DE102022000070B3 - Acoustic underwater communication method for returning home of a returning subject, as well as corresponding computer program products - Google Patents

Abstract

A new underwater acoustic communication method for returning a sea-submerged returning subject to a home subject should be designed in such a way that it is both easy to implement in existing underwater facilities and works efficiently. After the returning subject (1a, 1b, 1c) enters a previously agreed meeting area and has reached the receiving range of the home subject (2a, 2b), the new method steps are as follows: a) the transmitter converter (12) of the homecoming communication device (10) sends out a ping message which has identification data of the homecoming subject (1a, 1b, 1c), b) the hydrophone arrangement (23) of the home communication device (20) receives the ping message, c). the home communication computer (21) checks the identification data of the ping message, d) the transmitter converter (22) of the home communication device (20) sends back a pong message with time data relating to receipt of the ping message and sending of the pong message, e) the hydrophone arrangement (13) of the homecoming subject (1a, 1b, 1c) receives the pong message,f) the homecomer communication computer (11) calculates a current distance value via the runtime of the ping message and the runtime of the pong message,g) the homecomer communication computer (11) calculates with pong message reception data of the hydrophone arrangement of the homecoming subject (1a, 1b, 1c ) a current direction value to the home subject (2a, 2b),h) the returning subject (1a, 1b, 1c) moves to the home subject (2a, 2b) based on at least the current direction value and the current distance value,i) repeating steps a multiple times ) to h).

Description

The invention relates to an acoustic digital underwater communication method for returning a homecoming subject submerged at sea to a home subject, as well as corresponding computer program products.

From a specialist book (post-proceedings of the DWT conference, sound and vibration waves and turbulence in a sensitive environment, conference in Kiel, September 17-20, 2012, ISBN 978-3-935938-94-5, https://www.researchgate. net/publication/269873931) underwater communication methods are described. Under the topic "Underwater communication with special forces" low-treason communication is discussed. In addition, the structure of an underwater communication device in the form of a modem for divers is described.

From an article (TY-BOOK; AU-Schreiber, Sabrina; AU-Nissen, Ivor; PY- 2015/06/04; T1 - Digital distance and channel measurements with the underwater telephone UT 3000; https://www.researchgate. net/publication/281904054)
is in the text to 3 the calculation of a distance value using the transit times of messages is described.

The JANUS (STANAG 4748, ANEP 87) underwater communication standard defines a digital underwater communication method.

From the U.S. 2016/0315717 A1 An acoustic underwater communication method and a method for localization is known for scuba divers.

the U.S. 8600 592 B2 relates to a mobile acoustic receiver for underwater applications, which determines its position via a stationary acoustic transmitter.

the U.S. 10,139,469 B1 shows a mobile receiver and a stationary transmitter operating in the ultrasonic range for underwater positioning.

From the U.S. 5,570,323 A and the U.S. 6,272,073 B1 other underwater acoustic communication methods for returning a sea-submerged returnee subject to a homeee are known.

The invention is based on the object of developing an underwater acoustic communication method for returning a sea-submerged returnee subject to a home subject in such a way that it is both easy to implement in existing underwater facilities and works efficiently.

According to the invention, this object is achieved by the features of method claim 1, which is directed to a method. Furthermore, this object is achieved by the features of the independent claims 6 and 7 directed to computer program products.

The advantages of the invention are based on the fact that when “coming home” the initiative comes from the homecoming subject (initiator) and that the home subject takes on a supporting role (responder). After the homecoming subject has arrived at a prearranged meeting area and reached the home subject's service area, question-and-answer messages are exchanged. From sent and received digital messages and their data, the returning subject calculates a distance value using the acoustic propagation times of the messages and an estimated water speed of sound and a direction value to the home subject using direction formation.

