Gas Mass Flow Controller

A gas mass flow controller (MFC) is a closed-loop field instrument that measures the mass flow rate of a gas and simultaneously drives it to a commanded set point by modulating an integrated proportional valve. It combines three functions in one body: a mass-sensing element, a control valve, and an embedded PID loop that compares measured flow against the set point and adjusts the valve until they match. Unlike a rotameter or a volumetric flow meter, an MFC reports mass flow (referenced to standard or normal conditions), so its reading does not drift when process temperature or line pressure changes.

MFCs are the workhorse of any process that must deliver a precise, repeatable quantity of gas: semiconductor deposition and etch, analytical instruments, fuel-cell test stands, burner and furnace control, coating, and laboratory gas blending. This guide explains the three dominant sensing principles, the spec-sheet terms that actually drive selection, and the gas-reference and gas-conversion pitfalls that cause most field errors.

LAMBDA MASSFLOW benchtop gas mass flow controller unit with digital set-point display reading 340 and ON/OFF, SET, REMOTE, RUN and PROGRAM control buttons

Photo: ரோஜா, CC BY-SA 3.0, via Wikimedia Commons

This guide is written for procurement engineers and design engineers specifying gas delivery hardware. It covers 6 chapters from definition and history, controller types, sensing technologies, gas reference and conversion, key specification parameters, to selection decisions, with 7 selection FAQs and manufacturer comparisons. Parameters reference public manufacturer datasheets (Bronkhorst, MKS, Alicat, Brooks) and the SEMI E16, SEMI E52 (now SEMI AUX030), SEMI E67 and SEMI F1 standards.

Chapter 1 / 06

What is a Gas Mass Flow Controller

A gas mass flow controller is an active instrument that does two jobs at once: it measures the mass flow rate of a gas and it forces that flow to a value you command. A mass flow meter only measures; a controller adds a proportional control valve and an embedded PID (proportional-integral-derivative) loop that continuously compares the measured flow against the set point and modulates the valve until measured equals commanded. This distinction is the first thing to settle on any purchase order, because a meter and a controller of the same range and accuracy can differ severalfold in price.

Structurally, an MFC contains four functional blocks. First, a flow-splitting inlet, where a precise fraction of the gas is routed through a small sensor tube (or, in through-chip designs, the full stream passes a MEMS sensor). Second, the sensing element, which converts flow into an electrical signal by a thermal, differential-pressure, or Coriolis principle. Third, the control valve, typically a solenoid-actuated or piezo-actuated proportional valve that throttles the main stream. Fourth, the electronics: a PID controller, the analog or digital set-point interface, temperature compensation, and self-diagnostics. When all four are integrated and the device outputs and accepts standardized signals, the industry calls it an MFC.

The instrument answers the engineering question how do I deliver exactly 47.5 slm of argon to this chamber regardless of upstream pressure swings. Because the reading is mass-referenced (expressed as a volumetric-equivalent at a fixed reference temperature and pressure, for example sccm or slm), it does not wander when the gas warms up or the supply regulator droops. This temperature and pressure immunity is the core reason MFCs displaced rotameters and needle valves in any process where film thickness, stoichiometry, or analytical repeatability depend on gas dose.

The technology traces to the United States space program. A Tylan-developed mass flow meter built for the Apollo program, later acquired by Brooks Instrument, became the foundation of the first commercial MFCs; the Tylan FC-260 let early semiconductor fabs automate process-gas delivery for higher yield and throughput. From the 1970s onward, thermal capillary MFCs became standard in chip manufacturing, and the SEMI standards body codified leak-rate description (SEMI E16), reliability testing (SEMI E67), and reference-gas indexing (SEMI E52, now carried as SEMI AUX030). Brooks Instrument marked 75 years of fluid measurement and control in 2021, an indication of how mature the supply base is.

Today the MFC market is anchored by the semiconductor industry, where a single deposition or etch tool may carry dozens of MFCs feeding a gas panel, and broadened by analytical instruments, hydrogen and fuel-cell testing, burner control, and laboratory gas mixing. Modern devices have evolved toward pressure-insensitive control, multi-gas calibration tables, and digital fieldbus integration. Four engineering metrics determine whether a given MFC fits a duty: accuracy and its reference basis, the controllable flow range and turndown, the settling time, and the seal and material grade. The rest of this guide decodes each.

