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Posted to reviews@spark.apache.org by GitBox <gi...@apache.org> on 2022/09/13 12:47:02 UTC

[GitHub] [spark] wbo4958 commented on pull request #37855: [WIP][SPARK-40407][SQL] Fix the potential data skew caused by df.repartition

wbo4958 commented on PR #37855:
URL: https://github.com/apache/spark/pull/37855#issuecomment-1245363471

   This PR just uses the partitionId as the default starting position to do the RoundRobin and there is also an alternative simple way to replace Random by XORShiftRandom which can also avoid outputting the same position for different partition id. see the tests
   
   ``` scala
   scala> (1 to 50).foreach(numPartitions => { println(s"\n numPartitions is $numPartitions"); (0 to 200).foreach(partitionId => print(new XORShiftRandom(partitionId).nextInt(numPartitions) + " "))})
   
    numPartitions is 1
   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
    numPartitions is 2
   0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 
    numPartitions is 3
   2 0 1 2 1 1 2 1 2 2 2 2 0 2 1 1 0 2 1 0 0 0 1 0 2 1 0 0 0 2 2 1 1 1 2 2 1 1 2 0 0 1 2 0 0 0 0 1 0 0 0 2 1 0 1 1 1 0 2 0 2 2 1 0 0 0 2 2 2 2 0 2 0 0 0 2 0 1 1 0 0 1 2 2 2 0 1 1 0 1 2 1 2 0 2 0 1 1 1 2 1 2 2 1 0 1 1 1 1 2 2 1 0 2 0 2 0 1 0 2 2 0 0 2 1 0 0 2 0 0 1 1 1 1 2 1 1 2 0 0 0 2 1 2 2 2 0 1 0 2 0 1 1 0 0 0 1 0 2 0 0 2 1 2 1 1 1 0 2 1 0 0 0 1 2 2 1 2 1 2 0 2 1 2 2 1 2 0 0 1 1 1 0 2 1 1 2 2 1 2 0 
    numPartitions is 4
   0 0 3 2 2 3 3 1 2 2 0 2 2 2 1 2 2 0 3 2 0 3 3 1 1 1 1 0 0 2 3 1 3 0 1 1 2 0 2 1 3 3 0 0 1 1 3 0 2 1 1 2 0 1 3 0 0 0 1 0 3 2 1 3 3 3 0 1 0 3 0 0 0 3 0 2 1 0 2 0 2 2 0 3 0 2 3 0 1 1 1 1 3 3 3 3 3 0 1 3 1 3 0 2 1 2 1 3 0 1 1 0 2 0 0 3 0 2 1 1 2 0 3 1 3 1 0 0 2 3 1 2 1 3 0 1 2 2 2 1 3 3 3 0 2 2 3 0 1 0 3 0 2 1 2 1 2 1 1 3 3 0 2 0 0 1 1 1 1 2 0 0 1 0 1 3 0 3 1 1 3 2 3 1 2 3 0 3 3 2 3 0 0 1 1 0 2 1 0 0 2 
    numPartitions is 5
   3 3 3 2 3 0 0 0 0 3 4 2 0 4 1 3 4 0 3 4 3 4 4 3 1 1 3 4 3 3 0 2 0 3 0 3 4 0 4 2 0 0 4 2 3 2 3 3 3 0 2 0 3 1 2 1 4 2 1 4 1 3 2 3 0 0 1 2 0 4 0 4 2 1 4 3 2 1 3 2 1 4 4 3 3 2 4 4 4 0 0 2 4 0 3 2 0 3 3 0 0 1 1 0 0 4 4 4 2 4 2 2 4 3 2 3 3 3 3 2 3 3 3 1 0 4 3 3 3 0 1 0 3 0 2 1 3 3 3 3 0 1 2 3 1 2 3 0 0 3 2 3 4 0 2 4 3 3 0 0 0 4 0 1 1 4 1 2 0 2 3 1 4 2 0 3 1 3 1 4 4 0 2 1 3 2 1 1 3 0 1 1 1 0 0 4 4 1 1 3 3 
    numPartitions is 6
   2 3 4 5 1 1 2 4 5 2 5 2 3 2 1 4 3 2 1 3 3 3 1 0 5 4 3 3 3 2 2 1 1 4 2 5 1 1 2 3 3 4 5 3 3 3 0 1 0 0 3 2 4 3 4 4 4 3 5 0 5 2 4 3 3 3 2 5 5 2 3 5 0 3 0 2 3 1 1 3 0 4 2 2 5 0 1 1 0 1 5 4 5 3 5 3 4 1 4 5 1 5 5 4 3 1 4 1 4 2 2 4 3 5 3 5 3 4 0 5 2 0 3 2 1 3 3 2 3 0 1 4 4 4 5 4 4 5 0 3 3 2 1 5 2 5 3 1 3 5 3 1 4 0 0 0 4 0 2 3 0 2 4 2 4 1 1 3 5 1 3 3 0 4 5 5 4 2 4 2 0 5 4 2 5 4 2 0 3 4 4 1 0 5 1 4 2 2 1 5 3 
