MPU-6050
MPU-6000 and MPU-6050 Product Specification Revision 3.4
The MPU-6050 is an electronic component from TDK InvenSense. MPU-6000 and MPU-6050 Product Specification Revision 3.4. View the full MPU-6050 datasheet below including electrical characteristics, absolute maximum ratings.
Manufacturer
TDK InvenSense
Overview
Part: MPU-6000 and MPU-6050 Type: MotionTracking Device
Key Specs:
- Operating voltage range: 2.375V-3.46V
- Accelerometer Intelligence Function increment value: 1mg/LSB
- Latch-up rating: Level A and ±100mA
Features:
- MotionInterface™
- Small package size
- Low power consumption
- High accuracy and repeatability
- High shock tolerance
- Application specific performance programmability
- Three-Axis MEMS Gyroscope with 16-bit ADCs and Signal Conditioning
- Three-Axis MEMS Accelerometer with 16-bit ADCs and Signal Conditioning
- Digital Motion Processor
- I2C Primary and SPI Serial Communications Interfaces (SPI for MPU-6000 only)
- I2C Auxiliary Serial Interface
- Self-Test
- Internal Clock Generation
- Sensor Data Registers
- FIFO
- Interrupts
- Digital-Output Temperature Sensor
- Bias and LDO
- Charge Pump
- Programmable Interrupts
Applications:
- Gesture commands for applications and phone control
- Enhanced gaming
- Augmented reality
- Panoramic photo capture and viewing
- Pedestrian and vehicle navigation
- Health and fitness monitoring
- Location-based services
Package:
- null
Features
5.1 Gyroscope Features
The triple-axis MEMS gyroscope in the MPU-60X0 includes a wide range of features:
- Digital-output X-, Y-, and Z-Axis angular rate sensors (gyroscopes) with a user-programmable fullscale range of ±250, ±500, ±1000, and ±2000°/sec
- External sync signal connected to the FSYNC pin supports image, video and GPS synchronization
- Integrated 16-bit ADCs enable simultaneous sampling of gyros
- Enhanced bias and sensitivity temperature stability reduces the need for user calibration
- Improved low-frequency noise performance
- Digitally-programmable low-pass filter
- Gyroscope operating current: 3.6mA
- Standby current: 5μA
- Factory calibrated sensitivity scale factor
- User self-test
5.2 Accelerometer Features
The triple-axis MEMS accelerometer in MPU-60X0 includes a wide range of features:
- Digital-output triple-axis accelerometer with a programmable full scale range of ±2g, ±4g, ±8g and ±16g
- Integrated 16-bit ADCs enable simultaneous sampling of accelerometers while requiring no external multiplexer
- Accelerometer normal operating current: 500μA
- Low power accelerometer mode current: 10μA at 1.25Hz, 20μA at 5Hz, 60μA at 20Hz, 110μA at 40Hz
- Orientation detection and signaling
- Tap detection
- User-programmable interrupts
- High-G interrupt
- User self-test
5.3 Additional Features
The MPU-60X0 includes the following additional features:
- 9-Axis MotionFusion by the on-chip Digital Motion Processor (DMP)
- Auxiliary master I2C bus for reading data from external sensors (e.g., magnetometer)
- 3.9mA operating current when all 6 motion sensing axes and the DMP are enabled
- VDD supply voltage range of 2.375V-3.46V
- Flexible VLOGIC reference voltage supports multiple I 2C interface voltages (MPU-6050 only)
- Smallest and thinnest QFN package for portable devices: 4x4x0.9mm
- Minimal cross-axis sensitivity between the accelerometer and gyroscope axes
- 1024 byte FIFO buffer reduces power consumption by allowing host processor to read the data in bursts and then go into a low-power mode as the MPU collects more data
- Digital-output temperature sensor
- User-programmable digital filters for gyroscope, accelerometer, and temp sensor
- 10,000 g shock tolerant
- 400kHz Fast Mode I2C for communicating with all registers
- 1MHz SPI serial interface for communicating with all registers (MPU-6000 only)
- 20MHz SPI serial interface for reading sensor and interrupt registers (MPU-6000 only)
- MEMS structure hermetically sealed and bonded at wafer level
- RoHS and Green compliant
5.4 MotionProcessing
- Internal Digital Motion Processing™ (DMP™) engine supports 3D MotionProcessing and gesture recognition algorithms
- The MPU-60X0 collects gyroscope and accelerometer data while synchronizing data sampling at a user defined rate. The total dataset obtained by the MPU-60X0 includes 3-Axis gyroscope data, 3- Axis accelerometer data, and temperature data. The MPU's calculated output to the system processor can also include heading data from a digital 3-axis third party magnetometer.
