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Our Famous Original Dyna St-70 Rebuild Plans
From Audio Basics, July, 1982
Article By Frank Van Alstine
www.avahifi.com 

  Hello again, am glad that the feedback I am getting from many of you indicates that you are happy with the information and ideas I have been describing. Some of you have complained that you want more "meat" - technical information on audio equipment. So, this month we will get a bit more technical and go through the operation of a vacuum tube amplifier, what it does, what it cannot do, and what you can do about it. The data will pertain to vacuum tube amplifiers in general, and the Dyna St-70 specifically, as we get so many requests for information on how to modify them.

 

Vacuum Tube Amplifiers
Why audio amplifier can essentially be modeled as a two stage device; a voltage amplifier (which amplifies the amplitude of the signal) followed by a current amplifier (which supplies the drive current to drive the now large amplitude signal into a low impedance load - the speaker system). Although many tube circuits will also have voltage gain in the current amplifier section, that is not important to the discussion that follows. The closed loop gain of the amplifier is determined by a voltage divider which sends a portion of the output signal back to the input of the voltage amplifier out of phase. The amplifier then does not amplify the input signal, it amplifies a signal being the difference between input and feedback signal.

If the voltage amplifier and current amplifier were perfectly linear, the difference between the input and feedback signal would be only a small version of the input signal and the results would be "perfect." In theory, any difference between input and output is supposed to be eliminated by feedback. The feedback signal, which is a duplicate of the output signal, when subtracted from the input signal, should create a "difference signal" which is "pre-distorted" by the amount of distortion in the circuits, but out of phase with the circuit's distortion. The "pre-distortion" in the "difference" signal, when added out of phase to the actual distortion in the circuits, cancels exactly, giving a "perfect" output signal. That is the way it is supposed to work.

By the way, there ain't no such thing as a no feedback amplifier! There are many different feedback schemes. One can choose to use lots of local feedback in each stage and little overall loop feedback, but each device in itself (whether it is transistor or tube) has internal feedback. If one attempts to make an amplifier with "no feedback" except for that inherent in the devices themselves then the design becomes absolutely dependent of the characteristics of each independent device. No two tubes or transistors, even of the same type, are identical. Even if you painstakingly select and bias each individual device one at a time, its characteristics will change with variations in temperature, current, voltage, and age. It will be impossible to make any two channels the same and to keep them the same. The main characteristics of a so called "no feedback" amplifier are: very high cost (each unit is essentially a one off), very hot running as the devices have to be biased on very hard, unstable operation as the unit changes characteristics with age and temperature, no two samples will sound the same as they are device dependent, and lots of "blow-ups." Obviously, repairs will be expensive as a repair is essentially a re-engineering of that unit with new devices and re-biasing of each device. I can live without it. The "wonderful" sound of a "no feedback" amplifier is the wonderful sound of lots of instabilities and underdamped oscillations. You may like it, I don't, it isn't music.

Thus, those that choose to build stable, repeatable, and rationally priced amplifiers will use some feedback. The catch is in knowing what the feedback can and cannot do in the real world, and to use the feedback properly, so that the unit does not only measure well, but actually performs well under transient conditions in the real world.

Now, back to that vacuum tube amplifier. Remember we mentioned that if the voltage amplifier and the current amplifier were perfect, everything would be just fine. Sorry folks, the internal circuits are not perfect and that is where the troubles start.

Inasmuch as the feedback is supposed to compensate for any non-linearities between input and output, it is nice to know what non-linearities exist.

First of all each individual active device is nonlinear. Its transfer characteristics are exponential, not linear, be it tube, FET, or transistor. Refer to the sketches below. If the device was perfect, its transfer function would be a straight line, and the slope would remain the same at all frequencies. The actual characteristics are shown in the second and third sketches. Note that the characteristics are actually exponential. The device is only very linear near the center-line of its operation, and the harder it is "worked", the less linear it becomes, finally becoming 100% nonlinear when its absolute limitations are reached. In addition, the slope of the transfer function becomes less at higher frequencies as the gain of the device reduces. Thus if one attempts to get the same output from any given device at higher frequency, one will drive it into gross non-linearity sooner, as its headroom is less. In a similar fashion, at very low frequencies (approaching DC) the device becomes more nonlinear and its gain drops. In addition, because the slope changes with frequency, a kind of phase distortion is introduced which is not measured in standard IHF distortion tests, which measure only single frequency performance.