    numPartitions is 7
   2 5 1 6 1 1 3 1 1 4 4 2 4 3 6 4 4 3 5 3 3 1 5 6 6 6 2 6 5 1 4 6 0 6 1 3 4 0 5 1 5 6 6 6 2 4 4 6 6 2 2 2 5 5 3 2 5 4 0 5 6 0 6 0 0 5 2 0 2 4 5 0 4 1 1 2 4 4 0 2 1 4 4 4 2 3 4 5 3 1 4 4 0 6 6 6 4 0 1 2 4 2 6 1 0 2 5 5 4 2 3 6 5 2 5 3 5 6 3 4 5 3 0 4 0 3 1 2 1 4 3 2 3 6 1 2 1 1 5 5 4 0 0 6 2 0 3 2 1 2 3 5 3 3 5 2 4 4 4 5 5 6 2 2 3 1 1 3 5 1 6 4 2 3 1 5 5 1 0 3 0 3 3 0 5 1 6 4 6 3 6 5 1 4 1 3 0 4 2 6 6 
    numPartitions is 8
   1 1 7 5 4 7 6 3 4 5 1 5 4 4 3 4 5 0 7 5 1 7 6 3 2 2 2 0 1 5 7 3 6 1 3 2 5 0 5 3 6 7 1 0 3 3 7 1 5 3 2 5 0 2 7 0 0 1 3 1 6 4 3 6 7 6 0 2 1 7 0 0 0 7 0 4 2 0 5 1 4 4 1 6 0 4 7 0 2 2 3 3 6 6 7 6 6 1 3 7 2 6 0 5 3 5 2 6 1 2 2 0 5 1 0 7 0 5 2 3 5 1 6 2 7 2 0 1 4 6 2 4 2 7 1 2 4 4 5 2 7 6 7 0 4 5 6 1 3 1 6 1 4 2 4 3 5 3 3 6 6 1 5 1 1 3 2 2 2 5 1 0 2 0 3 6 1 7 3 3 6 4 7 3 4 6 1 6 7 4 6 0 0 2 3 1 4 3 0 0 4 
    numPartitions is 9
   5 0 4 2 7 1 8 4 5 5 5 2 0 2 1 7 6 2 7 3 6 0 1 6 8 7 0 6 6 2 5 4 4 7 2 8 7 7 8 3 3 4 2 3 6 6 3 4 0 3 0 8 4 3 4 7 1 0 2 3 5 5 1 6 3 3 2 8 5 8 3 2 3 0 3 5 6 1 1 6 0 1 5 2 5 0 1 7 6 7 2 7 2 6 8 0 1 7 7 2 7 2 2 1 3 1 1 4 1 5 5 1 6 2 6 2 6 4 6 8 8 6 3 2 1 3 6 5 0 0 7 1 1 7 2 4 4 8 0 3 3 8 4 5 8 5 6 1 3 8 0 7 4 0 0 6 1 6 5 6 6 5 4 5 1 1 7 0 2 4 6 6 0 7 2 5 1 8 7 2 3 2 4 2 8 7 5 6 0 7 7 1 3 5 4 1 5 2 7 5 0 
    numPartitions is 10
   8 3 8 7 3 5 0 0 5 8 9 2 5 4 1 8 9 0 3 9 3 9 9 8 1 6 3 9 3 8 0 7 5 8 0 3 9 5 4 7 5 0 9 7 3 7 8 3 8 0 7 0 8 1 2 6 4 7 1 4 1 8 2 3 5 5 6 7 5 4 5 9 2 1 4 8 7 1 3 7 6 4 4 8 3 2 9 9 4 5 5 2 9 5 3 7 0 3 8 5 5 1 1 0 5 9 4 9 2 4 2 2 9 3 7 3 3 8 8 7 8 8 3 6 5 9 3 8 3 0 1 0 8 0 7 6 8 3 8 3 5 6 7 3 6 7 3 5 5 3 7 3 4 0 2 4 8 8 0 5 0 4 0 6 6 9 1 7 5 7 3 1 4 2 5 3 6 8 6 4 4 5 2 6 3 2 6 6 3 0 6 1 6 5 5 4 4 6 1 3 3 
    numPartitions is 11
   3 10 10 10 4 5 4 2 5 6 8 6 9 6 4 1 3 8 5 9 10 5 3 5 1 0 0 8 8 2 4 3 3 0 6 2 4 8 1 7 8 6 0 5 9 4 5 5 0 1 0 7 3 7 3 2 2 6 2 7 5 0 2 1 10 9 7 8 0 10 1 8 7 10 2 7 5 8 8 6 0 8 6 10 7 8 9 4 7 8 8 10 0 8 2 2 2 0 10 4 4 3 5 2 8 10 7 6 6 5 7 10 5 1 7 3 5 1 6 10 9 2 2 3 5 8 9 1 8 1 10 0 10 0 10 10 2 9 1 10 8 10 9 8 1 1 4 6 6 1 7 3 7 10 7 10 3 5 1 1 2 8 6 1 8 10 1 4 1 8 5 7 10 7 5 10 5 4 10 2 8 8 0 9 8 0 9 1 5 7 2 5 2 0 0 1 0 0 3 8 2 
    numPartitions is 12
   8 3 4 11 1 1 2 4 11 8 5 2 3 2 7 10 9 8 7 9 9 9 1 0 11 4 3 3 9 8 8 1 7 4 8 5 7 1 2 9 3 10 11 9 9 9 0 1 6 6 3 8 4 9 4 4 4 3 5 0 5 8 4 3 9 9 2 11 5 2 9 5 6 3 0 8 3 7 7 9 0 4 8 8 11 0 1 1 6 7 11 10 5 3 5 3 10 7 10 11 1 5 5 10 3 1 4 7 10 8 2 10 3 5 9 5 3 10 0 5 2 0 9 8 7 9 9 8 3 6 7 10 10 4 11 10 10 11 0 3 3 8 1 11 2 11 3 7 9 11 9 1 10 0 6 0 10 0 8 3 6 8 4 2 10 1 1 3 5 1 3 9 6 10 11 5 4 8 10 2 6 5 10 2 5 10 2 6 9 10 10 1 6 5 1 4 2 8 7 5 3 
    numPartitions is 13