- The FIFO buffers the complete data set, reducing timing requirements on the system processor by allowing the processor burst read the FIFO data. After burst reading the FIFO data, the system processor can save power by entering a low-power sleep mode while the MPU collects more data.
- Programmable interrupt supports features such as gesture recognition, panning, zooming, scrolling, tap detection, and shake detection
- Digitally-programmable low-pass filters
- Low-power pedometer functionality allows the host processor to sleep while the DMP maintains the step count.
5.5 Clocking
- On-chip timing generator ±1% frequency variation over full temperature range
- Optional external clock inputs of 32.768kHz or 19.2MHz
Applications
- BlurFree™ technology (for Video/Still Image Stabilization)
- AirSign™ technology (for Security/Authentication)
- TouchAnywhere™ technology (for "no touch" UI Application Control/Navigation)
- MotionCommand™ technology (for Gesture Short-cuts)
- Motion-enabled game and application framework
- InstantGesture™ iG™ gesture recognition
- Location based services, points of interest, and dead reckoning
- Handset and portable gaming
- Motion-based game controllers
- 3D remote controls for Internet connected DTVs and set top boxes, 3D mice
- Wearable sensors for health, fitness and sports
- Toys
Electrical Characteristics
6.1 Gyroscope Specifications
VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD, TA = 25°C
| PARAMETER | CONDITIONS | MIN | TYP | MAX | UNITS | NOTES |
|---|---|---|---|---|---|---|
| GYROSCOPE SENSITIVITY | ||||||
| Full-Scale Range | FS_SEL=0 FS_SEL=1 FS_SEL=2 FS_SEL=3 | ±250 ±500 ±1000 ±2000 | º/s º/s º/s º/s | |||
| Gyroscope ADC Word Length | 16 | bits | ||||
| Sensitivity Scale Factor | FS_SEL=0 FS_SEL=1 FS_SEL=2 FS_SEL=3 | 131 65.5 32.8 16.4 | LSB/(º/s) LSB/(º/s) LSB/(º/s) LSB/(º/s) | |||
| Sensitivity Scale Factor Tolerance | 25°C | -3 | +3 | % | ||
| Sensitivity Scale Factor Variation Over | ±2 | % | ||||
| Temperature | ||||||
| Nonlinearity | Best fit straight line; 25°C | 0.2 | % | |||
| Cross-Axis Sensitivity | ±2 | % | ||||
| GYROSCOPE ZERO-RATE OUTPUT (ZRO) | ||||||
| Initial ZRO Tolerance | 25°C | ±20 | º/s | |||
| ZRO Variation Over Temperature | -40°C to +85°C | ±20 | º/s | |||
| Power-Supply Sensitivity (1-10Hz) | Sine wave, 100mVpp; VDD=2.5V | 0.2 | º/s | |||
| Power-Supply Sensitivity (10 - 250Hz) | Sine wave, 100mVpp; VDD=2.5V | 0.2 | º/s | |||
| Power-Supply Sensitivity (250Hz - 100kHz) | Sine wave, 100mVpp; VDD=2.5V | 4 | º/s | |||
| Linear Acceleration Sensitivity | Static | 0.1 | º/s/g | |||
| SELF-TEST RESPONSE | ||||||
| Relative | Change from factory trim | -14 | 14 | % | 1 | |
| GYROSCOPE NOISE PERFORMANCE | FS_SEL=0 | |||||
| Total RMS Noise | DLPFCFG=2 (100Hz) | 0.05 | º/s-rms | |||
| Low-frequency RMS noise | Bandwidth 1Hz to10Hz | 0.033 | º/s-rms | |||
| Rate Noise Spectral Density | At 10Hz | 0.005 | º/s/√Hz | |||