Performance curves

Obviously, to optimize internal linearity, it is very desirable to operate each device within as narrow a bandwidth and as limited an amplitude range as possible while still covering the audio frequency range of interest.

In a vacuum tube amplifier another major non-linearity is the output transformer. The output transformer's primary coil is just that-a very large coil (inductor) in series with the output tubes. Obviously the coil becomes very resistive as the frequency goes up, and in an audio amplifier this happens well within the audio range, rolling off the high frequency output. At very low frequencies the core of the transformer saturates giving very nonlinear bass performance. If one wants good high frequency performance then one must have very small output transformers so that the coil inductance is low. If one wants good low frequency performance one must have very large transformers so the core does not saturate. These requirements are mutually self exclusive. These requirements become more difficult to meet as the power rating goes up. If one attempts to "get around" this by designing a tube amplifier without output transformers, then one is faced with the problem that output tubes have very high output impedance and will not drive normal loudspeaker loads (8 s nominal) without severe non-linearities.

Since the output transformer is a very narrow band and nonlinear device, it is obviously necessary to not feed into the transformer a signal that it cannot handle-the bandwidth of the amplifier must be limited to within the bandwidth of the output transformer. You cannot stuff 10 pounds in a 1 pound sack.

The power supply is another source of distortion. The power supply can be considered to be in series with and part of the output circuit. All current that flows through the output circuit and speaker load first must flow through the power supply. The frequency limits of a power supply are real. It can be modeled as an inductor in series with a capacitor. Obviously at DC the capacitor's impedance is infinitely high, and at high frequencies the inductance is infinitely high.

Thus, at very low and very high frequencies, the power supply is not capable at all. Unless great care is used in the power supply design, it may have multiple resonances, and actually be high impedance at many frequencies within the audio range. Consider also that since the power supply is part of the output circuit, if somebody offers a "wonderful" vacuum tube amplifier with a "wonderful" solid state power supply, you no longer have a vacuum tube amplifier, but a solid state amplifier, so how can it be a "wonderful" tube amplifier?

Of course the power supply is also attached to the voltage amplifier section. Consider that all current draw by the output section causes a signal to show up on the power supply feeds. Any given device or circuit will work best when its supply is absolutely stable. Circuits are designed to reject power supply variations, but the supply rejection isn't absolute. Thus the more signal that shows up on the power supply feed to the voltage amplifier, the more distortion and instabilities there will be, as this is a signal injected into the circuit at the wrong place. Since we already know that the power supply is less effective at very high and very low frequencies, obviously the power supply related distortions will be greater at very high and very low frequencies. Again, a very good reason to bandwidth limit the amplifier to within the capability of its power supply.

Understand of course that we are considering basic ground rules in general. There are many different kinds of voltage amplifier and current amplifier configurations that work fairly well, some simple, some complex. The important thing to know is that unless the circuits are executed to obey the guidelines established above the distortion will be very high under real world conditions, no matter what the linearity of each section is and no matter how high a quality of parts are used.

Another common problem with vacuum tube amplifiers is the value chosen for the interstage coupling capacitors. In the case of the Dynaco St-70 for example (see attached schematic) coupling capacitors C10 and C11 are 0.1 uF. This introduces another large low frequency roll-off within the feedback loop. Since the amplifier actually amplifies the difference between input and feedback, and since the feedback is the difference between input and feedback, and since the feedback is taken off the output of the amplifier, at low frequencies the difference signal becomes very large partially due to the roll-off caused by the 0.1 uF coupling capacitors. Now remember that we have shown that any circuit becomes less linear with increasing amplitude and at the frequency extremes. The roll-off caused by the small value interstage coupler makes the front end work very hard to generate a large low frequency correction signal. This causes the front end to run in a very nonlinear mode at low frequencies. You hear it as "muddy bass." The "cure" is quite simple, make the interstage capacitor large enough in value so that the loop roll-off is minimized, thus reducing the correction required, and letting the front end run in a more linear mode. The low frequency correction signal is easy to see on an oscilloscope. Using a low frequency square wave as a source (20 Hz is fine) look at the signal on the output side of the interstage coupler. Note that it looks much like the input signal. Now look at the signal on the input side of the coupler. You will find the circuit is generating a signal with a large bass boost! (This is true in most tube preamps too!) What is happening is that the "flat" input signal is rolled off by the interstage coupling capacitor. Then the rolled off signal is fed back to the input and a correction signal is generated with a large bass boost to make up for the roll-off. The boosted signal is then rolled off again by the coupling capacitor and its output looks just fine. But the "monkey motion" has ruined the voltage amplifier's linearity at low frequencies.

Now let's look at what is wrong with the original Dyna St-70 in detail. Refer to the audio channel schematic again, keeping in mind that the "dashed" section is our addition, the original has the input connected to V2 directly with a piece of wire.

What we have is a typical vacuum tube amplifier with unlimited bandwidth input acceptance (DC coupled) but with limited bandwidth output transformers and small interstage coupling capacitors. The power supply is also limited bandwidth, being pretty feeble at both low and high frequencies.

A very low frequency signal is rolled off by the interstage coupling capacitors, turned into a "lump" as the output transformer core saturates, and is further distorted as the power supply runs out of steam. The feedback signal, being taken off after all the disasters occur is very different from the input signal. This generates an enormous "difference" signal which drives the front end into 100% distortion trying to make an impossible correction. Inasmuch as the circuits are underdamped too, the "blob" makes the amp ring for a few cycles attempting to digest the mess. Some people call these distortions and ringing, which extends up into the mid-range, "concert hall sound." Sorry, it isn't concert hall sound, it is distortion. If you like it you have bad taste.

At high frequencies the compensation in the voltage amplifier rolls off the signal, the active devices roll it off further, and the output transformers attenuate the highs further yet. This generates another huge correction signal at high frequencies, again more than the headroom of the front end, clipping the correction signal once again. Of course the high impedance of the supply has further compounded the problems. The amp is driven into hard slew limiting and all signal entering the amp while any internal device is slewing is erased. Gobs of high frequency distortion are added and part of the music is forever lost. It is very strange to think that some people use the St-70 to drive tweeters when it doesn't "tweet" at all-it does kind of "squeak."

Obviously the power supply of the St-70 must be much improved. NO! Not necessarily! Think a minute. Consider that the power bandwidth of the power supply must be greater than the bandwidth of the audio circuit. There are two ways to get this ratio in proper order. The expensive (and stupid) way is to build a huge power supply-and if the amp has DC coupled inputs you can never make it big enough. The easy and smart way is to limit the bandwidth of the circuit to within the capabilities of the existing power supply, especially if it is absolutely necessary to bandwidth limit the inputs anyway to make the input bandwidth within the capabilities of the output transformers.

As mentioned earlier, the interstage coupling capacitors, C10 and C11 are too small. Note that as long as the input is DC coupled, it is not possible to make C10 and C11 big enough, as even a very large capacitor will have an inside the loop roll off when compared to DC input acceptance.

To install the input bandwidth limited filter on the St-70 you will need 8 parts: (2) 10,000 resistors, (2) 470,000 resistors (5% carbon film 1/4 watt parts from Radio Shack are just fine, and it would be better if you could use a meter and "pair" them, so they are matched within 1%.) You will also need (2) 1000 pF capacitors (mica, polystyrene, or mylar are O.K., of about 100 volt rating - the capacitors used should be physically small) and (2) 0.02 uF capacitors (film) 100 volt rating, again physically as small as possible. Again, Radio Shack will have adequate parts and if you can match them on a precision capacitance meter it will be helpful. The capacitor values suggested are not absolute. Anything from about 0.02 to 0.033 uF is O.K. for the larger cap, and 800 to 1200 pF for the smaller capacitor.

The new 6 dB per octave low pass and high pass filter is installed on the input jacks on the bottom inside of the chassis. We suggest that the mono-stereo switch wiring be eliminated as the performance is poorer when bridged mono because of the difference between the two channels (no two output tubes or output transformers are identical).

 

If you decide to eliminate the mono-stereo switch, then do the following:
1. Remove all the wires from the input jack and mono-stereo switch except for the two wires going directly from the input jack ground lugs to the PC card (these are actually extensions of the leads of two 10 resistors mounted on the card). These remain. Also remove the two original 470,000 resistors from the jack and switch.

2. Remove the two wires running from the hot lugs of the input jack to eyelets 7 and 17 on the PC card.

3. Connect a 10,000 resistor in series with a 0.02 uF capacitor and connect the capacitor end of the series set to the left channel hot input jack and the resistor end to eyelet 7 on the PC card.

4. Connect another 10,000 resistor in series with a 0.02 uF capacitor and connect the capacitor end to the right channel hot input jack and the resistor end to eyelet 17 on the PC card.

5. Connect a 1000 pF capacitor in parallel with a 470,000 resistor and install the resistor between the left channel ground lug and eyelet 7 on the PC card.

6. Connect another 1000 pF capacitor in parallel with a 470,000 resistor and connect the resistor from the right channel ground lug on the input jack to eyelet 17 on the PC card.

 

If you must keep the mono-stereo switch option, do the following instead of the last set of instructions:
1. Remove the two wires running from the left and right channel hot lugs on the input jacks to eyelets 7 and 17 on the PC card.

2. Connect a 10,000 resistor in series with a 0.02 uF capacitor and connect the capacitor end to the left channel hot input lug and the resistor end to eyelet 7 on the PC card.

3. Connect another 10,000 resistor in series with a 0.02 uF capacitor and connect the capacitor end to the right channel hot input lug and the resistor end to eyelet 17 on the PC card.

4. Install a 1000 pF capacitor in parallel with each of the two existing 470,000 resistors on the input jack and mono-stereo switch.

For mono operation, the amp is switched to mono, only one input jack is used (either left or right, but not both). Connect a jumper wire from the left output ground to the right output ground terminal. Connect a jumper wire from the left 16 tap to the right 16 tap (for 8 speakers). Take the output from the same channel that you have the input jack connected to, using the 16 and ground terminals (for 8 speakers). To use 4 speakers connect the jumper from the left 8 output tap to the right 8 output jack and connect the load from ground to 8 on the channel used. This arrangement parallels the two channels for somewhat higher power, but lower definition performance.

Now that the input bandwidth is set to a rational, finite limit, it is possible to make the interstage coupling capacitors "big enough." You will need to acquire four 1 uF at 400 volt film capacitors (mylar, polypropylene, or whatever). Again Radio Shack will have adequate parts.

Locate and remove the four large identical black tubular 0.1 uF at 400 volt capacitors from the PC card. They are positioned parallel with the front of the chassis, one at each corner of the PC card.

Replace each with a 1.0 uF at 400 volt capacitor. The exact value of the replacements is not critical. They can be anything between 0.8 uF to 2.0 uF at 400 volts or higher. It is important that all four new capacitors be exactly the same.

Further detail improvements can be made to the St-70. The bias supply capacitors in old St-70 amps should be replaced. We suggest that the two original 50 uF capacitors (C3 and C4, located on the 7 lug terminal strip under the chassis) be replaced with new 100 uF at 80 volt electrolytic capacitors (again, available at Radio Shack). Note that the positive end of each cap is connected to ground. Do not use a larger capacitor in this application or the supply will come up too slowly, over-biasing the output tubes at turn on.

Although the original power supply is now adequate, further reductions in hum and noise can be made by installing an additional 100 uF at 500 volt electrolytic capacitor (a 450 volt rated cap with a 500+ volt surge rating is adequate unless you have high line voltage) from pin 8 of the power supply tube (V1-5AR4) to chassis ground at the ground lug near the quad filter. The positive end of the cap goes to the tube socket, the negative end to ground.

Inasmuch as the perceived "image" and "depth" of an audio system is dependent upon both channels having exactly the same gain and phase response, and because the resistors in the St-70 (and other tube amps) may have drifted out of specification over the years, it is helpful to replace all of the resistors with new tight tolerance parts. The gain determining resistors especially should be matched to each other within 1%. The RN60D and RL42S metal film resistors shown on the attached St-70 parts list are a good choice. However using 1/2 watt carbon film resistors for the RN60s and 2 watt carbon film resistors for the RL42S types is just fine, except you will have to sort more of them to get a tight channel-to-channel match.

