This means additional shipping costs and more complex fulfillment workflows. It also requires clear communication so customers understand they’ll receive multiple shipments.
For guidance on integrating pre-orders with your fulfillment operations, see our guides on managing pre-orders with your 3PL and managing pre-orders with your ERP.
Backorders + Pre-Orders
Use both approaches for different parts of your catalog. Run backorders for core items with quick, predictable restocks. Use pre-orders for new releases, seasonal items, or products with longer lead times.
The key is using different messaging and buttons so customers clearly understand which type of purchase they’re making. “Backorder (ships in 2 weeks)” versus “Pre-Order (ships in June)” sets clear expectations.
Platform Implementation: Shopify, BigCommerce, WooCommerce
The technical implementation varies by ecommerce platform.
Shopify Pre-Orders and Backorders
Shopify offers basic built-in functionality through inventory settings, but most merchants need more advanced features. The “continue selling when out of stock” checkbox lets products pass through checkout at zero inventory, which works for simple backorders.
For more sophisticated pre-order management, specialized apps like PreProduct offer:
- Flexible payment timing (charge-upfront, charge-later, deposits, capture-only)
- Automatic fulfillment holds to prevent premature shipping
- Customer communication tools and portals
- Shopify Flow integration for automated workflows
- Inventory-based automations
PreProduct’s charge-later capability uses Shopify’s vaulted card technology, letting you capture payment details without charging until you’re ready to ship. This is particularly valuable for pre-orders with uncertain timelines.
BigCommerce Considerations
BigCommerce has native backorder support through inventory settings, but pre-order functionality typically requires third-party apps like PreProduct. The platform’s checkout flexibility allows for custom pre-order implementations, including charge-later models through Stripe integration.
For BigCommerce stores, focus on:
- Clear product page messaging about pre-order status
- Expected shipping date display
- Email communication workflows
- Integration with your existing fulfillment systems
WooCommerce Options
WooCommerce pre-orders typically work through plugins that extend the platform’s functionality like PreProduct. The open-source nature of WooCommerce means more customization flexibility but requires more technical setup.
Key WooCommerce considerations:
- Payment gateway compatibility (ensure your gateway supports tokenization for charge-later)
- Plugin compatibility with your theme and other extensions
- Email notification customization
- Stock management integration
Headless and Custom Implementations
For brands with custom storefronts or headless commerce setups, pre-orders require API-based solutions or supporting apps like PreProduct. Stripe pre-orders offer flexibility for charge-later implementations through Stripe’s payment intents and customer tokenization.
Custom implementations provide maximum flexibility but require development resources to build:
- Payment capture and tokenization logic
- Customer communication workflows
- Order management and fulfillment holds
- Reporting and analytics
Customer Communication and Transparency Best Practices
Success with pre-orders, backorders, and waitlists depends heavily on clear communication.
Setting Clear Expectations
Product Page Messaging
Use clear, prominent labels: “Pre-order,” “Backorder,” or “Join Waitlist.” Avoid generic language like “Add to Cart” that doesn’t signal the purchase type.
Display expected shipping dates or ranges prominently. “Ships in June 2025” or “Expected restock: 2-3 weeks” tells customers exactly what to expect. If you don’t have specific dates, provide ranges: “Ships in 3-4 months.”
Explain What Happens Next
Tell customers what the purchase process looks like. “You’ll be charged today, and we’ll ship when your item is ready” versus “We’ll hold off charging you until we’re ready to ship” makes the experience clear.
Cancellation Policies
State your cancellation and refund policies upfront. Customers are more likely to commit when they know they can cancel if needed. For charge-later pre-orders, make it clear that customers can cancel before being charged with no penalty.
Email Communication Strategy
Order Confirmation
Send immediate confirmation with timeline expectations. Include the expected shipping date or date range, what payment was collected (if any), and how customers can check their order status.
Progress Updates
For pre-orders with long timelines, send periodic updates. “Your spring collection pre-order is on track for March delivery” or “Production is underway and everything is on schedule” maintains excitement and reduces support inquiries.
Proactive Delay Communication
If timelines change, communicate immediately. Don’t wait for customers to ask. “Due to shipping delays, your order will arrive in April instead of March. You can cancel for a full refund if you prefer” maintains trust even when things don’t go according to plan.
Shipping Notifications
When items ship, send tracking information and estimated delivery dates. This is the payoff moment customers have been waiting for.