| GYROSCOPE MECHANICAL | ||||||
| FREQUENCIES | ||||||
| X-Axis | 30 | 33 | 36 | kHz | ||
| Y-Axis | 27 | 30 | 33 | kHz | ||
| Z-Axis | 24 | 27 | 30 | kHz | ||
| LOW PASS FILTER RESPONSE | ||||||
| Programmable Range | 5 | 256 | Hz | |||
| OUTPUT DATA RATE | ||||||
| Programmable | 4 | 8,000 | Hz | |||
| GYROSCOPE START-UP TIME | DLPFCFG=0 | |||||
| ZRO Settling (from power-on) | to ±1º/s of Final | 30 | ms |
6.2 Accelerometer Specifications
VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD, TA = 25°C
| PARAMETER | CONDITIONS | MIN | TYP | MAX | UNITS | NOTES |
|---|---|---|---|---|---|---|
| ACCELEROMETER SENSITIVITY | ||||||
| Full-Scale Range | AFS_SEL=0 AFS_SEL=1 AFS_SEL=2 AFS_SEL=3 | ±2 ±4 ±8 ±16 | g g g g | |||
| ADC Word Length | Output in two's complement format | 16 | bits | |||
| Sensitivity Scale Factor | AFS_SEL=0 AFS_SEL=1 AFS_SEL=2 AFS_SEL=3 | 16,384 8,192 4,096 2,048 | LSB/g LSB/g LSB/g LSB/g | |||
| Initial Calibration Tolerance | ±3 | % | ||||
| Sensitivity Change vs. Temperature | AFS_SEL=0, -40°C to +85°C | ±0.02 | % |
2. Please refer to the following document for further information on Self-Test: MPU-6000/MPU-6050 Register Map and Descriptions
6.3 Electrical and Other Common Specifications
VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD, TA = 25°C
| PARAMETER | CONDITIONS | MIN | TYP | MAX | Units | Notes |
|---|---|---|---|---|---|---|
| TEMPERATURE SENSOR | ||||||
| Range | -40 to +85 | °C | ||||
| Sensitivity | Untrimmed | 340 | LSB/ºC | |||
| Temperature Offset | 35°C | -521 | LSB | |||
| Linearity | Best fit straight line (-40°C to +85°C) | ±1 | °C | |||
| VDD POWER SUPPLY | ||||||
| Operating Voltages | 2.375 | 3.46 | V | |||
| Normal Operating Current | Gyroscope + Accelerometer + DMP Gyroscope + Accelerometer (DMP disabled) Gyroscope + DMP (Accelerometer disabled) Gyroscope only (DMP & Accelerometer disabled) Accelerometer only (DMP & Gyroscope disabled) | 3.9 3.8 3.7 3.6 500 | mA mA mA mA μA | |||
| Accelerometer Low Power Mode Current | 1.25 Hz update rate 5 Hz update rate 20 Hz update rate 40 Hz update rate | 10 20 70 140 | μA μA μA μA | |||
| Full-Chip Idle Mode Supply Current | 5 | μA | ||||
| Power Supply Ramp Rate | Monotonic ramp. Ramp rate is 10% to 90% of the final value | 100 | ms | |||
| VLOGIC REFERENCE VOLTAGE | MPU-6050 only | |||||
| Voltage Range | VLOGIC must be ≤VDD at all times | 1.71 | VDD | V | ||
| Power Supply Ramp Rate | Monotonic ramp. Ramp rate is 10% to 90% of the final value | 3 | ms | |||
| Normal Operating Current | 100 | μA | ||||
| TEMPERATURE RANGE | ||||||
| Specified Temperature Range | Performance parameters are not applicable beyond Specified Temperature Range | -40 | +85 | °C |
6.4 Electrical Specifications, Continued
VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD, TA = 25°C
| PARAMETER | CONDITIONS | MIN | TYP | MAX | Units | Notes |
|---|---|---|---|---|---|---|
