merging what s cracked cracking what s merged
play

Merging Whats Cracked, Cracking Whats Merged Adaptive Indexing in - PowerPoint PPT Presentation

Merging Whats Cracked, Cracking Whats Merged Adaptive Indexing in Main-Memory Column-Stores Stratos Idreos, Stefan Manegold, (CWI) Harumi Kuno, Goetz Graefe (HP Labs) PVLDB 2011, 4(9) Physical design problem Database systems perform


  1. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 Result tuples 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A

  2. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Gain knowledge Q1: 16 9 2 on how data is select * 4 2 1 organized Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 Result tuples 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A

  3. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Gain knowledge Q1: 16 9 2 on how data is select * 4 2 1 organized Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 Result tuples 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  4. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  5. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  6. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  7. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  8. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  9. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  10. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  11. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  12. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  13. Database Cracking CIDR 2007 Cracking Example Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Result tuples Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  14. Database Cracking CIDR 2007 Cracking Example The more we crack, the more we learn Each query is treated as an advice on how data should be stored Physically reorganize based on the selection predicate Column A Cracker column of A Cracker column of A 13 4 4 Q1: 16 9 2 select * 4 2 1 Piece 1: A <= 7 Piece 1: from R 9 7 3 A <= 10 where R.A > 10 2 1 6 and R.A < 14 12 3 7 Q1 Q2 7 8 9 Piece 2: 7 < A <= 10 1 6 8 (copy) (in−place) Result tuples Q2: 19 13 13 Piece 2: select * 3 12 12 10 < A < 14 Piece 3: 10 < A < 14 from R 14 11 11 where R.A > 7 11 16 14 Piece 3: Piece 4: 14 <= A <= 16 and R.A <= 16 8 19 16 14 <= A 6 14 19 Piece 5: 16 < A Dynamically/on-the-fly within the select-operator

  15. Database Cracking, SIGMOD 09 Self-organizing behavior (TPC-H) MonetDB Sel. Crack MySQL Presorted Sid. Crack Presorted 10000 Response time (milli secs) 1000 764 TPC-H Query 15 330 420 300 250 200 150 100 70 0 5 10 15 20 25 30 Query sequence

  16. Database Cracking, SIGMOD 09 Self-organizing behavior (TPC-H) MonetDB Sel. Crack MySQL Presorted Sid. Crack Presorted 10000 Response time (milli secs) 1000 764 TPC-H Query 15 330 420 300 Normal MonetDB 250 200 selection cracking 150 100 70 0 5 10 15 20 25 30 Query sequence

  17. Database Cracking, SIGMOD 09 Self-organizing behavior (TPC-H) MonetDB Sel. Crack MySQL Presorted Sid. Crack Presorted 10000 Response time (milli secs) 1000 764 TPC-H Query 15 330 420 300 Normal MonetDB 250 200 selection cracking 150 Presorted 100 MonetDB 70 0 5 10 15 20 25 30 Preparation cost Query sequence 3-14 minutes

  18. Database Cracking, SIGMOD 09 Self-organizing behavior (TPC-H) MonetDB Sel. Crack MySQL Presorted Sid. Crack Presorted 10000 Response time (milli secs) 1000 764 TPC-H Query 15 330 420 300 Normal MonetDB 250 200 selection cracking 150 MonetDB with Presorted 100 sideways cracking MonetDB 70 0 5 10 15 20 25 30 Preparation cost Query sequence 3-14 minutes

  19. Database Cracking, SIGMOD 09 Self-organizing behavior (TPC-H) MonetDB Sel. Crack MySQL Presorted Sid. Crack Presorted 10000 Response time (milli secs) 1000 764 TPC-H Query 15 330 420 300 Normal MonetDB 250 200 selection cracking 150 MonetDB with Presorted 100 sideways cracking MonetDB 70 0 5 10 15 20 25 30 Preparation cost Query sequence 3-14 minutes

  20. Database Cracking, SIGMOD 09 Self-organizing behavior (TPC-H) MonetDB Sel. Crack MySQL Presorted Sid. Crack Presorted 10000 Response time (milli secs) 1000 764 TPC-H Query 15 330 420 300 Normal MonetDB 250 200 selection cracking 150 MonetDB with Presorted 100 sideways cracking MonetDB 70 0 5 10 15 20 25 30 Preparation cost Query sequence 3-14 minutes

  21. Database Cracking, SIGMOD 09 Self-organizing behavior (TPC-H) MonetDB Sel. Crack MySQL Presorted Sid. Crack Presorted 10000 Response time (milli secs) 1000 764 TPC-H Query 15 330 420 300 Normal MonetDB 250 200 selection cracking 150 MonetDB with Presorted 100 sideways cracking MonetDB 70 0 5 10 15 20 25 30 Preparation cost Query sequence 3-14 minutes

  22. Indexing Overview offline indexing workload analysis index building query processing workload analysis workload analysis

  23. Indexing Overview offline indexing workload analysis index building query processing online indexing workload analysis index building query processing workload analysis workload analysis

  24. Indexing Overview offline indexing workload analysis index building query processing online indexing workload analysis index building query processing adaptive indexing adaptive indexing workload analysis workload analysis

  25. Indexing Overview offline indexing workload analysis index building query processing offline workload knowledge online indexing workload analysis index building online query processing adaptive adaptive indexing idle time adaptive indexing workload analysis workload analysis

  26. Database Cracking Each query is treated as an advice on how data should be stored CIDR’07 Selection cracking SIGMOD’07 Updates SIGMOD’09 Sideways and partial cracking Can be thought of as an incremental quicksort