   10 6 5 9 10 12 3 12 1 1 3 12 3 8 5 0 3 10 2 9 7 8 5 1 10 7 2 10 7 11 5 3 8 0 10 11 1 9 4 8 6 0 10 6 3 12 3 11 5 9 11 11 11 11 11 6 8 1 11 7 4 4 12 2 5 6 5 1 10 1 10 9 0 11 4 2 2 12 7 10 12 3 3 8 11 4 6 3 1 5 2 11 5 5 9 0 2 11 4 4 12 8 8 8 8 2 5 3 9 4 8 8 3 5 6 12 2 10 9 1 12 7 1 6 0 8 4 6 5 2 2 0 12 1 10 2 4 3 2 3 3 12 9 10 9 6 6 10 3 9 12 4 1 5 1 4 5 1 0 0 6 9 11 4 7 4 7 11 1 9 7 10 11 3 5 11 11 5 8 9 8 3 5 8 9 9 0 6 7 1 9 4 8 5 7 10 2 0 4 6 11 
    numPartitions is 14
   2 5 8 13 1 1 10 8 1 4 11 2 11 10 13 4 11 10 5 3 3 1 5 6 13 6 9 13 5 8 4 13 7 6 8 3 11 7 12 1 5 6 13 13 9 11 4 13 6 2 9 2 12 5 10 2 12 11 7 12 13 0 6 7 7 5 2 7 9 4 5 7 4 1 8 2 11 11 7 9 8 4 4 4 9 10 11 5 10 1 11 4 7 13 13 13 4 7 8 9 11 9 13 8 7 9 12 5 4 2 10 6 5 9 5 3 5 6 10 11 12 10 7 4 7 3 1 2 1 4 3 2 10 6 1 2 8 1 12 5 11 0 7 13 2 7 3 9 1 9 3 5 10 10 12 2 4 4 4 5 12 6 2 2 10 1 1 3 5 1 13 11 2 10 1 5 12 8 0 10 0 3 10 0 5 8 6 4 13 10 6 5 8 11 1 10 0 4 9 13 13 
    numPartitions is 15
   8 3 13 2 13 10 5 10 5 8 14 2 0 14 1 13 9 5 13 9 3 9 4 3 11 1 3 9 3 8 5 7 10 13 5 8 4 10 14 12 0 10 14 12 3 12 3 13 3 0 12 5 13 6 7 1 4 12 11 9 11 8 7 3 0 0 11 2 5 14 0 14 12 6 9 8 12 1 13 12 6 4 14 8 8 12 4 4 9 10 5 7 14 0 8 12 10 13 13 5 10 11 11 10 0 4 4 4 7 14 2 7 9 8 12 8 3 13 3 2 8 3 3 11 10 9 3 8 3 0 1 10 13 10 2 1 13 8 3 3 0 11 7 8 11 2 3 10 0 8 12 13 4 0 12 9 13 3 5 0 0 14 10 11 1 4 1 12 5 7 3 6 9 7 5 8 1 8 1 14 9 5 7 11 8 7 11 6 3 10 1 1 6 5 10 4 14 11 1 8 3 
    numPartitions is 16
   3 3 15 11 9 14 12 6 9 11 3 11 9 9 7 9 11 1 15 11 2 14 12 6 4 4 5 1 3 10 15 6 13 3 6 4 10 0 10 6 13 15 3 1 7 7 15 3 11 6 4 10 1 4 14 0 0 3 6 3 13 8 6 13 14 12 1 4 2 15 0 1 1 14 1 9 5 0 11 2 9 9 3 12 0 9 15 1 5 5 7 7 12 12 15 12 13 3 6 14 4 12 1 10 7 10 4 13 2 5 5 0 10 2 1 14 1 10 4 7 11 2 13 5 14 5 1 3 9 13 4 8 5 14 3 5 9 9 10 4 14 13 15 1 8 10 13 2 6 3 12 3 9 5 9 6 10 6 7 12 12 2 11 2 3 6 5 4 5 10 3 0 5 0 7 12 2 15 6 6 13 8 14 7 9 13 3 12 14 8 12 0 1 4 7 3 8 6 1 0 9 
    numPartitions is 17
   2 14 12 4 16 8 14 13 0 13 6 10 6 12 9 16 5 8 2 15 1 11 5 12 10 5 12 5 14 4 15 3 8 7 5 12 2 5 12 2 13 5 2 12 7 11 12 15 7 8 16 1 11 6 13 2 13 1 13 3 8 15 1 12 5 15 10 16 8 4 15 13 16 8 2 2 12 0 0 14 15 14 8 15 0 13 11 5 10 3 0 16 13 7 1 15 12 11 4 10 10 16 7 10 11 11 16 14 12 7 14 6 6 2 0 11 9 13 6 2 6 15 6 15 15 13 11 9 11 8 13 2 11 5 9 2 11 4 1 4 9 8 5 12 2 0 16 15 9 13 6 3 2 8 2 1 6 12 6 2 15 12 1 3 8 13 4 4 15 9 14 16 16 12 0 10 5 8 8 1 13 16 14 8 15 5 11 14 11 1 13 6 7 7 16 1 13 13 12 0 15 
    numPartitions is 18
   14 9 4 11 7 1 8 4 5 14 5 2 9 2 1 16 15 2 7 3 15 9 1 6 17 16 9 15 15 2 14 13 13 16 2 17 7 7 8 3 3 4 11 3 15 15 12 13 0 12 9 8 4 3 4 16 10 9 11 12 5 14 10 15 3 3 2 17 5 8 3 11 12 9 12 14 15 1 1 15 0 10 14 2 5 0 1 7 6 7 11 16 11 15 17 9 10 7 16 11 7 11 11 10 3 1 10 13 10 14 14 10 15 11 15 11 15 4 6 17 8 6 3 2 1 3 15 14 9 0 7 10 10 16 11 4 4 17 0 3 3 8 13 5 8 5 15 1 3 17 9 7 4 0 0 6 10 6 14 15 6 14 4 14 10 1 7 9 11 13 15 15 0 16 11 5 10 8 16 2 12 11 4 2 17 16 14 6 9 16 16 1 12 5 13 10 14 2 7 5 9 
    numPartitions is 19
   10 0 14 15 4 4 11 8 15 11 9 11 9 13 6 18 14 3 6 11 10 8 13 13 10 6 4 17 16 11 4 16 3 8 0 8 5 4 18 3 0 18 16 16 11 18 8 12 3 0 12 6 0 9 14 2 3 8 18 6 14 12 0 3 5 17 9 4 9 16 13 9 11 13 8 7 2 12 14 16 1 17 11 7 2 18 2 9 15 17 3 5 1 13 6 7 5 12 4 12 18 9 8 5 5 8 8 14 0 5 2 2 7 10 9 0 5 15 2 14 10 13 13 12 8 4 7 16 2 7 12 5 1 11 6 15 12 0 18 12 11 4 17 16 3 0 8 13 13 11 8 0 2 10 14 6 16 4 15 4 11 1 11 12 16 6 3 11 5 4 6 18 3 18 15 10 3 1 13 13 18 1 1 3 10 18 5 6 11 16 10 10 7 0 1 13 7 11 7 7 14 
    numPartitions is 20
   8 3 8 7 13 5 10 0 15 8 9 2 15 14 11 18 9 0 3 9 13 9 9 8 11 16 3 19 13 8 0 17 15 8 0 13 19 5 14 17 15 10 19 17 13 17 8 13 18 10 7 0 8 1 12 16 4 7 1 4 1 8 12 3 5 5 6 7 5 14 5 9 2 11 4 8 7 11 3 17 16 4 4 8 3 12 9 9 14 15 15 2 9 15 13 7 10 3 18 15 5 1 1 10 15 9 4 19 2 4 2 2 19 13 17 13 3 18 8 17 18 8 13 16 15 9 13 8 3 10 11 10 18 0 7 6 18 3 8 3 15 16 17 3 6 7 3 15 5 3 17 13 14 0 2 4 18 8 0 15 10 4 0 6 6 9 1 7 5 17 3 1 14 2 15 13 16 8 6 14 14 5 2 6 13 2 6 6 13 10 6 1 6 5 5 4 14 16 11 13 3 
    numPartitions is 21
   2 12 1 20 1 1 17 1 8 11 11 2 18 17 13 4 18 17 19 3 3 15 19 6 20 13 9 6 12 8 11 13 7 13 8 17 4 7 5 15 12 13 20 6 9 18 18 13 6 9 9 2 19 12 10 16 19 18 14 12 20 14 13 0 0 12 2 14 2 11 12 14 18 15 15 2 18 4 7 9 15 4 11 11 2 3 4 19 3 1 11 4 14 6 20 6 4 7 1 2 4 2 20 1 0 16 19 19 4 2 17 13 12 2 12 17 12 13 3 11 5 3 0 11 7 3 15 2 15 18 10 16 10 13 8 16 1 8 12 12 18 14 7 20 2 14 3 16 15 2 3 19 10 3 12 9 4 18 11 12 12 20 16 2 10 1 1 3 5 1 6 18 9 10 8 5 19 8 7 17 0 17 10 14 5 1 20 18 6 10 13 19 15 11 1 10 14 11 16 20 6 
    numPartitions is 22
   14 21 10 21 15 5 4 2 5 6 19 6 9 6 15 12 3 8 5 9 21 5 3 16 1 0 11 19 19 2 4 3 3 0 6 13 15 19 12 7 19 6 11 5 9 15 16 5 0 12 11 18 14 7 14 2 2 17 13 18 5 0 2 1 21 9 18 19 11 10 1 19 18 21 2 18 5 19 19 17 0 8 6 10 7 8 9 15 18 19 19 10 11 19 13 13 2 11 10 15 15 3 5 2 19 21 18 17 6 16 18 10 5 1 7 3 5 12 6 21 20 2 13 14 5 19 9 12 19 12 21 0 10 0 21 10 2 9 12 21 19 10 9 19 12 1 15 17 17 1 7 3 18 10 18 10 14 16 12 1 2 8 6 12 8 21 1 15 1 19 5 7 10 18 5 21 16 4 10 2 8 19 0 20 19 0 20 12 5 18 2 5 2 11 11 12 0 0 3 19 13 
    numPartitions is 23