| SERIAL INTERFACE | ||||||
| SPI Operating Frequency, All Registers Read/Write | MPU-6000 only, Low Speed Characterization MPU-6000 only, High Speed Characterization | 100 ±10% 1 ±10% | kHz MHz | |||
| SPI Operating Frequency, Sensor and Interrupt Registers Read Only | MPU-6000 only | 20 ±10% | MHz | |||
| I²C Operating Frequency | All registers, Fast-mode All registers, Standard-mode | 400 100 | kHz kHz | |||
| I²C ADDRESS | AD0 = 0 AD0 = 1 | 1101000 1101001 | ||||
| DIGITAL INPUTS (SDI/SDA, AD0, SCLK/SCL, FSYNC, /CS, CLKIN) | ||||||
| VIH, High Level Input Voltage | MPU-6000 MPU-6050 | 0.7VDD 0.7VLOGIC | V V | |||
| VIL, Low Level Input Voltage | MPU-6000 MPU-6050 | 0.3VDD 0.3VLOGIC | V V | |||
| CI, Input Capacitance | < 5 | pF | ||||
| DIGITAL OUTPUT (SDO, INT) | ||||||
| VOH, High Level Output Voltage | RLOAD=1MΩ; MPU-6000 RLOAD=1MΩ; MPU-6050 | 0.9VDD 0.9VLOGIC | V V | |||
| VOL1, LOW-Level Output Voltage | RLOAD=1MΩ; MPU-6000 RLOAD=1MΩ; MPU-6050 | 0.1VDD 0.1VLOGIC | V V | |||
| VOL,INT1, INT Low-Level Output Voltage | OPEN=1, 0.3mA sink Current | 0.1 | V | |||
| Output Leakage Current | OPEN=1 | 100 | nA | |||
| tINT, INT Pulse Width | LATCH_INT_EN=0 | 50 | μs |
6.5 Electrical Specifications, Continued
Typical Operating Circuit of Section 7.2, VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD, TA = 25°C
| Parameters | Conditions | Typical | Units | Notes |
|---|---|---|---|---|
| Primary I²C I/O (SCL, SDA) | ||||
| VIL, LOW-Level Input Voltage | MPU-6000 | -0.5 to 0.3*VDD | V | |
| VIH, HIGH-Level Input Voltage | MPU-6000 | 0.7*VDD to VDD + 0.5V | V | |
| Vhys, Hysteresis | MPU-6000 | 0.1*VDD | V | |
| VIL, LOW Level Input Voltage | MPU-6050 | -0.5V to 0.3*VLOGIC | V | |
| VIH, HIGH-Level Input Voltage | MPU-6050 | 0.7*VLOGIC to VLOGIC + 0.5V | V | |
| Vhys, Hysteresis | MPU-6050 | 0.1*VLOGIC | V | |
| VOL1, LOW-Level Output Voltage | 3mA sink current | 0 to 0.4 | V | |
| IOL, LOW-Level Output Current | VOL = 0.4V | 3 | mA | |
| VOL = 0.6V | 5 | mA | ||
| Output Leakage Current | 100 | nA | ||
| t_of, Output Fall Time from V_IHmax to V_ILmax | Cb bus capacitance in pF | 20+0.1Cb to 250 | ns | |
| C_I, Capacitance for Each I/O pin | < 10 | pF | ||
| Auxiliary I²C I/O (AUX_CL, AUX_DA) | MPU-6050: AUX_VDDIO=0 | |||
| VIL, LOW-Level Input Voltage | -0.5V to 0.3*VLOGIC | V | ||
| VIH, HIGH-Level Input Voltage | 0.7*VLOGIC to VLOGIC + 0.5V | V | ||
| Vhys, Hysteresis | 0.1*VLOGIC | V | ||
| VOL1, LOW-Level Output Voltage | VLOGIC > 2V; 1mA sink current | 0 to 0.4 | V | |
| VOL3, LOW-Level Output Voltage | VLOGIC < 2V; 1mA sink current | 0 to 0.2*VLOGIC | V | |
| IOL, LOW-Level Output Current | VOL = 0.4V | 1 | mA | |
| VOL = 0.6V | 1 | mA | ||
| Output Leakage Current | 100 | nA | ||
| t_of, Output Fall Time from V_IHmax to V_ILmax | Cb bus capacitance in pF | 20+0.1Cb to 250 | ns | |
| C_I, Capacitance for Each I/O pin | < 10 | pF |
6.6 Electrical Specifications, Continued
Typical Operating Circuit of Section 7.2, VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD, TA = 25°C
| Parameters | Conditions | Min | Typical | Max | Units | Notes |
|---|---|---|---|---|---|---|
| INTERNAL CLOCK SOURCE | CLK_SEL=0,1,2,3 | |||||
| Gyroscope Sample Rate, Fast | DLPFCFG=0 SAMPLERATEDIV = 0 | 8 | kHz | |||
| Gyroscope Sample Rate, Slow | DLPFCFG=1,2,3,4,5, or 6 SAMPLERATEDIV = 0 | 1 | kHz | |||
| Accelerometer Sample Rate | 1 | kHz | ||||
| Clock Frequency Initial Tolerance | CLK_SEL=0, 25°C | -5 | +5 | % | ||
| CLK_SEL=1,2,3; 25°C | -1 | +1 | % | |||
| Frequency Variation over Temperature | CLK_SEL=0 CLK_SEL=1,2,3 | -15 to +10 ±1 | % % | |||
| PLL Settling Time | CLK_SEL=1,2,3 | 1 | 10 | ms | ||
| EXTERNAL 32.768kHz CLOCK | CLK_SEL=4 | |||||
| External Clock Frequency | 32.768 | kHz | ||||
| External Clock Allowable Jitter | Cycle-to-cycle rms | 1 to 2 | μs | |||
| Gyroscope Sample Rate, Fast | DLPFCFG=0 SAMPLERATEDIV = 0 | 8.192 | kHz | |||
| Gyroscope Sample Rate, Slow | DLPFCFG=1,2,3,4,5, or 6 SAMPLERATEDIV = 0 | 1.024 | kHz | |||
| Accelerometer Sample Rate | 1.024 | kHz | ||||
| PLL Settling Time | 1 | 10 | ms | |||
| EXTERNAL 19.2MHz CLOCK | CLK_SEL=5 | |||||
| External Clock Frequency | 19.2 | MHz | ||||
| Gyroscope Sample Rate | Full programmable range | 3.9 | 8000 | Hz | ||
| Gyroscope Sample Rate, Fast Mode | DLPFCFG=0 SAMPLERATEDIV = 0 | 8 | kHz | |||
| Gyroscope Sample Rate, Slow Mode | DLPFCFG=1,2,3,4,5, or 6 SAMPLERATEDIV = 0 | 1 | kHz | |||
| Accelerometer Sample Rate | 1 | kHz | ||||
| PLL Settling Time | 1 | 10 | ms |
6.7 I 2C Timing Characterization
Typical Operating Circuit of Section 7.2, VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD, TA = 25°C
| Parameters | Conditions | Min | Typical | Max | Units | Notes |
|---|---|---|---|---|---|---|
| I²C TIMING | I²C FAST-MODE | |||||
| fSCL, SCL Clock Frequency | 400 | kHz | ||||
| tHD:STA, (Repeated) START Condition Hold Time | 0.6 | μs | ||||
| tLOW, SCL Low Period | 1.3 | μs | ||||
| tHIGH, SCL High Period | 0.6 | μs | ||||
| tSU:STA, Repeated START Condition Setup Time | 0.6 | μs | ||||
| tHD:DAT, SDA Data Hold Time | 0 | μs | ||||
| tSU:DAT, SDA Data Setup Time | 100 | ns | ||||
| tr, SDA and SCL Rise Time | Cb bus cap. from 10 to 400pF | 20+0.1Cb | 300 | ns | ||
| tf, SDA and SCL Fall Time | Cb bus cap. from 10 to 400pF | 20+0.1Cb | 300 | ns | ||
| tSU:STO, STOP Condition Setup Time | 0.6 | μs | ||||
| tBUF, Bus Free Time Between STOP and START Condition | 1.3 | μs | ||||
| Cb, Capacitive Load for each Bus Line | < 400 | pF | ||||
| tVD:DAT, Data Valid Time | 0.9 | μs | ||||
| tVD:ACK, Data Valid Acknowledge Time | 0.9 | μs |
I 2C Bus Timing Diagram
6.8 SPI Timing Characterization (MPU-6000 only)
Typical Operating Circuit of Section 7.2, VDD = 2.375V-3.46V, VLOGIC (MPU-6050 only) = 1.8V±5% or VDD,TA = 25°C, unless otherwise noted.
| Parameters | Conditions | Min | Typical | Max | Units | Notes |
|---|---|---|---|---|---|---|
| SPI TIMING | ||||||
| fSCLK, SCLK Clock Frequency | 1 | MHz | ||||
| tLOW, SCLK Low Period | 400 | ns | ||||
| tHIGH, SCLK High Period | 400 | ns | ||||
| tSU.CS, CS Setup Time | 8 | ns | ||||
| tHD.CS, CS Hold Time | 500 | ns | ||||
| tSU.SDI, SDI Setup Time | 11 | ns | ||||
| tHD.SDI, SDI Hold Time | 7 | ns | ||||
| tVD.SDO, SDO Valid Time | Cload = 20pF | 100 | ns | |||
| tHD.SDO, SDO Hold Time | Cload = 20pF | 4 | ns | |||
| tDIS.SDO, SDO Output Disable Time | 10 | ns |
SPI Bus Timing Diagram
6.9 Absolute Maximum Ratings
Stress above those listed as "Absolute Maximum Ratings" may cause permanent damage to the device. These are stress ratings only and functional operation of the device at these conditions is not implied. Exposure to the absolute maximum ratings conditions for extended periods may affect device reliability.
| Parameter | Rating |
|---|---|
| Supply Voltage, VDD | -0.5V to +6V |
| VLOGIC Input Voltage Level (MPU-6050) | -0.5V to VDD + 0.5V |
| REGOUT | -0.5V to 2V |
| Input Voltage Level (CLKIN, AUX_DA, AD0, FSYNC, INT, SCL, SDA) | -0.5V to VDD + 0.5V |
| CPOUT (2.5V ≤ VDD ≤ 3.6V ) | -0.5V to 30V |
| Acceleration (Any Axis, unpowered) | 10,000g for 0.2ms |
| Operating Temperature Range | -40°C to +105°C |
| Storage Temperature Range | -40°C to +125°C |
| Electrostatic Discharge (ESD) Protection | 2kV (HBM); 250V (MM) |
| Latch-up | JEDEC Class II (2),125°C ±100mA |
Absolute Maximum Ratings
Stress above those listed as "Absolute Maximum Ratings" may cause permanent damage to the device. These are stress ratings only and functional operation of the device at these conditions is not implied. Exposure to the absolute maximum ratings conditions for extended periods may affect device reliability.
| Parameter | Rating |
|---|---|
| Supply Voltage, VDD | -0.5V to +6V |
| VLOGIC Input Voltage Level (MPU-6050) | -0.5V to VDD + 0.5V |
| REGOUT | -0.5V to 2V |
| Input Voltage Level (CLKIN, AUX_DA, AD0, FSYNC, INT, SCL, SDA) | -0.5V to VDD + 0.5V |
| CPOUT (2.5V ≤ VDD ≤ 3.6V ) | -0.5V to 30V |
| Acceleration (Any Axis, unpowered) | 10,000g for 0.2ms |
| Operating Temperature Range | -40°C to +105°C |
| Storage Temperature Range | -40°C to +125°C |
| Electrostatic Discharge (ESD) Protection | 2kV (HBM); 250V (MM) |
| Latch-up | JEDEC Class II (2),125°C ±100mA |
Package Information
24 Lead QFN (4x4x0.9) mm NiPdAu Lead-frame finish
| SYMBOLS | DIMENSIONS IN MILLIMETERS |
|---|---|
| MIN | |
| A | 0.85 |
| A1 | 0.00 |
| b | 0.18 |
| c | --- |
| D | 3.90 |
| D2 | 2.65 |
| E | 3.90 |
| E2 | 2.55 |
| e | --- |
| f(e-b) | --- |
| K | 0.25 |
| L | 0.30 |
| L1 | 0.35 |
| s | 0.05 |
Related Variants
The following components are covered by the same datasheet.
| Part Number | Manufacturer | Package |
|---|---|---|
| MPU-6050TM | TDK InvenSense | — |
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