  27. Database Cracking Each query is treated as an advice on how data should be stored CIDR’07 Selection cracking SIGMOD’07 Updates SIGMOD’09 Sideways and partial cracking Can be thought of as an incremental quicksort The core cracking algorithm is extremely lazy

  28. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps 100

  29. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps 100

  30. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) 100

  31. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) sort 100

  32. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) sort sort 100

  33. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) sort sort sort 100

  34. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) sort sort sort sort 100

  35. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search sort sort sort 100

  36. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search binary sort search sort sort 100

  37. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search binary sort search binary sort search sort 100

  38. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search binary sort search binary sort search binary sort search 100

  39. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search binary sort 50 search binary 100 sort search binary sort search 100

  40. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search binary sort 50 search binary 100 sort search binary sort search 100

  41. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search binary sort 50 sorted search binary 100 sort search binary sort search 100

  42. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) binary sort search binary sort 50 sorted search binary 100 sort search binary sort search Final Initial 100

  43. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) select(A,55,70) sort sort 50 sorted 100 sort sort Final Initial 100

  44. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) select(A,55,70) sort sort 50 50 sorted binary search 100 100 sort sort Final Initial 100

  45. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) select(A,55,70) select(A,150,170) sort sort 50 50 sorted 100 100 sort sort Final Initial 100

  46. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) select(A,55,70) select(A,150,170) sort 50 sort 50 50 sorted 100 100 100 sort sort Final Initial 100

  47. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) select(A,55,70) select(A,150,170) binary sort search binary 50 sort 50 50 sorted search 100 100 binary 100 sort search binary sort search Final Initial 100

  48. Adaptive Merging EDBT’10 , SMDB’10 , Goetz Graefe and Harumi Kuno Incremental sort via external merge sort steps select(A,50,100) select(A,55,70) select(A,150,170) binary sort search binary 50 sort 50 50 sorted search 100 100 binary 100 sort search binary 150 sort search 170 Final Initial 100

  49. Questions • Adaptive merging in column-stores? • Adaptive merging Vs Cracking? • Can we learn from both AM and Cracking?

  50. Performance Analysis c) All queries 200 set-up 100 10K random selections selectivity 10% random value ranges 10 in a 30 million integer column Scan Cumulative Average (secs) 1 (cf., Fig. 10b) 0.1 Sort AM 0.01 Crack 0.004 0.001 1 10 100 1000 10000 Query sequence

  51. Performance Analysis c) All queries 200 set-up 100 10K random selections selectivity 10% random value ranges 10 in a 30 million integer column Scan Cumulative Average (secs) 1 (cf., Fig. 10b) 0.1 Sort AM 0.01 Crack 0.004 0.001 1 10 100 1000 10000 Query sequence

  52. Performance Analysis c) All queries 200 set-up 100 10K random selections selectivity 10% random value ranges 10 in a 30 million integer column Scan Cumulative Average (secs) 1 (cf., Fig. 10b) 0.1 Sort AM 0.01 Crack 0.004 0.001 1 10 100 1000 10000 Query sequence

  53. Performance Analysis c) All queries 200 set-up 100 10K random selections selectivity 10% random value ranges 10 in a 30 million integer column Scan Cumulative Average (secs) 1 AM: high init overhead (cf., Fig. 10b) but fast convergence 0.1 Sort AM 0.01 Crack 0.004 0.001 1 10 100 1000 10000 Query sequence

  54. Performance Analysis c) All queries 200 set-up 100 10K random selections selectivity 10% random value ranges 10 in a 30 million integer column Scan Cumulative Average (secs) 1 AM: high init overhead (cf., Fig. 10b) but fast convergence 0.1 Sort Crack: low init overhead AM 0.01 Crack but slow convergence 0.004 0.001 1 10 100 1000 10000 Query sequence

  55. Questions Adaptive merging and Cracking are extremes

  56. Questions Adaptive merging and Cracking are extremes What is there in between?

  57. Crack-Crack vary initialization and incremental steps taken 100

  58. Crack-Crack vary initialization and incremental steps taken 100

  59. Crack-Crack vary initialization and incremental steps taken select(A,50,100) 100

  60. Crack-Crack vary initialization and incremental steps taken select(A,50,100) crack 100

  61. Crack-Crack vary initialization and incremental steps taken select(A,50,100) crack crack 100

  62. Crack-Crack vary initialization and incremental steps taken select(A,50,100) crack crack crack 100

  63. Crack-Crack vary initialization and incremental steps taken select(A,50,100) crack crack crack crack 100

  64. Crack-Crack vary initialization and incremental steps taken select(A,50,100) crack crack 50 crack 100 crack 100

  65. Crack-Crack vary initialization and incremental steps taken select(A,50,100) crack crack 50 crack 100 crack 100

  66. Crack-Crack vary initialization and incremental steps taken select(A,50,100) crack crack not sorted 50 crack 100 crack 100

  67. Crack-Crack vary initialization and incremental steps taken select(A,50,100) select(A,55,70) crack crack not sorted 50 crack 100 crack 100

  68. Crack-Crack vary initialization and incremental steps taken select(A,50,100) select(A,55,70) crack crack not sorted 50 50 crack 100 crack 100 crack 100

  69. Crack-Crack vary initialization and incremental steps taken select(A,50,100) select(A,55,70) select(A,150,170) crack crack not sorted 50 50 100 crack 100 crack 100

  70. Crack-Crack vary initialization and incremental steps taken select(A,50,100) select(A,55,70) select(A,150,170) crack crack not sorted 50 50 50 100 100 crack 100 crack 100

  71. Crack-Crack vary initialization and incremental steps taken select(A,50,100) select(A,55,70) select(A,150,170) crack crack crack not sorted 50 50 50 crack 100 100 crack 100 crack crack 150 crack 170 100

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend