Chainrings

"More power, better traction, less shifting. Wolf Tooth oval chainrings use our proprietary PowerTrac design that has all the benefits of oval, but without the funky, uneven pedal stroke. Ride one once and you’ll wonder why you waited so long to try oval. Think of an oval chainring as two chainrings in one. A major benefit of oval is how the shape of the chainring alters your gearing in two important phases of your pedal stroke by harnessing your body’s natural biomechanics. Here’s how it works. The area of the chainring with the larger diameter engages with the chain at the optimal point on the downstroke, which is what’s known as the Power Zone. If you were to look at a clock, the Power Zone would be between 1-5 and 7-11. Conversely, the Recovery Zone – back to the clock face, between 11-1 and 5-7 – is the weakest part of the pedal stroke, when the oval maximizes your efficiency. A 34T oval chainring behaves like a 36T chainring when you want power, while behaving like a 32T chainring when you’re climbing. We’ve also engineered our oval chainrings to provide smoother, more efficient pedal rotation. This equates to better traction because of steadier torque on the rear wheel. With a Wolf Tooth oval chainring, you can harness more of your strength in the Power Zone, while having easier pedaling in the Recovery Zone. These chainrings are for Race Face Cinch cranks such as Turbine, Next SL, Sixc & Aeffect. The Wolf Tooth Cinch chainrings feature our patented Drop-Stop® tooth profiles for the best wear life, chain retention and mud clearance. We have optimized tooth profiles for SRAM T-Type Transmission, Shimano Hyperglide+, and all 12, 11, 10, and 9-speed chains. Compatibility - Any Race Face Cinch™ system crankset (including Next SL, Sixc, Turbine, Aeffect) - Riders running SRAM Transmission w/ Race Face Cinch cranksets with a Boost 136/137mm spindle use a Cinch direct mount 0mm offset chainring. - Riders using a Cinch crankset with a Super Boost 151mm spindle use a Cinch direct mount 3mm offset chainring. - Standard (142mm rear hub spacing) 6mm offset, Boost (148mm hub spacing) 3mm offset, and Boost for T-Type Transmission 55mm chainline 0mm offset are available. - Use a 3mm offset chainring for Super Boost applications running standard drivetrains or Transmission. - Wolf Tooth’s patented Drop-Stop® wide/narrow tooth profile for the ultimate chain retention and mud shedding ability. - For 1x9, 1x10, 1x11 and 1x12 drivetrains (including SRAM Eagle) --- If using a 9-speed drivetrain use a 10-speed chain (shifts and works well on a 9-speed drivetrain and fits the ring tighter for better chain retention). - Maximum diameter is that of a chainring 2t bigger than the size you order (so be sure there is adequate chainstay clearance!) - Chainline 49mm (standard), 52mm (Boost), 55mm (T-Type Boost) - Available in multiple tooth profiles for optimal performance based on your chain type. Use Drop-Stop ST for use with Shimano 12-speed Hyperglide+ and 12spd KMC chains. Use Drop-Stop A for all 9, 10, and 11spd chains or 12spd SRAM Eagle, KMC, Connex or Wippermann chains. Drop-Stop B is optimized for SRAM 12 spd Transmission (T-type) and Road Flattop chains but is compatible with all chains that work with Drop-Stop A. Recommendations - If you plan to ride in very muddy conditions, we recommend a chainguide or chainkeeper in addition to a clutch-type rear derailleur! Without these precautions, you may experience chaindrops and/or chainsuck."