Because selenium rectifiers (the small little finned block located in the bottom middle of the chassis) become resistive with age, you may be able to increase the voltage to your bias supply by substituting a lN4004 silicon diode for this part (Dl). Because the negative voltage to the bias supply will now be higher than stock, it probably will also be necessary to change the value of Rl (10,000 2 watt resistor) to 18,000 2 watt to allow the amp to bias adjust at 1.56 volts DC across R20 in the center of rotation of P1 and P2.

The St-70 and other tube amplifiers run very hot. This tends to make solder joints deteriorate with time. Re-solder all solder connections in the amplifier, including all parts, leads, and the tube sockets on the PC card. Clean the input jacks, output terminals, the bias pots, and all the tube sockets with DeoxIT-D5 (we have 5 oz. spray cans available for $20). Usually lightly "crimping" the hot (inner) terminals of the input jacks will eliminate patch cable dropouts.

In the St-70 the noise characteristics, gain, power, and slew rate are dependent upon having high quality tubes in the unit. We have Sovtec EL34G+ output tubes available at $80 per set of four plus $6 shipping and a Sovtec 5AR4 rectifier tube available for $15 plus $6 shipping. We do not have 7199 tubes available.

Refer to the attached schematic and parts list for other service and adjustment notes on the St-70.

I assume you have noticed we have not spent much time on the inner details of the circuit topography of the St-70. There may, or may not be "better" input, phase inverter, and output circuits available. The point is that almost all tube amps are mistakenly DC coupled and whatever the internal circuits are, they are driven into gross nonlinearities. The important concept is that any tube amp in which the input is limited to within the internal capabilities of the circuit will outperform any tube amp that can be driven into internal overload, no matter how expensive or complex the circuits may be. And the final limitations of a tube amplifier are the output transformers. Lots of money spent trying to achieve a "better" drive circuit probably is of little value, because the output transformers still are the limits of performance.

 

Things You Should Not Do To Your Vacuum Tube Amplifier (And Why).
DO NOT install a solid state diode bridge to replace the vacuum tube rectifier. The supply is operating at 500 volts with line surges over 1000 volts! There are no reliable diodes available to operate at this voltage. You will be in great danger of blowing the diode bridge and damaging your power transformer and filter capacitor. In addition, the solid state supply will "turn on" instantly, and the full B+ voltage will be fed to the tubes before the heaters have warmed up and turned the tubes on. This will tend to over voltage the quad filter capacitor and capacitors downstream, which may damage them. The output tubes will run hotter than normal and have a short service life. There are no useful redeeming advantages to a solid state diode bridge.

DO NOT install solid state regulators. The "aftermarket" circuits we have seen use transistors with inadequate voltage ratings (operating in the "blow-up" mode) and have severe slew rate limitations. Remember, the bandwidth of your power supply must be greater than the audio circuits, and a series bipolar regulator is bog slow! It will change the sound, it makes it much worse!

DO NOT add external power capacitors. The long hookup wires will have lots of inductance and impair the high frequency performance.

DO NOT rewire the amplifier internally with "magic wire." The chances are you will screw up the lead routings, add longer lead runs than the original and increase stray inductances. The probabilities of internal short circuits and bad connections increase as the wires are too large for reliable termination.

DO NOT replace your capacitors with high priced and physically large "wonder caps." The larger the physical size of a given value capacitor, the greater its inductance will be, and the more trash it will dump into the circuit. Magic "wonder caps" do change the sound, they make it worse!

DO NOT use polystyrene capacitors near heat generating components. They change value with temperature, and near an output tube they may even melt.

DO NOT ship your vacuum tube amplifier to us to fix if you screw it up unless you CALL US FIRST at 952 890-3517. Output tubes don't survive shipping, tube amps are heavy and expensive to ship, and their performance is limited. One of the "joys" of owning a vacuum tube amplifier is learning how to fix it yourself. If you don't want to do this, you shouldn't own a vacuum tube amplifier.

 

2002 Note:

We can get much better results now with our complete $249 Super 70i Rebuild Kit. It includes a new mother board with all new audio circuits (using the information contained herein and much more), a new B+ supply built of modern PC-card-mounted high efficiency, high reliability capacitors, and a new bias supply (replacing the parts on the 7-lug terminal strip as part of the new mother board layout). It also includes new 6GH8A tubes to replace the now obsolete 7199 tubes. A new Input/Output jack set kit is available too for $65.00 with gold plated input jacks and high quality Pomona 5-way binding post output jacks. No cutting or drilling is required and step-by-step instructions, schematics, parts lists, and wiring diagrams are provided. The kit instruction manual is available for $25.00 separately, or the manual and bare mother board PC card for $55.00 if you want to provide your own parts. The price of the manual and PC card can be applied to the later purchase of the rest of the kit as long as they are current. The sonic quality is really special.

