Distance-of-Flight Mass Spectrometry: What, Why, and How?
Distance-of-flight mass spectrometry (DOFMS) separates ions of different mass-to-charge (m/z) by the distance they travel in a given time after acceleration. Like time-of-flight mass spectrometry (TOFMS), separation and mass assignment are based on ion velocity. However, DOFMS is not a variant of TOFMS; different methods of ion focusing and detection are used. In DOFMS, ions are driven orthogonally, at the detection time, onto an array of detectors parallel to the flight path. Through the independent detection of each m/z, DOFMS can provide both wider dynamic range and increased throughput for m/z of interest compared with conventional TOFMS. The iso-mass focusing and detection of ions is achieved by constant-momentum acceleration (CMA) and a linear-field ion mirror. Improved energy focus (including turn-around) is achieved in DOFMS, but the initial spatial dispersion of ions remains unchanged upon detection. Therefore, the point-source nature of surface ionization techniques could put them at an advantage for DOFMS. To date, three types of position-sensitive detectors have been used for DOFMS: a microchannel plate with a phosphorescent screen, a focal plane camera, and an IonCCD array; advances in detector technology will likely improve DOFMS figures-of-merit. In addition, the combination of CMA with TOF detection has provided improved resolution and duty factor over a narrow m/z range (compared with conventional, single-pass TOFMS). The unique characteristics of DOFMS can enable the intact collection of large biomolecules, clusters, and organisms. DOFMS might also play a key role in achieving the long-sought goal of simultaneous MS/MS.
KeywordsDistance-of-flight Time-of-flight Sector field mass spectrometry IonCCD Inductively coupled plasma Matrix-assisted laser-desorption ionization MALDI
Introduction and Perspective
Mass spectrometers are now ubiquitous in analytical laboratories, and the range of applications, environments, and measurements to which mass spectrometry (MS) is applied is extensive. An impressive but not comprehensive list of research fields outside analytical chemistry influenced by MS development includes forensics [1, 2], archaeology , physics , cosmology [5, 6, 7], geosciences , atmospheric sciences [9, 10], materials science , biosciences [12, 13], and medicine . Moreover, the analytical performance of modern mass spectrometers is compelling. For example, state-of-the-art ion-cyclotron resonance (ICR) mass spectrometers can routinely discriminate between species that are separated by only 0.001 m/z; this resolution is sufficient to discriminate between isobaric chemical species and to provide empirical chemical formulas directly . Modern sector-field mass spectrometers, in combination with the inductively coupled plasma (ICP) ionization source, can measure a wide range of ion fluxes, from <10 to 1012 counts per second, and deliver extremely low detection limits (<10 pg/L) . Time-of-flight (TOF) mass spectrometers can deliver entire mass-spectra at rates of thousands per second, which is often necessary for transient analyses .
Description of DOFMS
DOFMS features analytical performance characteristics similar to those of both TOFMS and multichannel SFMS. As a velocity-based approach (analogous to TOFMS), DOFMS has the potential to provide high-speed spectral generation, full-spectrum generation, high (10%–100%) duty-cycle data collection, and has a theoretically unlimited mass range. DOFMS also has a simple instrument design that requires only electrostatic components. As a spatially dispersive technique (akin to multichannel SFMS), DOFMS benefits from the measurement of ion flux across space, which allows the use of a charge-based detector array that could offer greater precision and dynamic range than is available with high-speed TOFMS detectors.
As Figure 2 highlights, there are clear similarities between DOFMS and both TOFMS and MHMS. DOFMS and TOFMS have very similar instrumental layouts (i.e., a field-free region, a reflectron, etc.); however, disparate from TOFMS, which utilizes constant-energy acceleration, DOFMS requires a constant-momentum acceleration (CMA) pulse, a linear-field reflectron, and a spatially selective detection system. This spatially selective detector can be identical to those found in MHMS instruments as shown in Figure 2. Just as in other spatially dispersive MS approaches, such as the MHMS, in DOFMS, when ions strike the detector, their impact position along the mass-separation axis is related to m/z. So, even though DOFMS separation accelerates packets of ions and the MHMS disperses a steady stream of ions, the same detectors can be used.
Common Mass Analyzers and Some of Their Defining Characteristics
Ion separation property/ mechanism
Spatially dispersive? Y/N
Limitation on upper mass
Magnetic field, acceleration voltage stability
Focusing mag. sect.