Legal and Regulatory Compliance
FTC Guidelines
In the United States, the FTC’s Mail or Telephone Order Rule requires you to ship within the timeframe stated or, if no time is stated, within 30 days. For longer pre-order timelines, you must clearly state the expected shipping date and get customer consent.
State Consumer Protection Laws
Various states have specific requirements around pre-orders, deposits, and refunds. Ensure your terms and conditions comply with applicable laws in jurisdictions where you sell.
International Considerations
Different countries have different consumer protection requirements. EU consumer protection laws, for example, require specific cancellation rights and refund timeframes. If you sell internationally, ensure compliance with relevant regulations.
Clear Refund Policies
State your refund policy clearly in your terms and conditions. Be specific about when customers can cancel, how refunds are processed, and what happens if you can’t fulfill an order.
Risk Management: When Things Don’t Go As Planned
Even with careful planning, complications arise. Being prepared reduces stress and maintains customer trust.

Common Challenges
Supply Chain Delays
Manufacturing or shipping delays are the most common pre-order challenge. COVID-19 demonstrated how quickly global supply chains can be disrupted.
Lower-Than-Expected Demand
Sometimes pre-order demand doesn’t meet expectations, requiring production adjustments or minimums you can’t meet.
Higher-Than-Expected Demand
The opposite problem: more orders than you can fulfill. This creates allocation challenges and potential customer disappointment.
Product Quality Issues
Discovering quality problems before shipping means delaying launch to fix issues or accepting returns after shipping.
Mitigation Strategies
Buffer Your Timelines
Under-promise and over-deliver. If you think production takes 90 days, quote 120 days. Early delivery delights customers; delays frustrate them.

Use Charge-Later for Uncertain Timelines
When you’re not confident in timing, charge-later pre-orders reduce refund risk. Our data shows 43.8% of pre-orders use this model, precisely because it provides flexibility when timelines are uncertain.
Maintain Clear Cancellation Policies
Make cancellation easy and fast. This encourages people to commit initially, knowing they can back out if needed. Our data shows just a 5.4% cancellation rate, meaning most customers follow through even when cancellation is easy.
Communicate Transparently
When problems arise, communicate immediately and honestly. Customers are remarkably understanding when you’re transparent, but they’re unforgiving when they feel misled or ignored.
Set Realistic Expectations
Don’t promise what you can’t deliver. It’s better to set conservative expectations and beat them than to promise aggressive timelines you miss.
When to Cancel and Refund
Sometimes the best choice is canceling orders and issuing refunds:
- Indefinite delays beyond 6 months past original estimates
- Product quality doesn’t meet standards and can’t be fixed in reasonable time
- Can’t fulfill all orders due to production issues (consider partial fulfillment or allocation)
- Supplier goes out of business or can’t deliver
While disappointing, handling cancellations professionally preserves your brand reputation for future launches.
Key Takeaways
Choosing between pre-orders, backorders, and waitlists depends on your specific situation:
Pre-orders work best for new launches and planned releases where you have known (or estimated) timelines. They offer maximum payment flexibility and help validate demand before committing to inventory. Use charge-later for uncertain timelines, upfront payment when you need immediate cash flow, or deposits for high-ticket items.
Backorders are ideal for temporary stockouts of proven products with quick, reliable restock timelines. They prevent lost sales when popular items sell out faster than expected. Keep backorder windows short (under 90 days) and only offer them when you’re confident in restocking.
Waitlists serve demand testing and email list building when timelines are uncertain or you’re not sure if you’ll produce something at all. They create low-commitment interest capture that you can later convert to pre-orders or direct sales.
All three can work together in your overall strategy. Use waitlists to build initial interest, convert to pre-orders when timing is clearer, and run backorders for core items with temporary stockouts.
Success requires clear communication, realistic timelines, and proper technical implementation. Our analysis of over one million pre-orders shows that when executed well, these strategies work: 43.8% of merchants use charge-later payments, 90.4% offer no discount (access matters more than price), and cancellation rates average just 5.4%.
The data proves that pre-orders, backorders, and waitlists all work when matched to the right situations and executed with transparency and clear customer communication.
Ready to start taking pre-orders? PreProduct offers flexible payment options, fulfillment holds, and automated workflows for Shopify, BigCommerce, and WooCommerce stores. Learn more about our Shopify pre-order solution or explore insights from $85M in pre-order sales.



