Chapter 2 / 06

Controller Types and Configurations

Gas mass flow controllers are classified along two axes that matter at selection time: the sensing principle (covered in detail in Chapter 3) and the mechanical configuration, which is the body style, seal type, and bus interface. Choosing the wrong configuration is a common and expensive mistake, because a controller correct in range and accuracy can still be unusable if its seal grade outgasses into an ultra-high-purity gas or if its body does not drop into the gas panel. The table below summarises the main configuration choices.

Configuration axisCommon optionsWhen to choose
Seal / wetted pathElastomer (Viton, Kalrez) vs all-metal (316L)Industrial blending tolerates elastomer; semiconductor and reactive gas require all-metal
Body styleInline compression fitting, VCR, surface-mount / downportSurface-mount for integrated gas systems; inline for general lab and process
Set-point interface0-5 V, 0-10 V, 4-20 mA analogSimple PLC or DCS loops, retrofit into legacy panels
Digital busRS232, RS485 Modbus, EtherCAT, PROFINET, EtherNet/IP, DeviceNetSmart fabs, multi-device gas panels, remote diagnostics
Valve actuatorSolenoid proportional vs piezoelectricPiezo for fast settling and low power; solenoid for cost and robustness

Seal grade is the first fork. General industrial gas blending, furnace air-fuel ratio, and laboratory mixing can use elastomer-sealed bodies (Viton or Kalrez O-rings and valve plugs), which are cheaper and tolerant of light contamination. Semiconductor and reactive-gas duty requires all-metal seals because elastomers permeate, outgas, and corrode. A representative metal-sealed semiconductor MFC uses a 316L stainless steel wetted path electropolished to roughly a 10 microinch (about 0.25 micrometre Ra) finish, with metal-to-metal seals throughout, qualifying it for high-purity service.

Body style and mounting follow the gas panel. Traditional inline MFCs use compression or VCR face-seal fittings and bolt into tubing runs. Modern fabs favour surface-mount (downport) bodies that seat onto a modular substrate so an entire gas stick can be assembled and leak-tested as one block, simplifying maintenance swap-out. SEMI component standards govern these footprints so devices from different makers interchange.

Interface and bus. The legacy interface is analog: a 0-5 V or 0-10 V set point and flow signal, or 4-20 mA. Most current MFCs add a digital bus, with RS232 and RS485 Modbus on lab and process units and industrial Ethernet variants (EtherCAT, PROFINET, EtherNet/IP) or DeviceNet on automated tools, enabling multi-gas tables, remote re-ranging, alarms, totalisers, and self-diagnostics that an analog wire cannot carry. Finally, the valve actuator splits into solenoid proportional valves (robust, low cost, the industrial default) and piezoelectric valves (faster settling, lower heat and power, favoured where dose timing is critical).

A separate configuration choice is normally-closed versus normally-open valve action for safety on power loss, and whether the MFC includes a downstream or upstream shut-off. For hazardous or pyrophoric gases, a normally-closed valve that fails shut on power loss is mandatory, and the body may carry additional purge and isolation provisions on the gas stick.

Chapter 3 / 06

Sensing Technologies Compared

Three sensing principles dominate gas mass flow control: thermal (capillary and MEMS), laminar differential pressure, and Coriolis. Each has an optimal flow band, accuracy basis, and gas-handling behaviour, and there is no universal principle. The choice fixes whether you depend on a gas conversion factor, how the device scales to high flow, and whether the accuracy is quoted as percent of reading or percent of full scale. The table compares the engineering essentials.

PrincipleTypical accuracyTypical rangeGas dependenceTypical applications
Thermal capillary±0.5% RD + 0.1% FS~0.01 mln/min to ~50 slmNeeds GCF or per-gas calibrationSemiconductor, lab, analytical
Thermal MEMS~1% FSsccm to a few slmNeeds GCF; fast responseOEM, embedded, consumer gas tools
Laminar differential pressure±0.5% RD or 0.05% FSsccm to hundreds of slmMulti-gas via NIST property tablesMulti-gas labs, R&D, high flow
Coriolis±0.5% RD (gas)low-flow gas and liquidDirect mass, gas-independentUnknown or mixed gases, custody

Thermal capillary is the classic MFC sensor. The gas stream is split: a small, precisely-defined fraction passes through a heated capillary sensor tube while the bulk passes a laminar bypass. Two temperature sensors on the capillary measure the temperature difference created as flowing gas carries heat downstream; that difference is proportional to mass flow through the gas heat capacity. Capillary designs give excellent linearity and high sensitivity at low flow (a few sccm up to several slm). Because the signal depends on the gas molar heat capacity, the device is calibrated on a surrogate (usually nitrogen) and corrected with a gas conversion factor, or factory-calibrated on the actual gas. Bronkhorst EL-FLOW Select and MKS G-series GE50A and GM50A are representative thermal capillary MFCs.

Thermal MEMS places the heater and temperature sensors on a micromachined chip. Modern through-chip designs measure the full flow rather than a sampled fraction and respond faster than traditional capillary sensors. MEMS units are compact and cost effective, which makes them the practical choice for embedded OEM and basic gas applications, but they typically cannot match the accuracy of laminar differential-pressure or Coriolis sensors and remain gas-dependent. Sensirion is a representative OEM MEMS supplier.

Laminar differential pressure forces the gas through a laminar flow element so the flow is smooth and the Poiseuille relation makes pressure drop proportional to volumetric flow; combined with measured pressure and temperature, the device computes mass flow. The strength is multi-gas flexibility: vendors embed NIST-traceable compressibility and viscosity data so one device can be re-tasked across dozens of gases without re-calibration. Alicat laminar DP MC-series controllers can handle dozens of gases with NIST-traceable accuracy, quote accuracy as good as plus-or-minus 0.5 percent of reading or 0.05 percent of full scale (whichever is greater), and achieve control response on the order of tens of milliseconds. The trade-off is that the pressure sensors create trapped volume and are sensitive to pressure spikes.

Coriolis vibrates a small tube and reads the Coriolis-induced phase shift, which is directly proportional to mass flow. This is a true direct mass measurement, independent of gas density, temperature, viscosity, pressure, and composition, so it needs no gas conversion factor and works on unknown or changing gas mixtures and even on liquids and supercritical fluids without re-calibration. Bronkhorst mini CORI-FLOW is a reference low-flow Coriolis series, with gas accuracy around plus-or-minus 0.5 percent of reading. The cost is higher price and larger size, so Coriolis is reserved for duties where gas-independence or the highest fidelity justifies it.

A fourth direction is pressure-based control for semiconductor process gas. Brooks Instrument introduced pressure-based MFCs (the GP200 series) that are fully pressure-insensitive, using a patented architecture to deliver precise, repeatable gas delivery for etch and CVD even as upstream pressure varies, which is a recurring problem on shared gas panels.

Chapter 4 / 06

Gas Reference, Units and Conversion Factors

More MFC field errors come from misreading the gas reference basis than from any hardware defect. Because an MFC reports mass as a volumetric-equivalent at a fixed reference temperature and pressure, the same physical mass flow can be quoted as two different numbers under two reference conventions. Getting this wrong silently biases a whole gas recipe. Two issues compound: the reference condition (standard versus normal) and the gas conversion factor (when one gas is used to calibrate for another).

Reference conditions. sccm (standard cubic centimetres per minute) and slm (standard litres per minute) are referenced to fixed conditions; the common semiconductor convention is 0 degrees Celsius and 1 atmosphere (760 Torr), although some vendors define standard at 20 or 25 degrees Celsius. The European convention separates normal from standard: ln/min and ls/min where normal uses 0 degrees Celsius and 1.013 bar, and standard uses 20 degrees Celsius. Because gas density scales inversely with absolute temperature, 1 normal litre is approximately 1.07 standard litres referenced to 20 degrees Celsius, a difference near 7 percent. The table makes the conventions explicit.

Unit / termReference TReference PNotes
sccm / slm (semiconductor)0 °C (some 20 or 25 °C)1 atm (760 Torr)Confirm vendor reference; not universal
ln/min (normal, EU)0 °C1.013 barBronkhorst normal litre convention
ls/min (standard, EU)20 °C1.013 bar~7% higher volume than normal litre
mln/min0 °C1.013 barMilli-normal litre, low-flow ranges

The practical rule: before comparing two datasheets or transferring a recipe between tools, confirm both the reference temperature and the reference pressure. A flow specified as 50 slm at a 0 degrees Celsius reference is a different mass flow than 50 slm at 25 degrees Celsius, and a control loop that assumes the wrong basis will under or over-dose by several percent.

Gas conversion factors. Thermal MFCs respond to the gas molar heat capacity, not to the species you intend to run, so a unit calibrated on nitrogen must be corrected when used on another gas. The correction is the gas conversion factor (GCF), also called a K-factor or relative gas correction factor. A GCF greater than 1 means the gas is lighter or has lower volumetric heat capacity than nitrogen (helium is roughly 1.40, hydrogen roughly 1.00), while a GCF less than 1 means denser or higher heat capacity (sulphur hexafluoride is roughly 0.27). Vendors tabulate GCFs and the semiconductor reference-gas index is standardised in SEMI E52, now carried as SEMI AUX030.

GCFs are convenient but only approximate. They typically add 1 to 5 percent of additional uncertainty and degrade for high-pressure, reactive, or polyatomic gases where the simple heat-capacity ratio breaks down. When the application needs tight accuracy on a specific gas, there are two clean paths: order the thermal MFC factory-calibrated on the actual process gas (eliminating the GCF), or select a laminar differential-pressure device with NIST-traceable multi-gas property tables, or a Coriolis device whose direct mass reading is intrinsically gas-independent and needs no conversion factor at all.

Chapter 5 / 06

Key Specification Parameters

Reading an MFC datasheet is a core procurement skill. A single device may list 20 or more parameters, but only a handful drive selection: accuracy and its reference basis, repeatability, full-scale range and turndown, minimum controllable flow, settling time, operating temperature and inlet pressure, leak integrity, and the set-point interface. Each is decoded below, with representative figures from public datasheets.

ParameterRepresentative figureWhy it matters
Accuracy (thermal)±0.5% RD + 0.1% FSCombined reading and full-scale error; FS term dominates at low set point
Accuracy (laminar DP)±0.5% RD or 0.05% FSWhichever is greater; strong percent-of-reading behaviour
Repeatability<±0.2% RDRun-to-run scatter; sets dose consistency
Turndown / control range~50:1 (extended)Usable span without changing the device
Settling time~30 ms to ~2 sSpeed to reach set point within an error band
Max inlet pressureup to ~400 bar(g)Series and body dependent; gate for high-pressure gas
Operating temperature−10 to +70 °CAmbient envelope for rated accuracy

Accuracy and its basis. Thermal MFCs commonly state accuracy as a combined term, for example plus-or-minus 0.5 percent of reading plus 0.1 percent of full scale; a representative low-flow thermal series quotes exactly this. The percent-of-full-scale term is the trap: on a 100 slm device the 0.1 percent FS term alone is 0.1 slm, but on a 10 slm device it is only 0.01 slm. That is why range selection (below) is inseparable from accuracy. Laminar DP devices often quote plus-or-minus 0.5 percent of reading or a small percent of full scale, whichever is greater, which holds accuracy better across turndown. Some semiconductor thermal MFCs instead state accuracy as a percent of set point, for example 1 percent of set point from 20 to 100 percent of full scale and a percent-of-full-scale floor below that.

Repeatability is the run-to-run scatter at the same set point under identical conditions and is the metric that sets dose consistency in a recipe; good thermal units specify better than plus-or-minus 0.2 percent of reading. Repeatability is independent of accuracy: a device can be highly repeatable yet biased, which is acceptable for relative dosing but not for absolute calibration.

Range, turndown and minimum controllable flow. Full-scale range fixes the device span; turndown (rangeability) is the ratio between the largest and smallest flow the device controls to spec, with extended digital turndown around 50:1 available on some thermal series. Critically, every MFC has a minimum controllable flow, often around 2 percent of full scale for thermal units, below which control degrades. Choose the range so the normal operating set point sits between roughly 20 and 80 percent of full scale.

Settling time is the interval from a set-point step until the flow stays inside a defined error band, for example plus-or-minus 2 percent of set point. It spans from roughly 30 milliseconds on fast laminar DP units to several hundred milliseconds on semiconductor metal-sealed thermal MFCs to 1 to 2 seconds on large high-flow units. Always compare settling figures at the same error band and the same step size, because a 2 percent band and a 1 percent band give very different numbers for the same hardware.

Operating temperature and inlet pressure. A representative thermal series rates an ambient operating range of −10 to +70 degrees Celsius and a maximum pressure up to 400 bar(g) on specific body variants; outside the rated ambient window accuracy is not guaranteed, and inlet pressure rating gates high-pressure gas duties. Leak integrity is decisive for hazardous or high-purity gas: SEMI E16 defines and describes MFC leak rates, distinguishing mechanical from diffusion leakage, and SEMI F1 sets leak-integrity requirements for high-purity gas piping and components. Set-point interface (analog 0-5 V, 0-10 V, 4-20 mA, or a digital bus) must match the control system; digital buses additionally unlock multi-gas tables, totalisers, and diagnostics.

Chapter 6 / 06

Selection Decision Factors

To turn the preceding chapters into a specific model, follow the decision sequence below. Most selection mistakes come not from a single wrong step but from deciding range or accuracy before the gas, pressure, and seal context is fixed. These eight steps work as a reusable RFQ template.

  1. Gas species and purity: Identify every gas the device will run and whether it is inert, reactive, corrosive, pyrophoric, or ultra-high-purity. Reactive and high-purity gas mandates all-metal 316L electropolished wetted paths; inert lab gas tolerates elastomer seals. Multi-gas duty favours laminar DP or Coriolis over single-gas thermal calibration.
  2. Reference basis and units: Lock the reference temperature and pressure (sccm or slm at 0 versus 20 or 25 degrees Celsius, or ln/min versus ls/min) before quoting any flow number, so the recipe is unambiguous across tools and vendors.
  3. Flow range and turndown: Size the full scale so the normal operating set point sits between about 20 and 80 percent of full scale, stay above the minimum controllable flow (often 2 percent of FS), and check turndown if a single device must cover a wide span.
  4. Accuracy basis and class: Decide whether percent-of-reading or percent-of-full-scale behaviour suits the duty; oversized ranges inflate the full-scale error term. Reserve Coriolis or laminar DP for wide-turndown or unknown-gas precision.
  5. Settling time: Match settling to the process: fast pulsed or analytical dosing needs tens to low hundreds of milliseconds (piezo valve, laminar DP), while steady furnace or blending loops tolerate 1 to 2 seconds.
  6. Mechanical body and connection: Inline compression or VCR for general process and lab; surface-mount or downport for integrated gas systems and field-replaceable gas sticks. Confirm fitting type, orientation, and inlet pressure rating.
  7. Interface and protocol: Analog 0-5 V, 0-10 V or 4-20 mA for simple loops and retrofits; RS485 Modbus or industrial Ethernet (EtherCAT, PROFINET, EtherNet/IP) or DeviceNet for automated multi-device panels needing multi-gas tables and diagnostics.
  8. Certifications and standards: For semiconductor and hazardous gas, require SEMI E16 leak-rate description, SEMI E67 reliability, SEMI F1 leak integrity, the SEMI E52 (now SEMI AUX030) reference-gas index, and where applicable hazardous-area or functional-safety certification.

One last commonly overlooked dimension is manufacturer serviceability: factory calibration on the actual process gas, recalibration turnaround, availability of multi-gas tables, firmware upgradability, and local spare-part and support presence. These look secondary at purchase but determine downtime after years of production. Bronkhorst, MKS, Brooks Instrument, Alicat, Sensirion, Horiba STEC, and Chinese supplier Sevenstar (北京七星华创) all maintain established calibration and support channels; matching seal type, accuracy basis, range, and bus protocol to the duty before shortlisting a series avoids the most expensive re-orders.

FAQ

What is the difference between a mass flow controller and a mass flow meter?

A mass flow meter (MFM) only measures and reports the gas mass flow rate; it has no actuator. A mass flow controller (MFC) adds a proportional control valve and an integrated PID loop on top of the same measuring element, so it both measures the flow and drives it to a commanded set point. You send the MFC a set point as an analog signal (0-5 V or 4-20 mA) or a digital command over RS232, RS485, EtherCAT, PROFINET, EtherNet/IP or DeviceNet, and the device modulates its valve until measured flow equals the set point. In short, a meter answers how much is flowing, while a controller also makes a specified amount flow.

What is the difference between sccm, slm, ln/min and standard versus normal conditions?

MFCs report mass flow as an equivalent volumetric flow referenced to a fixed temperature and pressure, so the unit only has meaning once those reference conditions are stated. sccm is standard cubic centimetres per minute and slm is standard litres per minute; the common semiconductor standard reference is 0 degrees Celsius and 1 atm (760 Torr), though some vendors use 20 or 25 degrees Celsius. ln/min and ls/min are the European normal and standard litre conventions: normal uses 0 degrees Celsius and 1.013 bar, standard uses 20 degrees Celsius. Because density scales with absolute temperature, 1 normal litre is roughly 1.07 standard litres at 20 degrees Celsius, a difference near 7 percent. Always confirm the reference basis before comparing two datasheets or you can be off by 7 percent or more.

How do thermal, pressure-based and Coriolis mass flow controllers differ?

Thermal (capillary or MEMS) MFCs infer mass flow from heat carried away by the gas; they dominate the 0 to roughly 100 slm range, are compact and cost effective, but depend on the gas heat capacity so they need a gas conversion factor or a per-gas calibration. Laminar differential-pressure MFCs force the gas through a laminar element and apply the Poiseuille relation between pressure drop and flow; they offer fast settling and broad multi-gas tables using NIST-traceable property data. Coriolis MFCs vibrate a tube and read the Coriolis deflection, giving a true direct mass reading that is independent of gas density, temperature, viscosity and composition, at the cost of higher price and size. Pressure-based and Coriolis units scale better to high flows and unknown gas mixtures than thermal units.

Why is full-scale range selection so important for an MFC?

Most MFC accuracy specifications include a percent-of-full-scale term, so an oversized range directly inflates absolute error at low set points. If an MFC is specified at plus-or-minus 0.5 percent of reading plus 0.1 percent of full scale, the full-scale term alone is 0.1 slm on a 100 slm device but only 0.01 slm on a 10 slm device. Best practice is to choose a range so the normal operating set point sits between about 20 and 80 percent of full scale, and never to run continuously below the manufacturer minimum controllable flow (often 2 percent of full scale for thermal units). A device with a pure percent-of-reading spec, such as a Coriolis MFC, tolerates wider turndown without this penalty.

What is a gas conversion factor and when can I rely on it?

A gas conversion factor (GCF), sometimes called a K-factor or relative gas correction factor, scales a thermal MFC calibrated on a surrogate gas (usually nitrogen) to a different process gas, because the thermal principle responds to molar heat capacity rather than to the gas you actually run. For example helium reads roughly 1.4 times and sulphur hexafluoride roughly 0.27 times the nitrogen-equivalent indication. GCFs are tabulated by vendors and standardised through references such as SEMI E52, now carried as SEMI AUX030. They are convenient but only approximate, typically adding 1 to 5 percent uncertainty, and they degrade for high pressure, reactive or polyatomic gases. For tight accuracy, order the MFC factory calibrated on the actual process gas, or choose a pressure-based or Coriolis device with direct multi-gas handling.

How fast can a mass flow controller settle to a new set point?

Settling time is the interval from a set-point change until the flow stays inside a defined error band, for example plus-or-minus 2 percent of set point. Modern low-flow thermal and laminar differential-pressure MFCs reach settling times below 300 milliseconds, and fast laminar units quote control response near 30 milliseconds, while large high-flow MFCs may take 1 to 2 seconds. Metal-sealed semiconductor MFCs such as common 5 to 50,000 sccm G-series units specify settling on the order of several hundred milliseconds. Settling depends on valve type, dead volume, inlet pressure stability and PID tuning, so always compare settling figures at the same error band and the same percent-of-full-scale step.

Which standards and seal types matter for semiconductor-grade MFCs?

Semiconductor process gas is corrosive and ultra-high-purity, so MFC wetted paths are typically 316L stainless steel electropolished to a 10 microinch (about 0.25 micrometre Ra) finish with all-metal seals, because elastomer seals outgas and permeate. SEMI standards govern this domain: SEMI E16 defines and describes MFC leak rates, SEMI E67 is the reliability test method, SEMI F1 sets leak integrity for high-purity gas piping and components, and the reference gas index lives in SEMI E52 (now SEMI AUX030). Surface-mount and downport bodies follow SEMI F-series component standards so MFCs drop into integrated gas systems. For general industrial gas blending, elastomer-sealed (Viton, Kalrez) bodies are acceptable and far cheaper.

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