"More power, better traction, less shifting. Wolf Tooth oval chainrings use our proprietary PowerTrac design that has all the benefits of oval, but without the funky, uneven pedal stroke. Ride one once and you’ll wonder why you waited so long to try oval. Think of an oval chainring as two chainrings in one. A major benefit of oval is how the shape of the chainring alters your gearing in two important phases of your pedal stroke by harnessing your body’s natural biomechanics. Here’s how it works. The area of the chainring with the larger diameter engages with the chain at the optimal point on the downstroke, which is what’s known as the Power Zone. If you were to look at a clock, the Power Zone would be between 1-5 and 7-11. Conversely, the Recovery Zone – back to the clock face, between 11-1 and 5-7 – is the weakest part of the pedal stroke, when the oval maximizes your efficiency. A 34T oval chainring behaves like a 36T chainring when you want power, while behaving like a 32T chainring when you’re climbing. We’ve also engineered our oval chainrings to provide smoother, more efficient pedal rotation. This equates to better traction because of steadier torque on the rear wheel. With a Wolf Tooth oval chainring, you can harness more of your strength in the Power Zone, while having easier pedaling in the Recovery Zone. These chainrings are for Race Face Cinch cranks such as Turbine, Next SL, Sixc & Aeffect. The Wolf Tooth Cinch chainrings feature our patented Drop-Stop® tooth profiles for the best wear life, chain retention and mud clearance. We have optimized tooth profiles for SRAM T-Type Transmission, Shimano Hyperglide+, and all 12, 11, 10, and 9-speed chains. Compatibility - Any Race Face Cinch™ system crankset (including Next SL, Sixc, Turbine, Aeffect) - Riders running SRAM Transmission w/ Race Face Cinch cranksets with a Boost 136/137mm spindle use a Cinch direct mount 0mm offset chainring. - Riders using a Cinch crankset with a Super Boost 151mm spindle use a Cinch direct mount 3mm offset chainring. - Standard (142mm rear hub spacing) 6mm offset, Boost (148mm hub spacing) 3mm offset, and Boost for T-Type Transmission 55mm chainline 0mm offset are available. - Use a 3mm offset chainring for Super Boost applications running standard drivetrains or Transmission. - Wolf Tooth’s patented Drop-Stop® wide/narrow tooth profile for the ultimate chain retention and mud shedding ability. - For 1x9, 1x10, 1x11 and 1x12 drivetrains (including SRAM Eagle) --- If using a 9-speed drivetrain use a 10-speed chain (shifts and works well on a 9-speed drivetrain and fits the ring tighter for better chain retention). - Maximum diameter is that of a chainring 2t bigger than the size you order (so be sure there is adequate chainstay clearance!) - Chainline 49mm (standard), 52mm (Boost), 55mm (T-Type Boost) - Available in multiple tooth profiles for optimal performance based on your chain type. Use Drop-Stop ST for use with Shimano 12-speed Hyperglide+ and 12spd KMC chains. Use Drop-Stop A for all 9, 10, and 11spd chains or 12spd SRAM Eagle, KMC, Connex or Wippermann chains. Drop-Stop B is optimized for SRAM 12 spd Transmission (T-type) and Road Flattop chains but is compatible with all chains that work with Drop-Stop A. Recommendations - If you plan to ride in very muddy conditions, we recommend a chainguide or chainkeeper in addition to a clutch-type rear derailleur! Without these precautions, you may experience chaindrops and/or chainsuck."

The radical new look and feel of SRAM's X-SYNC 2 Eagle chainring is a direct result of SRAM drivetrain engineers studying the performance and wear characteristics of thousands of X-SYNC chainrings. The longer, positive-rake tooth shape has been designed to work perfectly with the Eagle chain to increase chain retention and overall pedaling efficiency, while decreasing friction, noise and wear. - Can be used with Eagle 12 speed or SRAM 11 speed chains - Direct mount rings with 3mm offset fit Boost geometry Eagle cranks; direct mount rings with 6mm offset fit traditional geometry - Eagle cranks and GXP spindle XX1, X01, X0, X1 and X9 cranks

Mud and moving parts are enemies in the sport of cyclocross. That's why SRAM decided they were going to simplify things. Remove the front derailleur, increase the range of the cassette, make dropped chains a thing of the past, and you've got a cross drivetrain worthy of hammering. SRAM's CX1 X-Sync Chain Ring is an integral part of that system. It mates to 110 BCD cranks and features a wide-narrow-wide tooth profile to securely hold the chain through the roughest terrain. It's also specially designed with mud clearing in mind to keep your rig light and fast. A variety of sizes ranging from the spin-to-win 38T to the flat-out 46T let you dial in your rig for your strengths or course.

More power, better traction, less shifting. Wolf Tooth oval chainrings use our proprietary PowerTrac design that has all the benefits of oval, but without the funky, uneven pedal stroke. Ride one once and you'll wonder why you waited so long to try oval. Think of an oval chainring as two chainrings in one. A major benefit of oval is how the shape of the chainring alters your gearing in two important phases of your pedal stroke by harnessing your body's natural biomechanics. Here's how it works. The area of the chainring with the larger diameter engages with the chain at the optimal point on the downstroke, which is what's known as the Power Zone. If you were to look at a clock, the Power Zone would be between 1-5 and 7-11. Conversely, the Recovery Zone – back to the clock face, between 11-1 and 5-7 – is the weakest part of the pedal stroke, when the oval maximizes your efficiency. A 34T oval chainring behaves like a 36T chainring when you want power, while behaving like a 32T chainring when you're climbing. We've also engineered our oval chainrings to provide smoother, more efficient pedal rotation. This equates to better traction because of steadier torque on the rear wheel. With a Wolf Tooth oval chainring, you can harness more of your strength in the Power Zone, while having easier pedaling in the Recovery Zone. Compatibility: - These rings fit on the Shimano XT M8000, SLX M7000, Deore M6000, or FC MT5100 1x or 2x cranksets. - Use only the stock Shimano XT M8000 or SLX M7000 chainring bolts - These CAN be mounted to the XTR 9000 series cranks, but you will have to use the bolt caps that come with that crankset and you will need to file roughly 1mm off the threaded boss on each bolt cap (they are a little too long and don't allow the ring to be tightened down) - Wolf Tooth's patented Drop-Stop® wide/narrow tooth profile for the ultimate chain retention and mud shedding ability - If using a 9-speed drivetrain use a 10-speed chain (shifts and works well on a 9-speed drivetrain and fits the ring tighter for better chain retention). - Provide a great chainline on most boost bikes. See this explanation for details. - Drop-Stop A models will reduce the chainline (inward towards the frame) from the Shimano specified chainline for the crankset: 26T-28T = -3mm, 30T-34T = -2mm, and 36T-38T = -1mm - Drop-Stop ST models will have the same chainline as the Shimano specified chainline - Must use the stock chainring bolts. The Wolf Tooth chainring bolts are a different size. - Ovality of 10% and timing of 112° after TDC (top dead center) - Maximum diameter is that of a chainring 2t bigger than the size you order so be sure there is adequate chainstay clearance. - Available in multiple tooth profiles for optimal performance based on your chain type. Use Drop-Stop ST for use with Shimano 12-speed Hyperglide+ and 12spd KMC chains. Use Drop-Stop A for all 9, 10, and 11spd chains or 12spd SRAM Eagle, KMC, Connex or Wippermann chains. Drop-Stop B is optimized for SRAM 12 spd Transmission (T-type) and Road Flattop chains but is compatible with all chains that work with Drop-Stop A. DROP-STOP A - Wolf Tooth Drop-Stop A is the original patented wide/narrow chainring compatible with multiple drivetrain brands including 9, 10, 11, and 12s SRAM Eagle, KMC, Wippermann, etc. - NOT compatible with 12s SRAM Transmission (T-Type) Flattop, 12s Shimano HG+, or 12s Campy DROP-STOP ST - Compatible with 12s Shimano Hyperglide+ chain and 12s KMC chain only - Symmetric Trapezoidal (ST) tooth shape is optimized for Shimano HG+ chain Recommendations - - If you plan to ride in very muddy conditions, we recommend a chainguide or chainkeeper in addition to a clutch-type rear derailleur. Without these precautions, you may experience chaindrops and/or chainsuck. - Recommend the use of a clutch style rear derailleur for the best chain security. Tech Specs: - Weight: 30t/41g | 32t/50g | 34t/59g - Material: 7075-T6 aluminum - Made in the USA

Original equipment on SRAM and Truvativ cranks, these chainrings also work well with other drivetrains.

Gates Carbon Drive CDX Front belt drive rings are crafted with 6061 aluminum and work well for high-mileage touring or rugged off-roading. - Constructed of 6061 aluminum - 11mm pitch - CDX CenterTrack belts, cogs and rings do not interchange with any part of a CDC/CDX MudPort system

More power, better traction, less shifting. Wolf Tooth oval chainrings use our proprietary PowerTrac design that has all the benefits of oval but without the funky, uneven pedal stroke. Ride one once and you’ll wonder why you waited so long to try oval. Think of an oval chainring as two chainrings in one. A major benefit of the oval is how the shape of the chainring alters your gearing in two important phases of your pedal stroke by harnessing your body’s natural biomechanics. Here’s how it works. The area of the chainring with the larger diameter engages with the chain at the optimal point on the downstroke, which is what’s known as the Power Zone. If you were to look at a clock, the Power Zone would be between 1-5 and 7-11. Conversely, the Recovery Zone – back to the clock face, between 11-1 and 5-7 – is the weakest part of the pedal stroke, when the oval maximizes your efficiency. A 34T oval chainring behaves like a 36T chainring when you want power while behaving like a 32T chainring when you’re climbing. We’ve also engineered our oval chainrings to provide smoother, more efficient pedal rotation. This equates to better traction because of steadier torque on the rear wheel. With a Wolf Tooth oval chainring, you can harness more of your strength in the Power Zone, while having easier pedaling in the Recovery Zone. The direct mount chainrings for SRAM cranksets replace your existing spider and chainring with one clean-looking, lightweight, and stiff piece of machined billet. They are available in 3 different offsets: 6mm offset for 49mm chainline, 3mm offset for 52mm chainline, and 0mm offset for 55mm chainline and SRAM Transmission optimization. They are available in various tooth profiles to suit your drivetrain, including Drop-Stop B, which is optimized for SRAM T-Type Transmission and compatible with many other chains. Crankset and chainring compatibility questions? Check out our helpful guide here.

RaceFace Narrow Wide Chainrings feature tooth profiling for chain retention and a blend of weight and durability suitable for XC, DH, and everything in-between. - 7075-T6 aluminum, aerospace grade strength - Compatible with 9, 10, 11 and 12 speed - Stiff 4mm plate thickness and I-beam construction transfer loads without flexing - Reversible laser etched graphics - Non-threaded bolt holes

Shimano's Ultegra 6800 chainrings provide confidence-inspiring shifting and category-defining speed. Cold-forged aluminum comprises these super-stiff, hollow outer rings, and Shimano's unique system of ramps and pins means lightning fast shifts are at your command. - Bolt circle diameter: 4-bolt 110mm asymmetric - 50T pairs with 34T inner ring - 52T pairs with 36T inner ring - 53T pairs with 39T inner ring Inner rings sold separately

absoluteBLACK Premium Oval 110 BCD Road Chainrings utilize absoluteBLACK's top-tier design features to greatly improve traction and speed. They are for use with all pre-2014 Shimano 5-bolt cranks, such as Dura-Ace FC7950, Ultegra FC6750, Shimano 105 5750, and more. Optimized with smooth shifting in mind, premium chainrings have a 6-point ramp and recess design. Chainrings are crafted from CNC machined 7075 aluminum and feature an anodized finish for exceptional durability. - Oval shape reduces stress on knees, helps to keep your legs fresh, and does not feel any different while riding - Chainring design reduces the possibility of leg cramps and allows you to maintain a better cadence while climbing - Use with absoluteBLACK long chainring bolts - 6.5% ovality is ideal for road climbing

Original equipment on SRAM and Truvativ cranks, they also work well with other drive trains. - 7000 series aluminum provides strength and durability

An issue many people ran into when they began using 1x setups was chain retention with the front chainring. In the beginning of the 1x movement, many companies dealt with this by using aftermarket chain keepers that somehow bolted to the frame. Many people discovered that using a narrow-wide chainring in conjunction with some type of 'clutch' rear derailleur helped abate or eliminate these chain-jumping issues. Narrow-wide rings use alternating tooth profiles that more positively engage the chain and help control a deflecting chain in bumpy conditions. Your friends at Surly have partnered with SRAM to bring you stainless steel X-Sync chainrings. Stainless Steel is durable. This durability is pretty useful when you're talking about the one ring that is bearing the brunt of all your miles.

Shifting performance has helped Full Speed Ahead to become a world leader for high-end chainrings. No one studies the design and manufacturing of each system, and each tooth, as carefully as we do. Our dedication shows in every revolution of the crank, and every perfect shift achieved. To meet or exceed the needs of any drivetrain, Full Speed Ahead has developed sophisticated design, testing and manufacturing protocols. This allows Full Speed Ahead to match your needs as perfectly as our chainrings match a chain. We offer more options, levels, and finishes than our competitors. We use the best materials available, imported from the USA, Europe, or sourced from our qualified vendors in Asia, to guarantee the durability, performance, and appearance will out-perform, and outlast the competition. Full Speed Ahead chainrings have powered multiple World, Tour de France, and Olympic champions, and will exceed your expectations. True value and performance are found in this FSA road chainring. It offers both long wear life and smooth shifting. - Stamped AL7075/T6 - N11 chainrings are compatible with all 10 speed drivetrains, and compatible with FSA, SRAM and Shimano 11-speed drivetrains - Ramped and pinned for excellent shifting - FSA 110 BCD - 4-Bolt - Material: Aluminum - Ring Position/Type: Inner

Shimano XT M8000 11-Speed Chainrings - Chainring BCD: 96 Shimano Asymmetric - Color: Black - Drivetrain Speeds: 11 - Material: Aluminum - Ring Position/Type: Inner - Tooth Count: 34

Shimano XT CRM80 1x11 Chainrings - Hollow gear construction for optimized rigidity, weight, and rigidity - Durable teeth using plated steel construction supported by a carbon composite (CFRP) carrier body - Dyna-Sys11 HG-X11 11-speed chain compatible - Chainring BCD: 96 Shimano Asymmetric - Color: Black - Drivetrain Speeds: 11 - Material: Steel/Carbon - Ring Position/Type: Chain Retaining Single Ring - Tooth Count: 30

64BCD chainring for MTB cranksets

This 94 BCD 5-bolt ring will serve all your Vintage crankset and Surly OD crankset needs. - Fits any 94 BCD 5-bolt crankset (modification may be needed) - Drop-Stop technology. On Wolf Tooth’s patented wide/narrow chainring, the wide side of the tooth has maximum contact on the drive side which spreads the load and improves chainring life. The narrow side allows clearance for mud and debris which reduces friction. - Alternating wide/narrow tooth pattern prevents chain derailment Compatibility: - Four of the holes are threaded and one is a normal through bolt hole (done for Surly compatibility). Use a stock 10mm chainring bolt for the fifth, hidden arm. - These rings fit any 94 BCD 5 bolt crankset (possible alterations needed to fit some crankarms) - For Plus size bike applications with the Surly OD crankset, e.g. Instigator and Krampus, you will need to use the stock spacers (Spacer Kit QBP Part number CR8609) that came with your 1x setup. You will also need some 16mm bolts which can be purchased from Problem Solvers. - If using a 9-speed drivetrain use a 10-speed chain (shifts and works well on a 9-speed drivetrain and fits the ring tighter for better chain retention). - Provides a great chainline on most boost bikes. - Chainline (approximate as BB centering and cranksets vary) DROP-STOP A Wolf Tooth Drop-Stop A is the original patented wide/narrow chainring compatible with multiple drivetrain brands including 9, 10, 11, and 12spd SRAM Eagle, KMC, Wippermann, etc. Recommendations If you plan to ride in very muddy conditions, we recommend a chainguide or chainkeeper in addition to a clutch-type rear derailleur. Without these precautions, you may experience chaindrops and/or chainsuck. Tech Specs: - Weight: 28t/37g | 30/48g | 32t/57g - Material: 7075-T6 aluminum - Made in the USA

The 102BCD chainring was made specifically for the XTR M960 crankset - Only fits on the M960 crankset in the middle ring position - Drop-Stop technology. On Wolf Tooth's patented wide/narrow chainring, the wide side of the tooth has maximum contact on the drive side which spreads the load and improves chainring life. The narrow side allows clearance for mud and debris which reduces friction - Alternating wide/narrow tooth pattern prevents chain derailment Compatibility: - These rings only fit on the M960 crankset in the middle ring position - If using a 9-speed drivetrain use a 10-speed chain (shifts and works well on a 9-speed drivetrain and fits the ring tighter for better chain retention) - 6mm chainring bolts needed - Chainline: 50mm - Use Drop-Stop A for all 9, 10, and 11spd chains or 12spd SRAM Eagle, KMC, Connex or Wippermann chains DROP-STOP A - Wolf Tooth Drop-Stop A is the original patented wide/narrow chainring compatible with multiple drivetrain brands including 9, 10, 11, and 12spd SRAM Eagle, KMC, Wippermann, etc. - NOT compatible with 12spd SRAM Transmission (T-Type) Flattop, 12spd Shimano HG+, or 12spd Campy Recommendations - If you plan to ride in very muddy conditions, try using a chainguide or chainkeeper in addition to a clutch-type rear derailleur. Without these precautions, you may experience chaindrops and/or chainsuck Tech Specs: - Weight: 32t/47g - Material: 7075-T6 aluminum

The SRAM X-Sync Steel 1x chainrings are the perfect replacement ring for the cost conscious with added durability of steel. The same SRAM X-Sync technology at a price well below competitors’ imitation “narrow wide” rings. Best performing chainrings at the best price. - Compatibility: Compatible with all SRAM 1x cranks, DM 28-tooth ring is not compatible with 30mm cranks that require a 0mm offset ring

612 Track rings are the perfect compliment to any 144mm B.C.D. crankset. They are made from 7000 series aluminum and feature a lovely and durable anodized finish. - BCD: 144 - Chain Compatibility: 1/2-inch x 1/8-inch

Deore M6000 series 10-speed chainrings provide smooth and reliable shifting, ideal for off-road riding conditions. - Shimano HG-X technology - Compatible with 4-arm crank design

- Trushift chainrings feature shift ramps and pins - Drivetrain compatibility: 8, 9, 10, 11 - 104mm BCD

Shimano XT M8000 11-Speed Chainrings - Chainring BCD: 64 Shimano Asymmetric - Color: Silver - Drivetrain Speeds: 11 - Material: Aluminum - Ring Position/Type: Inner

Original equipment on SRAM and Truvativ cranks, these chainrings also work well with other drivetrains.

SRAM's X-Sync 11-speed chainring features tall teeth with an alternating tooth profile to hold the chain amazingly well and still provide space for mud to clear. - Drivetrain Speeds: 10, 11 - Material: Aluminum - Ring Position/Type: Chain Retaining Single Ring

Shimano chainrings offer durability and confidence-inspiring performance, and go a long way towards getting a drivetrain back to optimum working condition.

- X-Range gearing technology gives you more range and a smoother gear progression, so you're always in the right gear - Specially designed tooth profiles for improved wear - More durable finish - Bolt Circle Diameter (BCD): 107 BCD - Speeds: 12 - Material: Aluminum

FSA Pro Road Chainrings deliver flawless shifting for any road drivetrain. - Precision CNC machined AL7075/T6 alloy

Wolf Tooth was first to market with cyclocross 1x specific chainrings because we saw cyclocross as the perfect use for our patent pending Drop-Stop® technology. These beautifully machined 110 BCD asymmetric 4-bolt chainrings are optimized for your 1x Shimano CX / road / gravel drivetrain whether you run Dura Ace 9000, Ultegra 6800, 105 5800, or Tiagra 4700. They are also offset for the ideal 1x chainline. - Fits 110 BCD Asymmetric 4-bolt Shimano cranks - Drop-Stop technology. On Wolf Tooth's patented wide/narrow chainring, the wide side of the tooth has maximum contact on the drive side which spreads the load and improves chainring life. The narrow side allows clearance for mud and debris which reduces friction. - Alternating wide/narrow tooth pattern prevents chain derailment Compatibility: - Fits 110 BCD asymmetric 4-bolt cranks - All sizes compatible with Dura Ace 9000, Ultegra 6800, 105 5800, RS510, Tiagra 4700 or 4703, Sora R3000 or R3030, and Claris R2000 or R2030 cranks. - 38-50t are compatible with 105 R7000, Ultegra R8000, and Dura-Ace R9100. The 36t chainring is NOT compatible with these cranks. - NOT compatible with Dura-Ace R9200, Ultegra R8100, and 105 R7100 Cranks - Size 42t and larger will work with the Dura Ace 9100 power meter - Mounts in the big ring position of the cranks but is offset inward for perfect chainline. - The stock 2x bolts will not work. You will need our 6mm bolts which are optimized for single ring mounting. - If using a 9-speed drivetrain use a 10-speed chain. It fits tighter for better chain retention - Chainline 47.5mm - Use Drop-Stop B for all SRAM Eagle, SRAM Road and Transmission (T-Type) Flattop chains, 9, 10, and 11spd chains or 12spd KMC, Connex, Wippermann, Campagnolo. DROP-STOP B Compatible 9, 10, 11, and 12spd SRAM Eagle, 12spd SRAM Transmission (T-type) Flattop, 12spd Campy, 12spd KMC Not compatible with 12spd Shimano HG+ chains