Magnetic field, acceleration voltage stability
Energy and momentum
Magnetic field, acceleration voltage stability
Detector, applied waveform characteristics
Quadrupole ion trap
Detector, applied waveform characteristics
Duration of frequency measurement
Detector, applied waveform characteristics
Comparison of TOFMS and DOFMS
One of the major obstacles in the development of TOFMS was achieving adequate ion focusing to realize meaningful results. The TOFMS ion-focusing problem arises because ions do not all start at the same position (spatial dispersion) or with the same kinetic energy along the TOF separation axis (energy dispersion). As a result, ions of the same m/z value do not have identical velocities in the flight tube and will not arrive at the detector at the same time if their velocity spread due to space and/or energy distributions is not compensated. Because of these limitations, the resolution of the first TOFMS instruments was so poor that they were easily displaced by early, relatively crude quadrupole analyzers.
With modern temperature-controlled electronics, clever pulsing schemes, and ion-beam collimation techniques, TOFMS is among the highest-resolution analyzers available. For the interested reader, a recent review of ion-focusing improvements was published by Radionova et al. . Since the initial realization of TOFMS, the incorporation multi-stage extraction and acceleration, the orthogonal acceleration geometry, and the reflectron into TOFMS instrument designs have significantly improved performance. The reflectron mirrors the space-focus plane onto the TOFMS detector and, thereby, extends the length of mass separation and helps compensate for energy dispersion. Introducing ions with orthogonal acceleration reduces both energy and spatial dispersion along the mass-separation axis. Both an orthogonal-acceleration region (or planar ion source) and a reflectron are used in DOFMS in order to operate optimally. However, the consequences from the use of each of these techniques differ for DOFMS and TOFMS, as the modes of ion acceleration and ion focusing are dissimilar.
In order to appreciate fully how and why DOFMS is distinct, particularly from TOFMS, it is necessary to understand the fundamental differences between constant-energy and constant-momentum acceleration .
Acceleration of ions to a constant energy for TOFMS is achieved by application of an electrostatic field over a known distance (from an ion’s initial position to the exit of the acceleration region). By this method, all ions starting from that point, regardless of m/z, are sent into the mass-separation region (the flight tube) with the same nominal boost in energy. Variations in initial ion position (spatial dispersion) result in different ion velocities after acceleration that are partly compensated at the space-focus plane of the acceleration region. Initial ion-energy disparities (energy dispersion) also result in ion-velocity differences after acceleration. These initial-energy-based disparities are partially corrected by the reflectron but cannot be perfectly compensated. The turnaround time that results from acceleration of rearward-moving ions causes unavoidable peak broadening  and is often the major source of peak width; in TOFMS analyzers, turnaround-time error can be minimized only by using delayed or high-field extractions, which makes the turnaround as quick as possible .
By contrast, in the case of constant-momentum acceleration (CMA), employed for DOFMS, ions in the acceleration region gather speed across a constant field-strength for a specified time and, therefore, receive the same change in nominal momentum, regardless of m/z . However, having the same momentum but different masses gives them m/z-dependent energies. Since no ions of interest exit the region during the brief CMA pulse, there is no measurable effect of an ion’s initial position on the outcome of acceleration. Instead, the original width of the ion packet is preserved during ion flight in the field-free region. In other words, there is no space-focus plane: the initial spatial distribution of ions is neither focused nor defocused after CMA and is exactly the same at the position of detection as in the acceleration region. This behavior favors, of course, a very narrow or focused input ion beam or ions originating from a planar surface. In CMA, an ion’s initial energy does, however, add to (or subtract from) its final velocity after acceleration. In DOFMS, this energy-dependent velocity difference is compensated in the linear-field reflectron, which energy-focuses ions at their m/z-dependent flight distances at a particular time called the energy focus time (tef). In DOFMS, all ions are detected at this single tef in order to provide best resolution. Importantly, at tef both initially forward- and reverse-moving ions are focused, which means there is no turnaround-time error. This error ultimately limits resolution in conventional TOFMS , although ion cooling, trapping, ion-beam shaping, and high extraction fields help to minimize turnaround-time errors. The key mathematical relationships that describe energy-focusing CMA operation have been described in detail elsewhere [29, 34, 38, 39, 40].
A prototype DOFMS instrument has been constructed and used to test the principles of DOFMS . The mass analyzer consists of a set of dc quadrupole ion optics to focus the input ion beam into an orthogonal-acceleration region, followed by an approximately 30-cm field-free flight zone and a linear-field reflectron. Along the flight path, and after the reflectron, a second acceleration region is used to orthogonally push m/z-separated ions onto a spatially selective detector. To date, several detection systems have been tested with the prototype system—they will be discussed in detail shortly. Initial experiments with DOFMS have been conducted with atomic ionization sources including a reduced-pressure direct-current glow discharge [39, 41, 42, 43] and an inductively coupled plasma [44, 45, 46].
Detector Requirements and Opportunities in DOFMS
where (m/z)LOW is the lower bound of the mass range and (m/z)HIGH is the upper limit of the mass range, LFF(HIGH) is the field-free (flight tube) length to the near side (high-mass side) of the DOFMS detector, s0 is the distance ions travel in the acceleration region, and LD is the detector length. Other constraints on the geometry of the DOFMS exist , but are beyond the scope of this overview.
In our 27-cm flight-length prototype DOFMS instrument described earlier, for example, a detector 1-inch (2.54 cm) in length will cover a mass range of 6.4 u at m/z = 100, but 64 u at m/z = 1000. Conveniently, the m/z dependence on distance means that the ratio of upper and lower m/z values remains constant, so the range of the mass window increases linearly with m/z. The spatial resolution of the detector is a major factor in determining the best spectral resolution that the instrument can achieve. As described previously, DOFMS makes use of primary ion-beam focusing to limit the initial spatial distribution of the ions; because that initial spatial width is mirrored on the detector surface, the mass resolution of DOFMS is strongly affected by the fidelity of the ion optics. In turn, this means that the spatial resolution required of the ion detector might depend upon the intended application. As a benchmark, for applications with a mass range around 4000 m/z and the same instrument geometry, a detector resolution of approximately 10 μm would be necessary to place 10 resolution elements across a peak; such a peak would be of similar width to that observed with sector-field mass spectrometers. Of course, these detector requirements will likely change as new applications are defined.
Let us contrast DOFMS detection with that of TOFMS. In TOFMS, a single detector is used, TOFMS peaks are temporally very narrow, and the detector time response directly affects mass resolution. In addition, dynamic range is often compromised to avoid detector saturation and consequently slow recovery. In contrast, DOFMS allows analog detection and continuous integration to be used because each m/z resolution element is at a discrete location. Not only does this capability expand dynamic range, it also enables better ratio precision to be achieved for a given integration time just by use of less dilute samples. Of course, continuous integration is not the only operational mode for DOFMS—short integration times (100–150 ms) have been utilized to record data for transient laser-ablation events . The ability to handle higher ion throughput will also improve quantitation in molecular analyses, perhaps competing with the quadrupole mass filter [42, 48].
Since temporal response is not directly linked to mass resolution in DOFMS, alternative detection schemes can be explored. For example, direct ion-charge integration, which is not practicable with TOFMS, is quite readily employed in DOFMS. Detection strategies that exploit secondary electron multiplication, such as microchannel plates (MCP), are well known to suffer from gain suppression due to saturation and to show a significant loss of sensitivity [49, 50, 51]. In contrast, direct ion-charge detection provides a signal that is directly proportional to ion charge and has no mass bias, so large biomolecules can be detected as easily as electrons, and positive and negative ions can be registered directly and with equal sensitivity . Finally, the physical separation of ions promises alternative approaches to simultaneous detection and collection of the ions. For example, a soft-landing probe could be incorporated into a DOFMS instrument for nondestructive ion or targeted isotope collection. These mass-separated, collected ions could then be further characterized with techniques such as surface-enhanced Raman spectroscopy or electron microscopy, which have already been demonstrated with soft-landing mass spectrometry [53, 54].
A substantial benefit of the EOID detector is that MCPs and phosphor screens can be made to almost any form factor. As illustrated by Figure 5a, the ion beam is taller than it is wide at the detection plane and the ability of the EOID system to integrate a large portion of the peak height can increase sensitivity. However, because a MCP detector is used to amplify all ions within the window, a common gain setting must be used and can limit the available dynamic range in a particular run. In practical application, a loss of mass resolution is also often observed because of spatial spreading of the electron image by Coulombic repulsion. Another limitation of the MCP-based detector is that mass range is limited because the kinetic energy of large biomolecular ions, for example, is converted largely into internal energy when the ion strikes the MCP surface.
A better approach for DOFMS detection is the use of semiconductor-based mass-spectrometry detectors. Here, fabrication strategies from the semiconductor industry can be leveraged in order to create high-performance detector arrays capable of very sensitive position-referenced ion-charge integration. A comprehensive review of these detectors can be found elsewhere [58, 59]. One example, the Focal-Plane Camera (FPC), has been tested with DOFMS and is depicted in Figure 5b . The FPC is comprised of a 1-D array of ion-collection electrodes termed Faraday strips, each of which is connected to a dedicated integrating amplifier circuit [56, 57, 58, 60, 61, 62]. The amplification circuitry is fabricated monolithically in silicon as a charge-integrating operational amplifier. As ions strike the Faraday strips, charge is integrated onto the feedback capacitor and converted to a proportional voltage by the operational amplifier integrator circuit. The charge-to-voltage gain has two levels achieved by switching between two capacitors. Semiconductor fabrication allows the feedback capacitance to be very low (~8 fF), so high gains are possible (~20 μV/fundamental charge), and detection limits competitive with those of conventional analog ion detectors can be obtained (~20–50 fundamental charges) . Further, the ability to computer-control the detection array offers significant benefits. For example, each ion-detection element can be fabricated with a number of computer-switchable gain settings and can be interrogated individually, with the gain being changed on-the-fly depending on the ion flux striking the element. Each detection element can also be read out repeatedly in a nondestructive manner, minimizing read noise and allowing each element to be queried at a rate dictated by the measurement requirements.
Characterization of DOFMS with a commercially available IonCCD camera (courtesy of O.I. Analytical) is currently underway . Being based on semiconductor array-detection technology, the IonCCD camera detector provides many of the same features as the FPC; namely, the IonCCD camera suffers no mass bias (i.e., it directly detects ion charge), has isolated charge-detection surfaces, and boasts nondestructive readout. In addition, the IonCCD camera is considerably larger than the FPC at 5.1 cm in length (compared with only 0.64 cm for the 512-pixel FPC tested with DOFMS). This extra detection span enables a much larger portion of the mass spectrum to be measured at once.
Unlike in TOFMS, mass-spectral acquisition time in DOFMS is highly dependent on the type of detector that is utilized. Each of the three detectors discussed here (EOID, FPC, and IonCCD) has a different integration and readout time for DOFMS. The EOID is limited by the CCD camera that is used to capture light from the phosphor screen. For the CCD camera (iKon CCD; Andor Technologies plc., UK) coupled to the DOFMS system for LA-ICP-DOFMS , typical exposure times were 100–150 ms, and CCD readout times for single-pulse LA acquisition (CCD was binned 4 × 4) were 0.09025 s. As a result, the CCD was integrating ion signal for 52%–63% of laboratory time . In the case of the FPC, the limiting factor is not the camera electronics but the software in place to read out the camera—LabVIEW. The readout rate of the setup is, therefore, limited to 1 kHz, but this rate is not a function of the DOFMS experiment itself . A brief discussion of ion-collection time with the IonCCD camera is provided above. Since the noise floor (or signal needed to generate a count) on the IonCCD camera is at least an order of magnitude higher than that of either the EOID or FPC, longer integration times (≥500 ms) were necessary to generate comparable signal-to-noise performance . Also, the detection readout speed of the IonCCD camera is limited to ≤360 Hz . Obviously, for all three detectors, at a sufficiently short integration time there will not be enough ion signal for peaks to be observed. The integration time at which the signal level is below detectable range is dependent not only on the detection and ion-focusing systems but also on the ionization source.
In summary, DOFMS is a high-repetition rate batch technique like TOFMS, but it uses ion travel distance as the means of m/z separation, an array of independent ion detectors, and focuses initial energy dispersion rather than spatial dispersion. In some respects, DOFMS more closely resembles the MHMS, except DOFMS uses a pulsed ion source and resolution does not depend on throughput-limiting ion slits. The commercial development of DOFMS clearly will depend on the evolution of solid-state ion detector arrays.
To date, DOFMS has been implemented with atomic ion sources that produce very hot ions. The beam formed from these high kinetic-energy ions suffers significant axial and radial dispersion, and appreciable defocusing from the second-order dispersion term in Equation 1. Even so, the proof-of-principle instrument platform designed, built, and tested at Indiana University has demonstrated the significant advantages that DOFMS can bring to elemental and isotope ratio analysis [39, 41, 42, 43, 44, 45, 46]. Based on this work, it is reasonable to anticipate that a molecular-analysis version of this instrument, employing the ion cooling and focusing techniques commonly used with atmospheric molecular-ion sources, will yield still better sensitivity and resolution.
Each new form of mass analyzer has expanded the range and impact of mass spectrometry, not just by providing better performance for existing applications and modes of operation but by opening new areas of application. That evolution has been true for each new breakthrough and it seems likely DOFMS will be no exception. In the following sections, we outline potential (some already demonstrated) new areas that can take advantage of the unique combination of characteristics that DOFMS offers.
Zoom-time-of-flight mass spectrometry (zoom-TOFMS) is a technique related to DOFMS that has recently been developed as a low-cost complementary mode of operation for existing or custom-designed TOFMS instrumentation . Stated simply, zoom-TOFMS is a combination approach that switches between conventional CEA-TOFMS and energy-focusing CMA-TOFMS. In CEA-TOFMS mode, the TOFMS instrument operates as a conventional TOFMS instrument. The system can then be switched to CMA-TOFMS “zoom” mode to interrogate a relatively narrow, selectable mass region with improved resolution and duty factor. This zoom mode operates identically to DOFMS, except a stationary TOFMS detector is used along the flight path instead of the spatially dispersive detector. In zoom mode, a target mass window is detected at tef by the TOF detector, which can be thought of as a single pixel in a DOFMS array detector. Since only ions detected at (or near) tef are energy-focused, only a narrow region of m/z-values can be interrogated with the zoom mode. In fact, the zoom mode is much like the operation of a zoom lens on a camera—you see a smaller region with greater clarity.
Zoom-TOFMS is capable of resolution improvements in CMA mode for a few reasons. First, the energy focus generated at tef for CMA is accompanied by a maintained (and controllably narrow) spatial distribution of ions from acceleration region to detector, which together produces narrower mass-spectral peaks than the space-focus provided by CEA . Second, the relationship between m/z and TOF is linear for CMA-TOFMS, whereas the same relationship is square-root-dependent in CEA-TOFMS . This difference in temporal mass spacing leads to increased distance between peaks (especially at high masses) and, therefore, improved mass resolution. The last reason for narrower peaks is the absence of turnaround-time errors from the orthogonal-acceleration process, which has already been discussed for DOFMS.
An existing, heavily modified commercial R.M. Jordan instrument was retrofitted with an extended orthogonal-acceleration region and a linear-field reflectron for initial zoom-TOFMS studies. With this instrument, we  demonstrated that zoom-mode operation provides up to a 1.7-fold improvement in mass resolution over CEA-TOFMS, while also enabling the ion-packet introduction rate to be increased up to 100 kHz in zoom mode for an m/z-window at least 12 mass units wide . Increased repetition rates in zoom mode are possible because ions have m/z-dependent energies and, therefore, the target mass range can be isolated by means of kinetic-energy filtering .
Mass Resolution for Both the CEA- and CMA-TOFMS Operational Modes of a 1-m Zoom-TOFMS Instrument. Reduced-Pressure Glow-Discharge Ion Source with Copper Cathode
Peak Width (ns, FWHM)
Peak Width (ns, FWHM)
The enhanced mass resolution in zoom mode is accompanied by improved sensitivity (from the enhanced duty factor) . In contrast, multi-turn and multi-pass TOFMS instruments can greatly improve mass resolution, but they do so at the expense of spectral-generation rate and duty factor. This means that zoom-TOFMS could be used to examine transient events such as chromatographic peaks with both a full-spectral scan (CEA-TOFMS) mode to determine and quantify sample constituents and also with the zoom mode to examine any spectral areas of interest with both improved mass resolution and sensitivity.
High Duty-Cycle DOFMS
The first results of interleaved DOFMS demonstrate a 2-fold duty-factor enhancement, and twice the sensitivity of conventional DOFMS. Future implementations of interleaved DOFMS will aim to improve the duty cycle to unity (100%), and thus match the ion throughput of continuous MS analyzers such as QMS and SFMS, but for a single m/z or a range of m/z values, respectively, measured across the DOFMS detector array. This improvement in duty cycle would be achieved with the use of the same method utilized to achieve 59% duty cycle for zoom-TOFMS . In this way, interleaved DOFMS could prove especially useful for high-sensitivity isotope-ratio measurements or other applications that demand high throughput. Moreover, the mass range available for interleaved DOFMS depends only on the length of the DOFMS detector. There is a tradeoff between detector length and the duty cycle available with interleaved DOFMS because, with a very long detection system, low-m/z ions from subsequent DOF pulses could be present in the DOF detection region at the tef of a preceding experiment. However, these spectral overlaps can be easily identified, and with a longer detector, each injected ion pulse will cover a broader mass range, so duty-cycle enhancement is less critical.
A clear limitation of DOFMS is its inability to analyze a wide range of m/z-values for each acceleration event, due to finite detector dimensions. There are several ways to improve mass-spectral coverage in DOFMS. First, a long ion-detection device can be used, but the fabrication of an overly long array of detector elements is impractical. Second, the field-free flight length can be shortened to reduce unit-mass spacing, but this approach will impair mass resolution. Third, different mass ranges can be scanned across the DOFMS detector in separate, sequential experiments. Fourth, mass-range acquisitions can be interleaved such that more than one m/z-range enters the DOFMS detection region (and is in focus) for each acquisition event—thus multiplexing the detection process. A fifth alternative is to combine DOFMS and TOFMS into a single instrument platform, to yield a new instrument concept labeled DOF/TOF-MS. In this concept, TOFMS functions as the whole-spectrum mass analyzer, while DOFMS is used over only critical mass windows in which the benefits of spatial dispersion and/or solid-state ion detection offer better performance than TOFMS. Here, a brief description of a hybrid DOF/TOF-MS instrument is given to illustrate the concept; more details can be found elsewhere [40, 69].
Very High Mass MALDI-DOFMS
Use of DOFMS for the analysis of ions of high molecular weight, ranging from 1MDa to beyond 1GDa, would leverage the advantages that MS holds over more conventional biochemical approaches for the characterization of complete biological constructs. Here, DOFMS provides three critical advantages. First, like TOFMS, DOFMS relies on a simple velocity-based mass-separation strategy that has no upper-mass limit. Thus, massive ions can be separated from each other without requiring that they possess a large number of charges. For comparison, high-mass FTICR and QIT analyses typically use ESI to create ions with multiple charges, reducing the m/z of the resulting ion and increasing the effective mass range of the analyzer. Second, DOFMS employs semiconductor array detectors, like the FPC or IonCCD camera, which also possess no upper-mass limit for ion detection and that operate with no mass bias. Finally, the physical separation of ions according to m/z opens the way to expanding the utility of mass spectrometry by employing simultaneous, multi-mass soft-landing technologies.
The development of such an instrument would present a number of challenges, but could be just one step beyond the development of a commercially available DOFMS instrument. The prospect of achieving a full map of product ions for a range of precursor masses on each acceleration pulse could further expand the practical applications of MS/MS.
The emerging, expanding, and evolving DOFMS approach opens up a new island of possibilities in the mass spectrometry landscape. The technique’s ability to energy-focus ions and spatially separate m/z-values without the use of magnets or cyclotron frequencies is unprecedented in the field. A broad range of applications can be envisioned and will likely expand in the future.
Time-of-flight mass spectrometry (TOFMS)
Sector-field mass spectrometry (SFMS)
Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS)
Quadrupole mass spectrometry (Q-MS)
Quadrupole-ion trap mass spectrometry (QIT-MS)
Triple quadrupole mass spectrometry (QqQ-MS)
Distance-of-flight mass spectrometry (DOFMS)
This study was supported in part by the U.S. Department of Energy through grant DE-FG02-98ER14890. Early studies in DOFMS were performed in collaboration with David W. Koppenaal and Charles J. Barinaga and supported in part by Pacific Northwest National Laboratory, operated for the U.S. DOE by Battelle Memorial Institute under Contract DE-AC06-76RLO-1830op.
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