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![Page 1: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/1.jpg)
SELFISHMIGRATE: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors
Janardhan Kulkarni, Duke University
Sungjin Im (UC Merced ), Kamesh Munagala (Duke), Kirk Pruhs (UPitt)
![Page 2: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/2.jpg)
1
2
M
ONLINE UNRELATED MACHINE MODEL
3- processing length
- rate of processing
- weight
![Page 3: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/3.jpg)
1
2
M
ONLINE UNRELATED MACHINE
3
100
(rate = 1, length=100)
(rate = 0.5, length 200)
(rate = 2, length =50)
Time
- processing length
- rate of processing
(rate = 0, length = infinity)
![Page 4: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/4.jpg)
1
2
M
NON-CLAIRVOYANCE
3
(rate = 1, length=100)
(rate = 0, infinity)
(rate = 0.5, length = 200)
(rate = 2, length =50)
- processing length
- rate of processing
- weight
Time
![Page 5: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/5.jpg)
FLOW-TIME (DELAY OR RESPONSE TIME)
![Page 6: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/6.jpg)
ANOTHER FORM
![Page 7: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/7.jpg)
SPEED-AUGMENTATION: - Online scheduler runs at higher speed
PREMPTION: - Stop a job in middle of processing and continue later.
MIGRATION: - Change the assignment of jobs to machines at no cost.
![Page 8: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/8.jpg)
NO PARALLEL PROCESSING
- No job is simultaneously processed on multiple machines.
1
2
OK
![Page 9: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/9.jpg)
NO PARALLEL PROCESSING:
- No job is simultaneously processed on multiple machines.
1
2
NOT ALLOWED
![Page 10: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/10.jpg)
How to schedule jobs to minimize sum of weighted flow-time
for unrelated machines in non-clairvoyant model?
![Page 11: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/11.jpg)
It was very difficult
Motivation
![Page 12: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/12.jpg)
• Heterogeneous architectures are ubiquitous
• Non-clairvoyance is very important in practice
Motivation
![Page 13: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/13.jpg)
SELFISHMIGRATE is -speed -competitive for minimizing
weighted flow-time on unrelated machines.
Result also extends to energy + weighted flow-time.
THE MAIN THEOREM
![Page 14: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/14.jpg)
CLAIRVOYANT ALGORITHM
Anand-Garg-Kumar, SODA ‘12Chadha-Garg-Kumar-Muralidhara, STOC ‘09
![Page 15: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/15.jpg)
SJF
SJF
ALGORITHM
53 70
101 10020
2020
Increase B = 28 + 20
Increase A = 31 + 20 NEW
![Page 16: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/16.jpg)
For all jobs
For all machines
![Page 17: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/17.jpg)
THE DUAL
For all jobs machines and time instants
![Page 18: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/18.jpg)
The whole frame work breaks down for non-clairvoyant settings…
1. We cannot measure the increase in the objective
2. Migrating jobs is necessary
3. Migration of jobs makes calculating the flow-times difficult and complicates how jobs interfere with each other
![Page 19: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/19.jpg)
SELFISHMIGRATE
![Page 20: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/20.jpg)
KEY IDEA I
Focus on speed at which jobs are getting processed and monotonicity of speed
Speed of a job =
fraction of the job processed at time
![Page 21: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/21.jpg)
If is monotone, then
![Page 22: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/22.jpg)
If is monotone, then
Dual Constraint:
![Page 23: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/23.jpg)
If is monotone, then
Dual Constraint:
![Page 24: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/24.jpg)
Fraction of processor allocated =
Round Robin or Proportional Sharing
![Page 25: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/25.jpg)
If is monotone, then
Dual Constraints:
![Page 26: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/26.jpg)
If is monotone, then
Dual Constraints:
But which machine we should assign the job ?
![Page 27: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/27.jpg)
If is monotone, then
Dual Constraints:
But which machine we should assign the job ? ANS IS MINIMUM
![Page 28: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/28.jpg)
Dual constraints need us…
For all jobs machines and time instants
1. BEST MACHINE- which maximizes speed.
2. The speed MONOTONICALLY increases.
![Page 29: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/29.jpg)
KEY IDEA II: VIRTUAL QUEUES, VIRTUAL SPEED
RR
j
![Page 30: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/30.jpg)
VIRTUAL QUEUES, VIRTUAL SPEEDS
RR
Inverse of instantaneous delay the job induces on the other jobs ahead of its virtual queue.
![Page 31: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/31.jpg)
KEY IDEA II: VIRTUAL QUEUES, VIRTUAL SPEED
RR
Total delay induced by job if it stays on the machine till its completion is proportional to
![Page 32: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/32.jpg)
KEY IDEA III: SELFISHMIGRATE
RULE 1: NO JUMPING (not even virtual ones!)
![Page 33: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/33.jpg)
Virtual speed of other jobs does not decrease if a job enters the machine!
RULE 1: NO JUMPING
![Page 34: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/34.jpg)
RULE 2: BE SELFISH!
Increases virtual speed… migrate! Any time!
![Page 35: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/35.jpg)
RULE 2: BE SELFISH!
Remains Same
Remains Same Increases!
![Page 36: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/36.jpg)
Jobs migrate whenever they can increase their virtual speed...
![Page 37: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/37.jpg)
Jobs migrate whenever they can increase their virtual speed…..
![Page 38: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/38.jpg)
Jobs migrate whenever they can increase their virtual speed…
![Page 39: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/39.jpg)
Jobs migrate whenever they can increase their virtual speed…..
![Page 40: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/40.jpg)
This cannot go on forever… as virtual speeds are finite
![Page 41: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/41.jpg)
We get …MONOTONICITY
Virtual speeds are monotone non-decreasing!
![Page 42: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/42.jpg)
BEST MACHINE
each job chooses the best machineon arrival
![Page 43: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/43.jpg)
BEST MACHINE (Nash Equilibrium on Virtual Speed)
SELFISHMIGRATE ensures this istrue at all times by design!
![Page 44: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/44.jpg)
BEST MACHINE
Entire process can be thought asCoordination ‘game’ on virtual speeds
![Page 45: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/45.jpg)
DUAL SETTINGS
The total delay job causes on the jobs ahead of its virtual queue over its entire sojourn
![Page 46: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/46.jpg)
![Page 47: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/47.jpg)
![Page 48: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/48.jpg)
![Page 49: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/49.jpg)
DUAL SETTINGS
The total delay job j causes on the jobs ahead of its virtual queue over its entire sojourn + its total processing time.
The flow-time of all jobs (Cost of the algorithm)
![Page 50: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/50.jpg)
The total number of jobs in the queue at time t.
The total flow-time of all jobs (Cost of the algorithm)
Dual setting
=
=
![Page 51: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/51.jpg)
DUAL OBJECTIVE
![Page 52: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/52.jpg)
What About Constraints?
For all jobs machines and time instants
![Page 53: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/53.jpg)
DELAY LEMMAS
(Follows from a property of Round Robin)
Total delay a job induced on jobs ahead of it over the interval
Total delay a job induced on jobs ahead of it in
![Page 54: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/54.jpg)
DELAY LEMMA
![Page 55: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/55.jpg)
DELAY LEMMA
MINIMUM
(BEST MACHINE)
![Page 56: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/56.jpg)
We gave a new framework to analyze non-clairvoyant scheduling problems
CONCLUSIONS and OPEN PROBLEMS
- norms of weighted flow-time
![Page 57: S ELFISH M IGRATE : A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors Janardhan Kulkarni, Duke University Sungjin Im (UC Merced.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649ca25503460f94961800/html5/thumbnails/57.jpg)
THANKS