Types of Cylinder Head Shims
A cylinder head shim is a precision-engineered component used between the cylinder head and engine block to adjust compression ratio, fine-tune head gasket sealing, or compensate for machining variations. These shims play a critical role in engine performance, combustion efficiency, and long-term reliability—especially in high-performance, modified, or rebuilt engines.
Available in various materials and designs, each type of cylinder head shim offers unique benefits and trade-offs in terms of durability, thermal conductivity, compressibility, and sealing performance. Below is a detailed breakdown of the most common types used in automotive and performance applications.
Metal Cylinder Head Shims
Typically constructed from steel, aluminum, or reinforced alloys, metal shims are ideal for high-stress and performance-oriented engines.
Advantages
- Exceptional strength and heat resistance
- Resists deformation under high cylinder pressure
- Precise thickness control for compression tuning
- Durable and reusable in many cases
Limitations
- Less flexible—requires perfectly machined surfaces
- May require additional sealing layers
- Higher installation precision needed
Best for: Performance engines, turbocharged/supercharged builds, diesel applications
Composite Cylinder Head Shims
Made from compressed fiber, graphite, or layered elastomers, these shims offer flexibility and excellent conformability to imperfect surfaces.
Advantages
- Excellent sealing on uneven or aged engine blocks
- Good vibration damping properties
- Cost-effective for standard repairs
- Often included in complete gasket sets
Limitations
- Less durable under extreme temperatures/pressures
- May degrade over time in high-performance setups
- Not ideal for repeated disassembly
Best for: Routine engine rebuilds, older vehicles, street-driven engines
MLS (Multi-Layer Steel) Shims
Composed of multiple thin steel layers, often nickel-plated and bonded, MLS shims combine strength with micro-flexibility for superior sealing.
Advantages
- Outstanding pressure and heat resistance
- Self-adjusting under thermal cycling
- Common in modern OEM high-performance engines
- Precision-engineered for tight tolerances
Limitations
- Higher cost compared to traditional shims
- Requires smooth, flat mating surfaces
- Sensitive to improper torque sequencing
Best for: Modern performance engines, factory turbo applications, OEM replacements
Copper Cylinder Head Shims
Pure copper shims are soft, malleable, and highly conductive—ideal for custom tuning and racing applications.
Advantages
- Excellent thermal conductivity helps manage head temperatures
- Highly conformable—even on slightly imperfect surfaces
- Reusable and easy to anneal for reinstallation
- Precise thickness options for compression tuning
Limitations
- Can creep or unwind over time under load
- Softer material requires careful torque control
- Needs proper surface finish and sealing techniques
Best for: Racing engines, high-compression builds, custom engine tuning
Fire Ring Shims
Specialized shims with integrated steel or copper fire rings that isolate and reinforce the combustion chamber sealing area.
Advantages
- Superior combustion sealing under extreme pressure
- Prevents head gasket blowout in high-boost engines
- Can be combined with copper or MLS base materials
- Localized reinforcement without affecting entire gasket
Limitations
- More complex installation process
- Higher cost due to precision manufacturing
- Requires exact alignment during assembly
Best for: Forced induction engines, drag racing, high-horsepower builds
| Type | Heat Resistance | Sealing Performance | Durability | Best Application |
|---|---|---|---|---|
| Metal | Excellent | Good | Excellent | Performance, diesel, high-load engines |
| Composite | Good | Very Good | Fair | Standard repairs, older engines |
| MLS | Excellent | Excellent | Excellent | Modern turbo engines, OEM replacements |
| Copper | Very Good | Excellent | Good | Racing, compression tuning, custom builds |
| Fire Ring | Exceptional | Exceptional | Very Good | High-boost, track, performance applications |
Expert Tip: When installing copper or metal shims, always use a high-temperature anti-seize compound on bolt threads and follow the manufacturer's torque specifications in sequence. For copper shims, consider annealing (heating and slow cooling) before installation to improve malleability and sealing.
Materials Used to Make Cylinder Head Shims: A Comprehensive Guide
Cylinder head shims are essential components in internal combustion engines, serving to fine-tune compression ratios, ensure proper sealing between the cylinder head and engine block, and accommodate manufacturing tolerances. The choice of material significantly impacts performance, durability, and compatibility with engine conditions such as temperature, pressure, and chemical exposure. Below is a detailed breakdown of the most commonly used materials for cylinder head shims, their properties, applications, and comparative advantages.