1. a) Der Sendewandler des Heimkehrerkommunikationsgerätes sendet eine Pingnachricht aus, die Identifikationsdaten des Heimkehrersubjektes aufweist,
2. b) die Hydrofonanordnung des Heimkommunikationsgerätes empfängt die Pingnachricht,
3. c) der Heimkommunikationsrechner überprüft die Identifikationsdaten der Pingnachricht,
4. d) der Sendewandler des Heimkommunikationsgerätes sendet eine Pongnachricht mit Zeitdaten betreffend Empfang der Pingnachricht und Absendung der Pongnachricht zurück,
5. e) die Hydrofonanordnung des Heimkehrersubjektes empfängt die Pongnachricht,
6. f) der Heimkehrerkommunikationsrechner berechnet über eine Laufzeit der Pingnachricht und eine Laufzeit der Pongnachricht einen aktuellen Entfernungswert,
7. g) der Heimkehrerkommunikationsrechner berechnet mit Pongnachrichtsempfangsdaten der Hydrofonanordnung des Heimkehrersubjektes einen aktuellen Richtungswert zum Heimsubjekt,
8. h) das Heimkehrersubjekt bewegt sich zum Heimsubjekt unter Zugrundelegung mindestens des aktuellen Richtungswertes und des aktuellen Entfernungswertes,
9. i) mehrfache Wiederholung der Schritte a) bis h).

Specifically, the steps are as follows:

1. a) The transmitter converter of the homecomer communication device sends out a ping message which contains the identification data of the homecomer subject,
2. b) the hydrophone arrangement of the home communication device receives the ping message,
3. c) the home communication computer checks the identification data of the ping message,
4. d) the transmitter converter of the home communication device sends back a pong message with time data relating to the receipt of the ping message and the sending of the pong message,
5. e) the returning subject's hydrophone assembly receives the pong message,
6. f) the returnee communication computer calculates a current distance value via a runtime of the ping message and a runtime of the pong message,
7. g) the returnee communication computer calculates a current direction value to the homeee subject using pong message reception data from the returnee subject's hydrophone arrangement,
8. h) the homecoming subject moves to the home subject using at least the current direction value and the current distance value,
9. i) multiple repetition of steps a) to h).

Digital devices are used which exchange messages via digital underwater communications.

Since the home subject only has to reply with a simple Pong message, the method can easily be implemented with the aid of a corresponding computer program.

The method can also be implemented in the returnee subject with the aid of a corresponding computer program. It should be noted that the hydrophone arrangement of the returning subject must have at least two hydrophones spaced apart in such a way that, with respect to an incoming pong message, it can be determined whether the pong message arrives from the right or left (stereolocation).

• • eine Entscheidungsalternative, die Bewegung des Heimkehrersubjektes unverändert fortzuführen,
• • eine Entscheidungsalternative, die Bewegungsrichtung der Bewegung des Heimkehrersubjektes abzuändern.

The features of dependent claim 2 indicate an advantageous embodiment of the invention. These specify feature h) of claim 1. The returnee communication computer determines a decision alternative from a group of decision alternatives comprising at least:

• • a decision alternative to continue the movement of the returnee subject unchanged,
• • A decision alternative to change the direction of movement of the returnee subject's movement.

If the returnee subject is a diver, the decision alternatives are communicated to the diver via a display device, for example. The diver then makes a decision based on the displayed decision alternative. If the returning subject is a robot (Autonomous Underwater Vehicle [AUV], Glider, etc.), a selected alternative decision is executed under computer control.

According to a further embodiment of the invention according to dependent claim 3, each ping message and each pong message has a checksum so that it can be checked whether the message was correctly decoded.

A special effect is achieved with the features of claim 4, which builds on the previous embodiment and states that the checksum of the previous ping message is also listed in each ping message. Ping-pong message pairs that belong to one another can be assigned to one another in terms of time via the checksum of the preceding ping message.

This particular benefit becomes even more significant when, as claimed in claim 5, a plurality of homecoming subjects arrive at the pre-arranged meeting area and reach the home subject's coverage area and the steps set forth in claim 1 are applied to each homecoming subject.

• 1a Taucher als Heimkehrersubjekte und ein U-Boot als Heimsubjekt, als einfache Prinzipskizze;
• 1b ein AUV als Heimkehrersubjekt und eine Unterwassergarage als Heimsubjekt, als einfache Prinzipskizze;
• 2 ein Heimkehrerkommunikationsgerät eines Heimkehrersubjektes und ein Heimkommunikationsgerät eines Heimsubjektes, als Blockdarstellung;
• 3 Schritte des Heimkehr-Verfahrens, die einerseits dem Heimkehrersubjekt und andererseits dem Heimsubjekt zugeordnet sind, als Ablaufdarstellung.

Exemplary embodiments of the invention are described in more detail below with reference to the figures. show:

• 1a Divers as homecoming subjects and a submarine as home subject, as a simple schematic;
• 1b an AUV as a homecoming subject and an underwater garage as a home subject, as a simple schematic;
• 2 a homecomer communication device of a homecomer subject and a home communication device of a home subject, as a block diagram;
• 3 Steps of the homecoming procedure, which are associated on the one hand with the homecoming subject and on the other hand with the home subject, as a flow diagram.

An underwater acoustic communication method for returning home from a sea-submerged returnee subject to a homeee subject will be described below. The drawings are designed so that the left side is associated with the homecoming subject and the right side is associated with the home subject.

1a illustrates a first embodiment. In the first embodiment, a crew of two divers who are homecoming subjects 1a and 1b return to their submarine, which is a home subject 2a. Each returnee subject 1a and 1b has an underwater communication device, hereinafter called returnee communication device 10 . The home subject 2a also has an underwater communication device, called home communication device 20 hereinafter. The homecoming communication device 10 is an underwater modem. The home communication device 20 is an underwater phone.

2 illustrates the structure of homecomer communication device 10 and the structure of home communication device 20. Homecomer communication device 10 has a computer, hereinafter referred to as homecomer communication computer 11, a hydrophone arrangement 13 that is designed for direction formation, and a transmitter converter 12. The home communication device 20 has a computer, referred to below as the home communication computer 21 , as well as a hydrophone arrangement 23 and a transmission converter 22 .

1. a) der Sendewandler 12 des Heimkehrerkommunikationsgerätes 10 sendet eine Pingnachricht aus, die Identifikationsdaten des Heimkehrersubjektes 1a aufweist,
2. b) die Hydrofonanordnung 23 des Heimkommunikationsgerätes 20 empfängt die Pingnachricht,
3. c) der Heimkommunikationsrechner 20 überprüft die Identifikationsdaten der Pingnachricht,
4. d) der Sendewandler 22 des Heimkommunikationsgerätes 20 sendet eine Pongnachricht mit Zeitdaten betreffend Empfang der Pingnachricht und Absendung der Pongnachricht zurück, wobei die Zeitdaten dazu dienen, im Schritt f) eine Laufzeit der Pingnachricht und eine Laufzeit der Pongnachricht zu bestimmen,
5. e) die Hydrofonanordnung 13 des Heimkehrersubjektes 1a empfängt die Pongnachricht,
6. f) der Heimkehrerkommunikationsrechner 11 berechnet über die Laufzeit der Pingnachricht und die Laufzeit der Pongnachricht einen aktuellen Laufzeitwert,
7. g) der Heimkehrerkommunikationsrechner 11 berechnet mit Pongnachrichtsempfangsdaten der Hydrofonanordnung des Heimkehrersubjektes 1a einen aktuellen Richtungswert zum Heimsubjekt 2a,
8. h) das Heimkehrersubjekt 1a bewegt sich zum Heimsubjekt 2a unter Zugrundelegung mindestens des aktuellen Richtungswertes und des aktuellen Entfernungswertes,
9. i) mehrfache Wiederholung der Schritte a) bis h).

3 illustrates, by way of example for the homecoming subject 1a, when entering a previously agreed meeting area and having reached the receiving area of the home subject 2a, the steps that take place:

1. a) the transmitter converter 12 of the homecomer communication device 10 sends out a ping message which has identification data of the homecomer subject 1a,
2. b) the hydrophone arrangement 23 of the home communication device 20 receives the ping message,
3. c) the home communication computer 20 checks the identification data of the ping message,
4. d) the transmitter converter 22 of the home communication device 20 sends back a pong message with time data relating to the receipt of the ping message and the sending of the pong message, the time data being used to determine a runtime of the ping message and a runtime of the pong message in step f),
5. e) the hydrophone arrangement 13 of the returning subject 1a receives the pong message,
6. f) the returnee communication computer 11 calculates a current runtime value via the runtime of the ping message and the runtime of the pong message,
7. g) the returnee communication computer 11 uses pong message reception data from the hydrophone arrangement of the returnee subject 1a to calculate a current direction value for the homeee subject 2a,
8. h) the homecoming subject 1a moves to the home subject 2a based on at least the current direction value and the current distance value,
9. i) multiple repetition of steps a) to h).

The aforementioned steps also apply to the returnee subject 1b.

In 3 the steps of the method are assigned to the homecoming subject on the one hand and to the home subject on the other hand. This form of representation particularly emphasizes that in the present homecoming method the homecoming subject has the determining role and that the home subject only reacts promptly to a received ping message with a pong message to be sent. This homecoming method can be implemented in any homecoming subject and home subject because it is characterized by a decentralized character. Underwater digital communications equipment already in place in a Navy can be used for the homecoming process without major modifications.

The method can be applied to a homecoming subject until the homecoming subject has reached close range relative to the home subject.

• • eine Entscheidungsalternative, die Bewegung des Heimkehrersubjektes 1a unverändert fortzuführen,
• • eine Entscheidungsalternative, die Bewegungsrichtung der Bewegung des Heimkehrersubjektes 1a abzuändern.

In step h), the returnee communication computer 11 determines, for example for the returnee subject 1a, a decision alternative from a group of decision alternatives comprising at least:

• • a decision alternative to continue the movement of the returnee subject 1a unchanged,
• • a decision alternative to change the direction of movement of the returnee subject 1a's movement.

The homecomer communication computer 11 calculates a decision alternative from a group of decision alternatives based on the self-knowledge of the homecomer subject and optionally also the foreign knowledge that the home subject provides as a response (response) in the pong message.

In order to be able to determine synchronization and the exact runtime, the processing time is mapped directly or indirectly to the digital pong message. If the transit time and thus the distance between the subjects is smaller than in the previous ping-pong message pair, then the direction of movement is correct and should be maintained. If the running time is longer than that of the previous pair, then they move away, and the direction of the returning subject is to be changed.

Every ping message and every pong message has a checksum to check if a message was received correctly.

The checksum of the previous ping message is also listed in each ping message. This allows a pong message to be associated with an associated ping message.

This is significant when, as in the present first embodiment, a plurality of homecoming subjects 1a, 1b arrive at the previously agreed meeting area and reach the reception area of the home subject 2a. The aforementioned steps a) to h) are used in this constellation for each returnee subject 1a, 1b.

A computer program product with a computer program is provided for a homecomer communication computer 11 of a homecomer subject 1a, 1b, 1c for carrying out the method when the computer program is executed on the homecomer communication computer 11.

A further computer program product with a computer program is provided for a home communication computer 21 of a home subject 2a, 2b for carrying out the method when the computer program is executed on the home communication computer 21.

A computer program product is generally to be understood as an item of commerce which, for example, has a data carrier with a program code in order to implement a computer program on a computer. One computer program product with a computer program for homecomer communication computer 11 and the other computer program product with a computer program for home communication computer 21 can be marketed by different developers. For example, the one developer may be a manufacturer of home subjects. The other developer may be, for example, a manufacturer of communication equipment for homecoming subjects.

In contrast to the first exemplary embodiment, the gang could also be a mixed gang consisting of a diver and an AUV.

1b illustrates a second embodiment. In the second embodiment, an AUV that is a homecoming subject 1c returns to its underwater garage that is a home subject 2b. The homecoming communication device 10 is an underwater modem. The home communication device 20 is also an underwater modem. The explanations for the first exemplary embodiment apply in a corresponding manner to the second exemplary embodiment. In contrast to the second exemplary embodiment, the home subject 2b could also be a ground node.

       <JANUS UserClass="Homing-Interrogator" Application="MARK-PING">

        <Wakeup type=BIT[1] choice={disable}/>
        <Baseline>

         <Version type=BIT[4] value2="0011" />
         <MobilityFlag type=BIT[1] choice={1=mobile} />
         <Schedule type=BIT[1] choice={0=off} />
         <TxRxFlag type=BIT[1] choice={0=Tx} />
         <Forwarding type=BIT[1] choice={0=No} />
         <ClassUserID type=BIT[8] value10=12 />
         <Application type=BIT[6] value10=44 />
         <AppDataBlock type=BIT[34]>

         <ID type=BIT[4] value2="1101"/>
         <SecondInMinute type=BIT[6] vatue 10="61" /> # in s
         <myDepths type=BIT[5] value10="24" /> # in 2 m Schritten
         <estimatedDirection type=BIT[5] /> #

          if FirstTransmission
             <IdentificationValue type=BIT[14] />
          else
             <estimatedDelayTime type=BIT[10] /> # delta
             <estimatedOffsetTime type=BIT[4] /> # psi
         </AppDataBlock>
         <CRC type=BIT[8] />

        </Baseline>
        <Cargo></Cargo>

       </JANUS>

In a third exemplary embodiment, without making reference to the figures, it is described how the ping messages and the pong messages are formed according to the JANUS transmission method. JANUS offers the possibility of providing the ping messages and the pong messages with an 8-bit checksum. Janus also provides the ability to push 34-bit as a build-in payload running under among other things, can be used for the identification and location data of the ping message. It should be noted that in the JANUS messages, the transmission frequency determines the spacing (wavelength/4) of the hydrophones of the returning subject's hydrophone array.

 <JANUS UserClass="Homing Interrogator"Application="MARK-PING"><Wakeup type=BIT[1] choice={disable}/><baseline><Version type=BIT[4] value2="0011"/><MobilityFlag type=BIT[1] choice={1=mobile} /><Schedule type=BIT[1] choice={0=off} /><TxRxFlag type=BIT[1] choice={0=Tx} /><Forwarding type=BIT[1] choice={0=No} /><ClassUserID type=BIT[8] value10=12 /><Application type=BIT[6] value10=44 /><AppDataBlocktype=BIT[34]><ID type=BIT[4] value2="1101"/><SecondInMinute type=BIT[6] value 10="61"/># in s
         <myDepths type=BIT[5] value10="24"/># in 2 m steps
         <estimatedDirection type=BIT[5] />#

          if FirstTransmission
             <IdentificationValue type=BIT[14] />
          else
             <estimatedDelayTime type=BIT[10] /># delta
             <estimatedOffsetTime type=BIT[4] />#psi</AppDataBlock><CRC type=BIT[8] /></Baseline><Cargo></Cargo></JANUS>

       <JANUS UserClass="Homing-Responder" Application="SNAP-PONG">

        <Wakeup type=BIT[1] choice={disable}/>
        <Baseline>

         <Version type=BIT[4] value2="0011" />
         <MobilityFlag type=BIT[1] choice={1=mobile} /> 
        <Schedule type=BIT[1] choice={0=off} />
        <TxRxFlag type=BIT[1] choice={0=Tx} />
        <Forwarding type=BIT[1] choice={0=No} />
        <ClassUserID type=BIT[8] value10=12 />
        <Application type=BIT[6] value10=45 />
        <AppDataBlock type=BIT[34]>

         <LastCRC type=BIT[8] />
         <SecondInMinute type=BIT[6] value10="12" /> # in s
         <ProcessingTime type=BIT[11] /> # in ms up to 2 seconds

          if MobilityFlag
            <myDirection type=BIT[5] />
            <mySpeed type=BIT[4] />
          else
            <Range type=BIT[9] /> # in m
         </AppDataBlock>
         <CRC type=BIT[8] />

        </Baseline>
       <Cargo></Cargo>

       </JANUS>

This MARK ping message is answered by the home subject with a SNAP ping message by inserting the correct CRC of the request into lastCRC. The immediately next or subsequent second is used as SecondInMinute and the corresponding ProcessingTime is used. In addition, there is the own vehicle speed and direction of the home subject as a responder.

 <JANUS UserClass="Homing Responder"Application="SNAP-PONG"><Wakeup type=BIT[1] choice={disable}/><baseline><Version type=BIT[4] value2="0011"/><MobilityFlag type=BIT[1] choice={1=mobile} /><Schedule type=BIT[1] choice={0=off} /><TxRxFlag type=BIT[1] choice={0=Tx} /><Forwarding type=BIT[1] choice={0=No} /><ClassUserID type=BIT[8] value10=12 /><Application type=BIT[6] value10=45 /><AppDataBlocktype=BIT[34]><LastCRC type=BIT[8] /><SecondInMinute type=BIT[6] value10="12"/># in s
         <ProcessingTime type=BIT[11] /># in ms up to 2 seconds

          if MobilityFlag
<myDirection type=BIT[5] /><mySpeed type=BIT[4] />
          else
            <Range type=BIT[9] /># in m
         </AppDataBlock><CRC type=BIT[8] /></Baseline><Cargo></Cargo></JANUS>

This SNAP-Pong message is received by the homecoming subjects, including the initializing homecoming subject, which recognizes from the lastCRC that this is a response to the message sent, as do the remaining homecoming subjects. The interrogator homecoming subject can now determine the runtime. Since it determines that its ping message has been answered, it uses the time it was sent from the MARK ping message and the time it was received from the SNAP ping message to estimate the runtime. The processing time of the home communication computer is not included in the term.

The running time is estimated by: $$\text{delta}=1/2\left({\text{RX}}_{\_}{}_{\text{interrogator}}-{\text{TX}}_{\text{\_}}{}_{\text{interrogator}}-{\text{processingTime}}_{\_}{}_{\text{responders}}\right)$$

In addition, the time offset to the home subject can be estimated by: $$\text{psi}={\text{RX}}_{\_\text{interrogator}}-{\text{TX}}_{\_}{}_{\text{responders}}\left(\text{secondlminute}\right)\text{-Delta}$$

All other homecoming subjects thus know their neighbors and their position. The estimated values delta and psi are entered in all subsequent ping messages. This means that the home subject also has the option of determining transit times, distances and directions.

Reference List

1a, 1b, 1c

homecoming subject

2a, 2b

home subject

10

homecomer communication device

11

Returning Communications Calculator

12

transmit converter

13

hydrophone arrangement

20

home communication device

21

home communication computer

22

transmit converter

23

hydrophone arrangement

Claims (7)

Acoustic underwater communication method for returning a homecoming subject (1a, 1b, 1c) submerged at sea to a home subject (2a, 2b), with the features: • the method uses an underwater communication device for the homecoming subject (1a, 1b, 1c), hereinafter homecoming communication device (10 ) mentioned, which has a computer, hereinafter called returnee communication computer (11), a hydrophone arrangement (13) which is designed for direction formation, and a transmission converter (12), • the method uses an underwater communication device for the home subject (2a, 2b), hereinafter referred to as home communication device (20), which has a computer, hereinafter referred to as home communication computer (21), as well as a hydrophone arrangement (23) and a transmitter converter (22), • such that after the homecoming subject (1a, 1b, 1c) enters a previously agreed meeting area and has reached a reception area of the home subject (2a, 2b), the following steps take place: a) the transmitting converter (12) of the homecoming communication device (10) sends out a ping message which has identification data of the returning subject (1a, 1b, 1c), b) the hydrophone arrangement (23) of the home communication device (20) receives the ping message, c) the home communication computer (21) checks the identification data of the ping message, d) the Transmitting converter (22) of the home communication device (20) sends back a pong message with time data relating to receipt of the ping message and sending of the pong message, e) the hydrophone arrangement (13) of the homecomer subject (1a, 1b, 1c) receives the pong message, f) the homecomer communication computer (11 ) calculates a current distance value over a runtime of the ping message and a runtime of the pong message, g) the home keeper The communication computer (11) calculates a current direction value to the home subject (2a, 2b) using pong message reception data from the hydrophone arrangement of the homecoming subject (1a, 1b, 1c), h) the homecoming subject (1a, 1b, 1c) moves to the home subject (2a, 2b). Taking as a basis at least the current direction value and the current distance value, i) repeating steps a) to h) several times. procedure after claim 1 , in which in step h) the returnee communication computer (11) selects a decision alternative from a group of decision alternatives comprising at least: • one decision alternative to continue the movement of the returnee subject (1a, 1b, 1c) unchanged, • one decision alternative to change the direction of movement of the to change the returnee subject (1a, 1b, 1c). procedure after claim 1 or 2 , where every ping message and every pong message has a checksum. procedure after claim 3 , in which the checksum of the previous ping message is also listed in each ping message. Procedure according to one of Claims 1 until 4 , in which a plurality of homecoming subjects (1a, 1b, 1c) arrive at the previously agreed meeting area and reach a reception area of the home subject (2a, 2b), and in which the im claim 1 said steps are applied for each returnee subject (1a, 1b, 1c). Computer program product with a computer program for a homecomer communication computer (11) of a homecomer subject (1a, 1b, 1c) for carrying out the method according to one of Claims 1 until 5 , when the computer program is executed on the returnee communication computer (11). Computer program product with a computer program for a home communication computer (21) of a home subject (2a, 2b) for carrying out the method according to one of Claims 1 until 5 , when the computer program is running on the home communication computer (21).

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