   12 22 12 12 18 8 9 11 9 6 22 6 10 12 18 16 10 0 20 15 14 15 1 2 10 22 18 4 9 2 19 2 22 8 0 6 8 14 19 9 18 14 11 7 17 3 5 1 20 9 10 19 0 13 15 3 17 7 14 5 8 21 21 5 13 7 1 12 20 8 10 19 9 5 20 2 10 0 8 1 18 21 8 2 4 3 16 3 19 22 1 6 7 21 8 9 17 11 16 14 14 7 3 0 0 4 20 14 6 14 19 20 19 6 13 15 19 22 7 5 20 17 8 14 1 15 5 6 16 15 4 4 14 0 20 2 10 18 2 9 11 9 7 16 2 14 7 14 18 17 20 10 3 6 13 0 22 15 11 18 5 1 11 12 8 4 6 18 7 0 4 17 2 18 14 0 6 12 17 10 5 12 6 18 3 16 10 4 14 20 22 4 15 8 7 10 5 8 14 22 20 
    numPartitions is 24
   20 15 4 23 13 1 2 16 11 20 17 14 3 14 19 10 9 20 7 9 21 9 13 12 11 4 15 3 21 8 20 1 19 16 8 5 19 1 2 21 3 22 23 21 9 9 12 1 18 6 15 8 16 9 4 16 4 3 5 0 17 20 16 3 9 9 14 23 17 2 9 5 6 3 0 8 15 7 19 21 12 16 20 20 23 12 1 1 6 7 11 22 17 3 17 3 10 7 22 23 13 5 5 10 15 1 4 19 22 20 2 10 15 17 21 17 3 22 12 17 14 12 9 8 7 21 9 8 3 6 19 22 10 16 11 22 10 23 12 15 3 20 13 11 2 23 15 19 9 11 21 1 22 12 6 0 22 12 20 15 6 8 16 2 10 13 1 15 17 13 15 21 6 22 11 17 4 8 10 14 6 17 10 2 17 22 14 6 21 22 10 13 6 17 1 16 14 20 19 5 3 
    numPartitions is 25
   3 3 3 22 3 0 15 10 0 13 14 2 20 19 21 3 4 5 8 19 3 19 19 18 1 1 3 14 23 8 0 17 15 23 10 3 14 10 9 12 0 20 4 2 8 7 13 3 13 0 7 5 13 6 22 1 9 12 16 4 21 8 22 3 10 15 1 22 15 4 5 9 7 1 9 8 2 21 3 7 11 14 14 13 18 7 14 19 19 0 20 7 9 10 3 22 20 13 23 15 5 21 6 15 0 19 4 9 12 24 7 17 19 18 12 3 23 13 3 17 13 23 23 11 0 9 8 13 3 5 1 20 8 20 12 6 18 23 18 13 20 11 12 18 11 22 13 20 15 3 7 8 9 15 17 19 13 23 10 15 0 24 10 16 11 4 6 17 10 2 18 1 24 12 10 23 6 18 16 19 14 0 17 21 13 12 11 6 13 0 1 21 16 0 20 9 19 21 21 23 3 
    numPartitions is 26
   10 19 18 9 23 25 16 12 1 14 3 12 3 8 5 0 3 10 15 9 7 21 5 14 23 20 15 23 7 24 18 3 21 0 10 11 1 9 4 21 19 0 23 19 3 25 16 11 18 22 11 24 24 11 24 6 8 1 11 20 17 4 12 15 5 19 18 1 23 14 23 9 0 11 4 2 15 25 7 23 12 16 16 8 11 4 19 3 14 5 15 24 5 5 9 13 2 11 4 17 25 21 21 8 21 15 18 3 22 4 8 8 3 5 19 25 15 10 22 1 12 20 1 6 13 21 17 6 5 2 15 0 12 14 23 2 4 3 2 3 3 12 9 23 22 19 19 23 3 9 25 17 14 18 14 4 18 14 0 13 6 22 24 4 20 17 7 11 1 9 7 23 24 16 5 11 24 18 8 22 8 3 18 8 9 22 0 6 7 14 22 17 8 5 7 10 2 0 17 19 11 
    numPartitions is 27
   23 9 4 2 7 1 17 22 23 14 5 20 9 20 1 7 24 11 7 3 6 0 10 24 8 7 0 24 15 11 23 22 4 16 20 26 25 25 26 3 12 4 11 12 24 24 12 13 9 21 0 26 13 3 13 25 19 18 11 3 5 5 10 6 21 21 20 26 23 8 12 20 12 9 21 5 24 19 19 15 18 1 14 2 5 18 1 7 6 16 20 7 2 15 8 0 1 7 7 2 7 11 11 10 3 1 1 13 10 14 23 10 24 2 15 2 15 4 15 17 17 24 3 2 1 21 24 23 9 0 25 10 10 25 11 22 13 26 9 21 12 17 22 14 26 5 24 19 3 8 0 25 13 0 9 24 1 6 14 15 15 23 4 5 19 1 16 9 11 22 6 24 18 16 20 5 1 17 16 11 12 2 4 20 26 25 5 24 18 16 16 10 3 23 13 1 23 2 16 14 0 
    numPartitions is 28
   16 19 8 27 1 1 10 8 15 4 25 2 11 10 27 18 25 24 19 17 17 1 5 20 27 20 23 27 5 8 4 13 7 20 8 17 11 21 26 1 19 6 27 13 9 25 4 13 6 2 23 16 12 5 24 16 12 11 21 12 13 0 20 7 21 5 2 7 9 18 5 21 18 15 8 16 11 11 7 9 8 4 4 4 23 24 25 5 10 15 11 18 21 27 13 27 18 7 22 23 25 9 13 22 7 9 12 19 18 16 10 6 19 9 5 17 19 6 24 25 26 24 21 4 7 17 1 16 15 18 3 2 10 20 15 2 22 15 12 19 11 0 21 27 2 7 3 23 1 23 17 5 10 24 26 16 18 4 4 19 26 20 16 2 10 1 1 3 5 1 27 25 2 10 15 5 12 8 14 10 14 17 10 14 5 22 6 18 13 10 6 5 22 25 1 24 14 4 23 13 27 
    numPartitions is 29
   20 17 16 14 3 2 28 24 7 9 24 27 27 1 13 23 2 28 9 8 27 14 27 9 9 23 10 2 0 24 2 20 28 8 19 5 0 5 21 15 27 6 26 20 19 6 0 16 15 13 14 28 14 1 2 23 27 21 0 16 27 20 15 26 7 14 25 11 19 17 25 8 0 23 1 0 14 21 21 24 14 21 7 14 28 13 7 6 0 16 12 6 27 13 20 18 17 14 0 14 18 16 0 14 15 2 2 14 26 3 17 22 12 17 14 5 5 6 25 16 10 3 26 20 15 7 0 15 23 1 23 3 5 27 27 28 15 22 12 6 3 20 5 18 7 14 11 12 3 25 23 25 18 15 19 22 11 16 7 11 9 7 6 9 8 12 1 6 16 15 12 5 22 19 5 17 10 24 26 1 0 6 1 14 3 10 5 10 26 21 17 24 8 23 13 24 3 18 4 17 8 
    numPartitions is 30
   8 3 28 17 13 25 20 10 5 8 29 2 15 14 1 28 9 20 13 9 3 9 19 18 11 16 3 9 3 8 20 7 25 28 20 23 19 25 14 27 15 10 29 27 3 27 18 13 18 0 27 20 28 21 22 16 4 27 11 24 11 8 22 3 15 15 26 17 5 14 15 29 12 21 24 8 27 1 13 27 6 4 14 8 23 12 19 19 24 25 5 22 29 15 23 27 10 13 28 5 25 11 11 10 15 19 4 19 22 14 2 22 9 23 27 23 3 28 18 17 8 18 3 26 25 9 3 8 3 0 1 10 28 10 17 16 28 23 18 3 15 26 7 23 26 17 3 25 15 23 27 13 4 0 12 24 28 18 20 15 0 14 10 26 16 19 1 27 5 7 3 21 24 22 5 23 16 8 16 14 24 5 22 26 23 22 26 6 3 10 16 1 6 5 25 4 14 26 1 23 3 
    numPartitions is 31
   12 15 5 10 5 22 2 27 18 17 23 24 12 6 5 15 15 15 1 1 11 24 9 18 8 9 12 0 11 23 18 29 9 8 5 30 20 11 30 7 6 20 25 6 26 28 15 24 30 19 9 19 2 18 11 29 26 3 4 24 20 26 18 24 14 5 9 12 30 27 19 10 29 28 27 2 29 15 27 14 26 9 20 23 21 20 8 24 29 6 10 6 14 12 20 23 3 6 29 4 8 12 20 3 21 7 16 23 0 14 1 23 20 18 24 21 29 22 0 29 25 1 1 7 9 15 30 3 25 6 29 5 6 29 3 30 13 12 13 23 20 18 4 27 20 11 0 10 4 27 12 14 15 17 14 30 16 3 15 5 9 11 5 0 13 0 18 16 22 25 21 10 15 4 20 9 19 28 19 17 11 10 2 26 4 19 11 11 22 19 2 22 22 7 15 14 19 19 3 25 18 
    numPartitions is 32
   7 7 30 23 18 29 24 13 19 22 7 22 19 19 14 19 23 2 31 23 5 28 25 12 8 8 11 2 6 21 30 12 27 7 13 9 21 1 20 13 27 31 6 2 15 15 30 7 23 12 8 21 3 8 28 1 0 6 13 6 27 17 12 26 28 25 2 8 5 30 0 2 2 28 3 18 10 0 22 4 18 18 7 24 1 18 31 3 10 11 15 14 24 24 30 24 26 6 13 28 8 25 3 21 15 20 8 26 5 11 11 1 20 5 2 29 3 21 9 14 22 4 27 11 28 10 2 6 18 27 9 17 10 29 6 10 18 19 20 9 29 27 30 2 16 21 26 4 13 7 25 6 19 11 19 12 20 12 14 25 24 5 22 5 6 13 11 9 10 21 6 0 11 1 14 24 4 30 13 13 26 17 29 15 18 26 6 25 29 16 24 0 2 9 14 7 16 12 3 1 19 
    numPartitions is 33
   14 21 10 32 4 16 26 13 5 17 8 17 9 17 4 1 3 8 16 9 21 27 25 27 23 22 0 30 30 2 26 25 25 22 17 2 4 19 23 18 30 28 11 27 9 15 27 16 0 12 0 29 25 18 25 13 13 6 2 18 5 11 13 12 21 9 29 8 11 32 12 8 18 21 24 29 27 19 19 6 0 19 17 32 29 30 31 4 18 19 8 10 11 30 2 24 13 22 10 26 4 14 5 13 30 10 7 28 28 5 29 10 27 23 18 14 27 1 6 32 20 24 24 14 16 30 9 23 30 12 10 22 10 22 32 10 13 20 12 21 30 32 31 8 23 23 15 28 6 23 18 25 7 21 18 21 25 27 23 12 24 8 28 23 19 10 1 15 23 19 27 18 21 7 5 32 16 26 10 2 30 8 22 20 8 22 20 12 27 7 13 16 24 11 22 1 11 11 25 8 24 
    numPartitions is 34
   2 31 12 21 33 25 14 30 17 30 23 10 23 12 9 16 5 8 19 15 1 11 5 12 27 22 29 5 31 4 32 3 25 24 22 29 19 5 12 19 13 22 19 29 7 11 12 15 24 8 33 18 28 23 30 2 30 1 13 20 25 32 18 29 5 15 10 33 25 4 15 13 16 25 2 2 29 17 17 31 32 14 8 32 17 30 11 5 10 3 17 16 13 7 1 15 12 11 4 27 27 33 7 10 11 11 16 31 12 24 14 6 23 19 17 11 9 30 6 19 6 32 23 32 15 13 11 26 11 8 13 2 28 22 9 2 28 21 18 21 9 8 5 29 2 17 33 15 9 13 23 3 2 8 2 18 6 12 6 19 32 12 18 20 8 13 21 21 15 9 31 33 16 12 17 27 22 8 8 18 30 33 14 8 15 22 28 14 11 18 30 23 24 7 33 18 30 30 29 17 15 
    numPartitions is 35
   23 33 8 27 8 15 10 15 15 18 4 2 25 24 6 18 4 10 33 24 3 29 19 13 6 6 23 34 33 8 25 27 0 13 15 3 4 0 19 22 5 20 34 27 23 32 18 13 13 30 2 30 33 26 17 16 19 32 21 19 6 28 27 28 0 5 16 7 30 4 5 14 32 1 29 23 32 11 28 2 1 4 4 18 23 17 4 19 24 15 25 32 14 20 13 27 25 28 8 30 25 16 6 15 0 9 19 19 32 9 17 27 19 23 12 3 33 13 3 32 33 3 28 11 0 24 8 23 8 25 31 30 3 20 22 16 8 8 33 33 25 21 7 13 16 7 3 30 15 23 17 33 24 10 12 9 18 18 25 5 5 34 30 16 31 29 1 17 5 22 13 11 9 17 15 33 26 8 21 24 14 10 17 21 33 22 6 11 13 10 6 26 1 25 15 24 14 11 16 13 13 
    numPartitions is 36
   32 27 4 11 25 1 26 4 23 32 5 2 27 2 19 34 33 20 7 21 33 9 1 24 35 16 27 15 33 20 32 13 31 16 20 17 7 25 26 21 3 22 11 21 33 33 12 13 18 30 27 8 4 21 4 16 28 27 29 12 5 32 28 15 21 21 2 35 5 26 21 29 30 27 12 32 15 19 19 33 0 28 32 20 23 0 1 25 6 7 11 34 29 15 17 27 10 7 34 11 25 29 29 10 3 1 28 31 10 32 14 10 15 29 33 29 15 22 24 17 26 24 21 20 19 21 33 32 27 18 7 10 10 16 11 22 22 35 0 3 3 8 13 23 26 23 15 19 21 35 9 25 22 0 18 24 10 24 32 15 6 32 4 14 10 1 25 27 29 13 15 33 18 34 11 5 28 8 34 2 30 29 22 2 17 34 14 6 9 34 34 1 30 5 13 28 14 20 7 5 27 
    numPartitions is 37
   14 18 10 8 28 25 7 36 28 33 5 0 16 33 6 6 35 24 33 17 2 13 19 16 30 6 33 18 14 8 18 26 19 16 22 2 26 32 7 3 0 20 4 21 27 16 30 26 8 1 4 14 36 6 8 32 21 27 25 28 9 4 19 12 35 20 8 24 23 14 26 1 34 11 1 35 23 14 17 30 23 4 34 8 27 0 23 9 29 31 21 26 25 25 27 26 33 30 5 36 23 4 14 15 31 21 22 0 30 18 11 7 6 34 19 0 13 36 22 0 33 30 23 9 35 8 21 1 32 15 1 17 27 17 11 19 31 19 24 36 27 34 15 2 23 14 28 10 22 21 34 6 26 17 4 20 2 26 22 1 25 21 16 33 16 15 24 20 25 23 28 32 33 2 2 34 27 9 9 11 29 26 35 29 15 35 26 19 36 23 16 27 22 32 32 22 34 22 14 20 2 
    numPartitions is 38
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    numPartitions is 39
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    numPartitions is 40
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    numPartitions is 41
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    numPartitions is 42
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    numPartitions is 43
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    numPartitions is 44
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    numPartitions is 45
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    numPartitions is 46
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    numPartitions is 47
   5 20 40 24 42 21 12 37 10 44 20 39 15 26 29 34 3 24 28 34 46 29 38 12 17 0 40 38 44 39 32 9 2 39 37 22 19 25 30 31 33 5 20 11 4 16 18 35 14 1 16 28 39 28 32 4 25 29 44 18 23 28 24 11 35 23 1 43 45 11 3 39 27 26 11 37 42 12 39 1 10 24 13 6 2 8 35 11 14 22 30 13 28 18 26 40 24 24 16 20 0 6 30 6 25 35 2 15 19 7 32 18 25 38 24 14 9 39 30 10 4 0 40 22 40 42 11 21 2 38 19 19 9 13 4 32 13 3 20 11 2 20 36 43 43 15 24 0 34 27 19 30 39 37 40 42 29 12 19 44 27 10 32 46 19 41 13 28 2 7 15 33 34 37 26 11 33 11 26 34 38 9 7 0 46 3 43 22 0 15 22 44 36 24 34 18 30 15 8 30 25 
    numPartitions is 48
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    numPartitions is 49
   9 47 43 27 36 8 3 8 22 46 46 37 25 45 6 46 4 3 19 3 38 36 26 48 6 41 44 27 5 1 11 48 42 41 1 17 4 28 26 15 33 20 13 20 9 11 25 20 27 16 9 9 40 47 38 37 47 39 35 26 41 21 41 0 21 40 16 21 37 25 19 42 4 8 29 9 46 39 21 16 29 39 46 32 16 10 25 12 38 8 46 11 28 48 6 34 4 14 36 16 32 44 6 8 0 9 33 5 46 2 3 41 33 44 5 24 26 34 38 11 26 24 42 18 21 45 8 44 1 11 38 16 45 34 1 9 43 8 26 19 46 0 42 27 44 0 3 37 1 23 31 26 24 3 19 23 25 39 18 47 26 48 23 9 31 22 1 31 47 29 13 32 16 17 22 26 5 22 14 24 21 45 10 28 33 1 20 32 27 45 41 12 43 11 29 31 14 39 9 34 20 
    numPartitions is 50
   28 3 28 47 3 25 40 10 25 38 39 2 45 44 21 28 29 30 33 19 3 19 19 18 1 26 3 39 23 8 0 17 15 48 10 3 39 35 34 37 25 20 29 27 33 7 38 3 38 0 7 30 38 31 22 26 34 37 41 4 21 8 22 3 35 15 26 47 15 4 5 9 32 1 34 8 27 21 3 7 36 14 14 38 43 32 39 19 44 25 45 32 9 35 3 47 20 13 48 15 5 21 31 40 25 19 4 9 12 24 32 42 19 43 37 3 23 38 28 17 38 48 23 36 25 9 33 38 3 30 1 20 8 20 37 6 18 23 18 13 45 36 37 43 36 47 13 45 15 3 7 33 34 40 42 44 38 48 10 15 0 24 10 16 36 29 31 17 35 27 43 1 24 12 35 23 6 18 16 44 14 25 42 46 13 12 36 6 13 0 26 21 16 25 45 34 44 46 21 23 3 
   
   ```


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