Common Materials for Cylinder Head Shims
Steel
Steel is one of the most widely used materials for cylinder head shims due to its excellent balance of strength, flexibility, and cost-effectiveness. It provides reliable sealing under standard operating conditions and is commonly used during engine rebuilds or performance tuning.
Steel shims are highly durable and resistant to mechanical stress, making them ideal for everyday use in passenger vehicles and light-duty engines. Their rigidity allows for precise thickness control, which is critical when adjusting compression ratios. However, they may require additional coatings or treatments to resist corrosion in high-moisture environments.
Aluminum
Aluminum shims offer a lightweight yet strong solution, combining good structural integrity with high pliability. This makes them particularly effective in engines where surface irregularities exist between the cylinder head and block, allowing the shim to conform slightly for a better seal.
Due to aluminum’s natural corrosion resistance and thermal conductivity, it performs well in both air- and liquid-cooled engines. It's often used in older engine designs or applications where weight reduction is a priority. While not as robust as steel under extreme pressure, aluminum remains a popular choice for moderate-performance and restoration projects.
Copper
Copper is the preferred material for high-performance and racing engines, primarily due to its exceptional thermal conductivity and malleability. Copper shims can deform slightly under torque, filling microscopic gaps and creating an almost perfect seal—ideal for engines with high compression ratios or forced induction.
While copper is less durable than steel and more prone to gasket creep over time, its ability to handle thermal cycling and create a gas-tight seal makes it invaluable in performance applications. Many racers reuse copper shims after careful inspection and re-annealing to restore softness.
MLS (Multi-Layer Steel)
Multi-Layer Steel (MLS) shims represent advanced engineering in sealing technology. Constructed from two or more layers of precision-cut steel, often with an elastomeric or fluoropolymer coating, MLS shims deliver superior resilience under extreme combustion pressures and thermal fluctuations.
The layered design allows for controlled elasticity, maintaining clamping force even as the engine expands and contracts. These shims are standard in modern turbocharged and high-efficiency engines, where reliability under high loads is non-negotiable. The pre-coated surfaces enhance resistance to oil, coolant, and combustion byproducts, extending service life.
Graphite
Graphite shims are known for their excellent heat resistance and compressibility, making them suitable for older engines or those operating at lower pressures. They conform easily to uneven surfaces and maintain a stable seal even under repeated thermal cycles.
These shims are chemically inert and highly resistant to corrosion, which enhances longevity in harsh environments. However, they are less robust mechanically and can degrade under very high combustion pressures or in engines with poor head bolt torque control. Often used in vintage or low-stress applications, graphite offers a forgiving and effective sealing solution.
Composites
Composite shims are engineered from fiber-reinforced materials such as aramid (e.g., Kevlar), regenerated cellulose, or fiberglass, often bonded with nitrile rubber or other elastomers. This combination delivers flexibility, good sealing characteristics, and enhanced resistance to oils and solvents.
While not typically used in high-performance engines, composite shims excel in moderate-duty applications where chemical resistance and dimensional stability are key. They are commonly found in industrial engines, marine applications, and some automotive contexts where consistent sealing under variable conditions is required.
| Material | Thermal Resistance | Mechanical Strength | Best Application | Durability |
|---|---|---|---|---|
| Steel | Moderate | High | Standard engine rebuilds, compression tuning | High |
| Aluminum | Good | Moderate | Lightweight engines, older models | Moderate |
| Copper | Excellent | Low-Moderate | Racing, high-compression engines | Moderate (reusable) |
| MLS | Excellent | Very High | Modern turbocharged, high-pressure engines | Very High |
| Graphite | Excellent | Low | Vintage engines, low-pressure systems | Moderate |
| Composites | Good | Moderate | Industrial, marine, chemical-exposed engines | High |
Selection Tips and Best Practices
Important: Using the wrong shim material can lead to head gasket failure, loss of compression, coolant leaks, or even engine damage. Always consult your engine’s service manual or a qualified mechanic when selecting or replacing cylinder head shims. Environmental factors, fuel type, and boost levels (in turbocharged engines) should all influence your material choice.
Applications of Cylinder Head Shims: Enhancing Engine Performance and Reliability
Cylinder head shims play a critical role in internal combustion engines by ensuring proper sealing, maintaining compression ratios, and compensating for mechanical variances. These thin, precision-engineered components are essential across a wide range of automotive applications—from routine repairs to high-performance tuning. Below is a comprehensive overview of their key applications and technical benefits.
1. Engine Rebuilding and Overhaul
Cylinder head shims are vital during engine rebuilds, where they help restore factory specifications and ensure a perfect seal between the cylinder head and engine block. Over time, surfaces can wear or become uneven due to thermal cycling and mechanical stress.
- Used to compensate for material removed during head resurfacing or block decking
- Help maintain correct head gasket compression for optimal sealing
- Adjust compression ratio slightly to restore engine efficiency and power output
- Prevent oil and coolant leaks by ensuring uniform clamping force
Key Insight: Proper shim thickness selection is crucial—too thick or thin can lead to poor combustion or head gasket failure.
2. Tuning High-Performance and Racing Engines
In performance applications, cylinder head shims are used strategically to fine-tune engine dynamics. Modifying the combustion chamber volume through shim thickness directly affects the compression ratio—a key factor in maximizing horsepower and torque.
- Enables precise control over compression ratio for optimized air-fuel mixture and ignition timing
- Supports forced induction (turbo/supercharged) setups by managing higher cylinder pressures
- Used with aftermarket cylinder heads to achieve target performance metrics
- Ensures reliable cylinder head gasket sealing under extreme thermal and mechanical loads
Pro Tip: Performance tuners often use multi-layer steel (MLS) gaskets with shims for enhanced durability and heat resistance.
3. Hybrid and Electric Vehicle Powertrains
While electric vehicles (EVs) don’t use traditional combustion engines, many hybrid models still rely on internal combustion engines (ICE) that operate under high efficiency and variable load conditions. These engines often require enhanced sealing solutions.
- Used in hybrid engines to maintain consistent sealing despite frequent start-stop cycles
- Help manage thermal expansion differences between aluminum heads and cast iron blocks
- Improve longevity in compact, high-efficiency engines with elevated cylinder pressures
- Support emissions compliance by preventing combustion gas leakage
Technical Note: Hybrid engines benefit from corrosion-resistant shims due to reduced operating temperatures and potential condensation.
4. Repairing Overheated or Warped Cylinder Heads
Engine overheating is a common cause of cylinder head warping, cracking, or surface distortion. During repair, shims can help compensate for minor imperfections when full machining isn’t feasible.
- Restore proper head alignment and clamping pressure after heat damage
- Act as a buffer to accommodate slight warpage when resurfacing isn’t an option
- Prevent recurring head gasket failures by improving sealing consistency
- Often used alongside high-temperature sealants in emergency or field repairs
Caution: Shims should not be used to mask severe warping—proper machining is always preferred for long-term reliability.
5. Diesel Engine Applications
Diesel engines operate under significantly higher compression ratios and cylinder pressures than gasoline engines, making robust sealing essential. Standard head gaskets may not suffice under these extreme conditions.
- Provide additional clamping support to prevent gasket blowout under high pressure
- Used in heavy-duty applications such as commercial trucks, buses, and agricultural machinery
- Enhance durability in engines with high torque output and prolonged idle cycles
- Help maintain compression in older diesel engines with worn or pitted block surfaces
Did You Know? Multi-layer copper or steel shims are often preferred in diesel applications for superior heat conductivity and resilience.
6. Custom Engine Builds and Modifications
For custom or stroker engines, achieving the ideal compression ratio is critical for performance, fuel efficiency, and engine longevity. Cylinder head shims offer a flexible solution for fine-tuning during assembly.
- Allow precise adjustment when mixing OEM and aftermarket components
- Used in racing, towing, and off-road builds to match engine specs to intended use
- Enable experimentation with different fuel types (e.g., E85, race gas) by adjusting compression
- Simplify engine balancing without permanent modifications to the block or head
Expert Advice: Always calculate compression ratio changes when using shims—software tools can help predict performance impact.
7. Prevention of Combustion Gas Leakage
One of the primary functions of cylinder head shims is to reinforce the seal between the combustion chamber and surrounding areas. Even minor leaks can lead to power loss, overheating, or engine damage.
- Strengthen the seal around combustion chambers, coolant passages, and oil galleries
- Reduce the risk of head gasket failure under high RPM or boost conditions
- Minimize cylinder pressure loss, maintaining engine efficiency and responsiveness
- Act as a secondary barrier in multi-layer gasket systems for added safety
Critical Benefit: Effective sealing improves fuel economy, reduces emissions, and extends engine life.
Professional Recommendation: When selecting cylinder head shims, always consider material compatibility (steel, copper, aluminum), thickness tolerance, and surface finish. For best results, pair shims with OEM-spec or performance-grade head gaskets and follow proper torque sequencing during installation. Consult service manuals or engineering guides for application-specific recommendations.
| Application | Shim Material | Primary Purpose | Common Use Cases |
|---|---|---|---|
| Engine Rebuilding | Steel or Copper | Sealing restoration | High-mileage vehicles, routine overhauls |
| Performance Tuning | Multi-layer Steel (MLS) | Compression adjustment | Race cars, turbocharged engines |
| Diesel Engines | Thick Steel or Copper | Pressure resistance | Trucks, buses, industrial equipment |
| Hybrid Vehicles | Corrosion-resistant Alloy | Thermal stability | Plug-in hybrids, stop-start systems |
| Custom Builds | Adjustable Thickness Kits | Precision tuning | Stroker engines, drag racing |
Additional Considerations
- Material Selection: Copper shims offer excellent thermal conductivity but may require annealing; steel provides durability and reusability.
- Thickness Tolerance: Precision shims (±0.05mm) ensure accurate compression control and prevent warping.
- Surface Preparation: Clean, flat mating surfaces are essential—any debris or oil can compromise the seal.
- Torque Specifications: Always follow manufacturer-recommended torque patterns and values when installing head components.
- Reusability: Some high-quality shims can be reused if undamaged, but inspection is critical before reinstallation.
How to Choose the Right Cylinder Head Shim: A Comprehensive Guide
Selecting the correct cylinder head shim is a critical step in engine tuning, rebuilds, and performance optimization. The shim plays a vital role in maintaining proper compression, sealing integrity, and overall engine efficiency. Whether you're rebuilding a stock engine or modifying a high-performance build, understanding the key selection factors ensures reliability, performance, and longevity. This guide covers the essential considerations—thickness, material, compression ratio, engine compatibility, tolerances, and OEM specifications—to help you make an informed decision.
Important Note: Incorrect shim selection can lead to catastrophic engine failure, including head gasket blowouts, detonation (engine knocking), or poor combustion efficiency. Always verify measurements and consult technical documentation before installation.
Key Factors in Cylinder Head Shim Selection
- Thickness: Balancing Compression and Clearance
Cylinder head shims typically range from 0.5 mm to 3.0 mm in thickness. The chosen thickness directly affects the combustion chamber volume and, consequently, the engine’s compression ratio.
- Thinner shims reduce the volume between the cylinder head and block, effectively increasing the compression ratio. This is often desirable in performance applications to boost power output.
- Thicker shims increase the head-to-block distance, lowering the compression ratio, which may be necessary when using lower-octane fuel or to prevent detonation in turbocharged/supercharged engines.
- The ideal thickness must align with your engine’s blueprint specifications, piston-to-head clearance, and target compression ratio. Always measure deck height and use precise calculations before selecting a shim.
- Material: Matching Performance and Durability Needs
The material of the head shim influences thermal conductivity, sealing ability, and durability under high pressure and temperature. Common materials include:
- Steel: Durable and dimensionally stable, steel shims are commonly used in stock or mildly modified engines. They are less compressible than softer materials, making them ideal for consistent, long-term sealing.
- Copper: Highly malleable and excellent at conforming to surface imperfections, copper shims provide superior sealing—especially on older or slightly warped heads. Often used in racing and high-compression builds. Requires annealing before installation for optimal performance.
- MLS (Multi-Layer Steel): Composed of multiple thin steel layers with elastomer coatings, MLS shims are standard in modern engines. They offer excellent resilience, thermal stability, and reusability. Ideal for engines with high cylinder pressures, such as turbocharged or direct-injection setups.
- Compression Ratio: Performance vs. Reliability
The compression ratio is a key performance metric defined as the ratio of the cylinder volume at bottom dead center (BDC) to that at top dead center (TDC). The head shim thickness directly alters the TDC volume.
- A higher compression ratio improves thermal efficiency and power output but increases the risk of engine knocking (detonation), especially with low-octane fuel or in forced-induction applications.
- A lower compression ratio reduces stress on engine components and is more forgiving with lower-quality fuel, but may sacrifice power and efficiency.
- Always calculate the final compression ratio using piston dome volume, head gasket volume, deck clearance, and combustion chamber volume. Use online calculators or engineering software for accuracy.
- Engine Type: Compatibility is Crucial
Head shims are not universal. They are designed to match specific engine families, bore patterns, and head bolt configurations. Using an incompatible shim can result in misalignment, coolant leaks, or combustion gas blow-by.
- Always verify the shim’s inner and outer diameters, bolt hole pattern, and alignment tabs match your engine block and cylinder head.
- Performance engines (e.g., Subaru EJ series, Honda B-series, Ford EcoBoost) often require specialized shims due to unique head gasket designs.
- Aftermarket performance heads may require custom shims or modified gasket solutions.
- Tolerance and Precision: Matching Engine Build Quality
High-performance and race engines are built to tighter tolerances, requiring shims that maintain exact deck height and consistent clamping force.
- Race engines demand precision-ground shims with tolerances within ±0.025 mm to ensure uniform head sealing and prevent warping.
- Stock or daily-driven engines can often use standard off-the-shelf shims with slightly looser tolerances, provided they meet OEM specs.
- Always measure the actual deck surface flatness and use a shim that compensates for any minor variations without over-compressing.
- OEM Recommendations: Trust the Manufacturer’s Data
Original Equipment Manufacturers (OEMs) provide detailed service specifications for head gasket thickness and material, especially during engine rebuilds or after machining the block or head.
- Consult the factory service manual (FSM) for recommended shim thickness and torque sequences.
- In some cases, OEMs offer multiple shim thicknesses to correct for machining variations—this is known as a "blueprint" or "go/no-go" shim selection process.
- Deviating from OEM recommendations without proper engineering analysis can void warranties and compromise engine reliability.
| Shim Characteristic | Ideal Use Case | Common Materials | Key Considerations |
|---|---|---|---|
| 0.5–1.0 mm (Thin) | Performance builds, high-compression NA engines | Copper, MLS | Ensure adequate piston-to-valve and piston-to-head clearance |
| 1.1–2.0 mm (Standard) | Stock replacements, mild modifications | Steel, MLS | Verify OEM specifications; most common in factory setups |
| 2.1–3.0 mm (Thick) | Forced induction, low-compression builds, deck correction | MLS, Steel | May require longer head bolts or studs; affects cam timing slightly |
| Multi-Layer (MLS) | Modern turbocharged, high-pressure engines | Stainless steel + elastomer coating | Reusable, excellent heat resistance, requires proper surface finish |
| Copper (Annealed) | Racing, high-heat applications, older engines | Pure copper | Must be annealed; not reusable; excellent conformability |
Pro Tip: When installing a copper head shim, always anneal it first by heating it to a cherry-red color and allowing it to cool slowly in air. This softens the copper, improving its ability to seal against minor surface imperfections. Also, apply a light coat of high-temperature assembly lube or copper grease to both sides to prevent galling and ensure even torque distribution.
Final Recommendations
- Always measure your engine’s deck height, head flatness, and piston protrusion before selecting a shim.
- Use a reliable compression ratio calculator to predict the impact of your chosen shim.
- Follow OEM torque specifications and tightening sequences—use a calibrated torque wrench.
- Consider using aftermarket head studs for improved clamping force, especially with performance builds.
- If in doubt, consult with a professional engine builder or machinist before finalizing your shim choice.
Choosing the right cylinder head shim is more than just a mechanical task—it's an engineering decision that affects power, efficiency, and engine life. By carefully evaluating thickness, material, compression goals, and compatibility, you can optimize your engine’s performance while maintaining long-term reliability. Remember, precision and attention to detail are paramount when working with critical sealing components like head shims.
Frequently Asked Questions About Engine Cylinder Head Shims
Q1: Can a head shim be reused?No, a cylinder head shim should not be reused after removal. Most head shims are engineered for single-use applications due to their design and material properties. During engine operation, shims undergo thermal cycling and mechanical compression, which can cause microscopic warping, surface deformation, or loss of tension.
- Sealing Integrity: Reusing a shim may compromise the critical seal between the cylinder head and engine block, increasing the risk of coolant or oil leaks.
- Compression Loss: A previously compressed shim might not maintain proper clamping force, leading to reduced compression and potential engine misfires.
- Manufacturer Recommendations: Automotive and engine manufacturers typically specify that head shims must be replaced during any disassembly involving the cylinder head.
To ensure engine reliability, longevity, and optimal performance, always install a new, OEM-specified or high-quality aftermarket shim during reassembly.
Q2: How long do shims last?Cylinder head shims are generally durable components designed to last between 30,000 to 70,000 kilometers (approximately 18,000 to 43,000 miles) under normal driving conditions. However, their actual lifespan depends on several key factors:
- Material Composition: Multi-layer steel (MLS) shims tend to outlast composite or elastomer-based gaskets due to superior heat and pressure resistance.
- Engine Type: High-performance, turbocharged, or diesel engines generate higher cylinder pressures and temperatures, which can accelerate wear on sealing components including shims.
- Driving Conditions: Frequent towing, stop-and-go traffic, or aggressive driving increases thermal stress and vibration, potentially shortening shim life.
- Maintenance History: Poor cooling system maintenance or incorrect torque sequences during prior repairs can lead to premature failure.
While shims themselves don’t require routine replacement, they should be inspected during major engine work. Signs of pitting, warping, or carbon tracking indicate the need for replacement—even if the engine appears to be running normally.
Q3: Are thicker shim gaskets better?Not necessarily. The effectiveness of a shim gasket is determined by its correct thickness for the specific engine application—not by being thicker. In fact, using an improperly thick shim can negatively impact engine performance:
- Reduced Compression Ratio: A thicker shim increases the volume of the combustion chamber, effectively lowering compression. While this may be desirable in high-boost turbocharged engines to prevent detonation, it reduces efficiency and power in naturally aspirated engines.
- Valve-to-Piston Clearance: Excessive shim thickness can alter valve timing dynamics and reduce clearance between valves and pistons, risking catastrophic contact at high RPMs.
- Head Bolt Stretch: Thicker shims may prevent head bolts from achieving proper clamping load, leading to uneven sealing and potential head gasket failure.
Thicker shims are sometimes used in performance tuning to lower compression in forced-induction engines, but only as part of a calculated build. Always follow manufacturer specifications or consult an engine specialist before altering shim thickness.
Q4: Are cylinder head shims good?Yes, cylinder head shims are essential and beneficial components in modern and performance engine designs. When properly selected and installed, they offer several critical advantages:
- Improved Sealing: They create a precise, leak-proof barrier between the cylinder head and engine block, preventing escape of combustion gases, coolant, and engine oil.
- Compression Control: Shims help fine-tune the combustion chamber volume, allowing for optimized compression ratios—especially important in turbocharged or modified engines.
- Vibration Damping: Certain multi-layer or coated shims absorb thermal expansion and mechanical vibrations, enhancing engine durability under load.
- Rebuild Flexibility: In engine rebuilds, shims can compensate for slight machining differences or surface irregularities after resurfacing the head or block.
In high-performance, racing, and heavy-duty applications, head shims are not just good—they are often indispensable for maintaining engine stability, efficiency, and longevity under extreme operating conditions.
Q5: What does a shim do in a head gasket?A shim integrated into or used alongside a head gasket plays a vital role in engine function by serving multiple interrelated purposes:
- Spacing and Alignment: It ensures the correct gap between the cylinder head and engine block, maintaining precise geometry for combustion and cooling passages.
- Compression Stabilization: By controlling the combustion chamber volume, the shim helps maintain consistent compression across all cylinders, improving engine balance and power output.
- Enhanced Sealing: Especially in high-pressure engines, a metal shim adds structural support to the gasket, reducing the chance of blowouts or leaks caused by extreme cylinder pressures.
- Thermal and Mechanical Protection: Shims help distribute clamping force evenly and reduce stress concentrations that could lead to gasket failure during rapid temperature changes or heavy loads.
In essence, the shim acts as a precision-engineered component that protects the head gasket, optimizes engine performance, and contributes to long-term reliability. It is particularly crucial in performance builds, diesel engines, and turbocharged applications where tolerances are tight and operating stresses are high.