 

Formula to Solve 6 dB/Octave High & Low Pass Filter Such as Recommended for the St-70

filter formulas

 

Service Notes
Examining the 1.56 volt biaset test point on the St-70 can tell you much about the condition of the amplifier. If the output tubes are old, it may be impossible to adjust the bias pots to bring the voltage up high enough. Replace the output tubes. A shorted output tube may cause the bias reading to run away high. 7199 tubes are best selected by examining the output of the amp on a scope. A low gain or noisy 7199 will show excess output hum and/or not make full power. Fuse blowing can be caused by two problems. A hard blow soon after turn-on indicates a power supply short, either a defective 5AR4 tube or a shorted quad filter cap. A fuse that blows soft or after a few minutes of operation indicates a problem with the audio circuits - probably a bad 6CA7 tube. Note that the bias setting will vary with AC line voltage so the value isn't an absolute. It is possible to swap tubes channel to channel (except the 5AR4) one at a time to locate a defective tube.

The new input filter circuit provides -3 dB poles at 16 Hz and 17 KHz which keeps the audio circuit working within the limits of the output transformers. The larger C10 and C11 effectively takes them out of circuit for AC signal purposes after the input filters have been installed. It is much more important to install the new input filter circuits than to replace all of the resistors and capacitors. Match R and C values channel to channel for a good gain match between the channels.

 

Dyna St-70 Amplifier Suggested Modifications Parts List

 
 C1 0.02 uF 1000V disc P1 10 k bias trimpot
 C2 0.02 uF 1000V disc P2 10 k bias trimpot
 C3 100 uF 80V electrolytic R1 10 k 2W
 C4 100 uF 80V electrolytic R2 10 k 2W
 C5A 30 uF 525V electrolytic R3 6.8 k 2W
 C5B 20 uF 525V electrolytic R4 22 k 2W
 C5C 20 uF 525V electrolytic R5 10 k 0.5W
 C5D 20 uF 525V electrolytic R6 475 k 0.5W
 C6 0.02 uF 50V film R7 10 ohm 0.5W
 C7 1000 pF 50V film R8 330 k 2W
 C8 0.05 uF 400V film R9 1.5 M 0.5W
 C8 0.05 uF 400V film R10 270 k 2W
 C10 1 uF 400V film R11 620 0.5W
 C11 1 uF 400V film R12 47 0.5W
 C12 390 pF 500V mica R13 18 k 0.5W
 D1 1N4003 or 1N4004 silicon diode R14 47 k 2W matched within 1% of R15
 V1 5AR4 rectifier tube R15 47 k 2W matched with 1% of R14
 V2 7199 pentode, triode tube R16 1 k 2W
 V3 6CA7/EL34 pentode tube R17 270 k 0.5W matched within 1% of R18
 V4 6CA7/EL34 pentode tube R18 270 k 0.5W matched within 1% of R17
 L1 choke, Dynaco C-354 R19 1 k 0.5W
 S1 power switch, SPST R20 15.6 1W
 F1 fuse, 3 ampere slo-blo 3AG R21 1 k 0.5W
 T1 power transformer, Dynaco PA-060 T2 output transformer, Dynaco A-470

 

Schematic

St-70 Revised Schematic

Note: Input circuit (C6, R5, C7, and R6) is new and replaces the original direct coupled input circuit. All wiring is removed from the input jacks except R7 leads and then the new input circuit is installed. The stereo-mono switch should be eliminated. C3, C4, C10, and C11 are revised values. Adjust bias (P1 & P2) for 1.56 volts across R20. L1 can be replaced with a 30 10 watt resistor to make amplifier operational if L1 is defective. This input filter circuit is also helpful for the Dyna MKIII and MKIV amplifiers.

 

Audio by Van Alstine, Inc.
2202 River Hills Drive
Burnsville, MN 55337-1100 USA

Voice: (952) 890-3517
Fax: (952) 894-3675
Website: www.avahifi.com

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

     
 

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