aboutsummaryrefslogblamecommitdiffstats
path: root/consensus/ethash/algorithm.go
blob: d6c871092ed30e54899f39fcfad7b97787f19b84 (plain) (tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820















                                                                                  
              


                         
              
                  
                 



                     
                

                                                
                                                        

                                                
                                  















                                                                                 









































                                                                                                        



                                                                             


                                                                                        
                                     










                                                                                        
                                               


                                         


         






                                                                                 
                                                          
                                                     
                                     








                                                                                

                                                                 
                                                                     
                                         
 

                           






                                                                                                       
           




                                                                
 
                                                                                           
                                  

                                     















                                                                                                                                                                                                       
                                                       
                                                          

                                                   
                              
                                                                             
                                                                         
                                              










                                                                                                                
                                                                                                              
                                                       

                                                      

                 










                                                                                              

 
















                                                                                  
                                                                                 
                                                                                   








                                                                                                 
                           














                                                                    

                           


                                                                  

                                                                   
                                                                     
                                         
 

                           






                                                                                                       
           
 








                                                                          
                                                                         
                                   
                                    









                                                                       
                                                                          

                                                                                 


                                                                                                               




                                                                 
                                                                    




                                                                                    

                                                                                                  
                                                                                                                                                                                         





                                                           




                                                                                                             
                                                                                   









































                                                                                              
                                                          















                                                                                
                                                                                  



                                                         
                                                                     

 

                     

                                                                                
                                    




























































































































































































































































































































































































































                                                                              
                                  






































































































































































































































































































































                                                                             
// Copyright 2017 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.

package ethash

import (
    "encoding/binary"
    "hash"
    "math/big"
    "reflect"
    "runtime"
    "sync"
    "sync/atomic"
    "time"
    "unsafe"

    "github.com/ethereum/go-ethereum/common"
    "github.com/ethereum/go-ethereum/common/bitutil"
    "github.com/ethereum/go-ethereum/crypto"
    "github.com/ethereum/go-ethereum/log"
    "golang.org/x/crypto/sha3"
)

const (
    datasetInitBytes   = 1 << 30 // Bytes in dataset at genesis
    datasetGrowthBytes = 1 << 23 // Dataset growth per epoch
    cacheInitBytes     = 1 << 24 // Bytes in cache at genesis
    cacheGrowthBytes   = 1 << 17 // Cache growth per epoch
    epochLength        = 30000   // Blocks per epoch
    mixBytes           = 128     // Width of mix
    hashBytes          = 64      // Hash length in bytes
    hashWords          = 16      // Number of 32 bit ints in a hash
    datasetParents     = 256     // Number of parents of each dataset element
    cacheRounds        = 3       // Number of rounds in cache production
    loopAccesses       = 64      // Number of accesses in hashimoto loop
)

// cacheSize returns the size of the ethash verification cache that belongs to a certain
// block number.
func cacheSize(block uint64) uint64 {
    epoch := int(block / epochLength)
    if epoch < maxEpoch {
        return cacheSizes[epoch]
    }
    return calcCacheSize(epoch)
}

// calcCacheSize calculates the cache size for epoch. The cache size grows linearly,
// however, we always take the highest prime below the linearly growing threshold in order
// to reduce the risk of accidental regularities leading to cyclic behavior.
func calcCacheSize(epoch int) uint64 {
    size := cacheInitBytes + cacheGrowthBytes*uint64(epoch) - hashBytes
    for !new(big.Int).SetUint64(size / hashBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
        size -= 2 * hashBytes
    }
    return size
}

// datasetSize returns the size of the ethash mining dataset that belongs to a certain
// block number.
func datasetSize(block uint64) uint64 {
    epoch := int(block / epochLength)
    if epoch < maxEpoch {
        return datasetSizes[epoch]
    }
    return calcDatasetSize(epoch)
}

// calcDatasetSize calculates the dataset size for epoch. The dataset size grows linearly,
// however, we always take the highest prime below the linearly growing threshold in order
// to reduce the risk of accidental regularities leading to cyclic behavior.
func calcDatasetSize(epoch int) uint64 {
    size := datasetInitBytes + datasetGrowthBytes*uint64(epoch) - mixBytes
    for !new(big.Int).SetUint64(size / mixBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
        size -= 2 * mixBytes
    }
    return size
}

// hasher is a repetitive hasher allowing the same hash data structures to be
// reused between hash runs instead of requiring new ones to be created.
type hasher func(dest []byte, data []byte)

// makeHasher creates a repetitive hasher, allowing the same hash data structures to
// be reused between hash runs instead of requiring new ones to be created. The returned
// function is not thread safe!
func makeHasher(h hash.Hash) hasher {
    // sha3.state supports Read to get the sum, use it to avoid the overhead of Sum.
    // Read alters the state but we reset the hash before every operation.
    type readerHash interface {
        hash.Hash
        Read([]byte) (int, error)
    }
    rh, ok := h.(readerHash)
    if !ok {
        panic("can't find Read method on hash")
    }
    outputLen := rh.Size()
    return func(dest []byte, data []byte) {
        rh.Reset()
        rh.Write(data)
        rh.Read(dest[:outputLen])
    }
}

// seedHash is the seed to use for generating a verification cache and the mining
// dataset.
func seedHash(block uint64) []byte {
    seed := make([]byte, 32)
    if block < epochLength {
        return seed
    }
    keccak256 := makeHasher(sha3.NewLegacyKeccak256())
    for i := 0; i < int(block/epochLength); i++ {
        keccak256(seed, seed)
    }
    return seed
}

// generateCache creates a verification cache of a given size for an input seed.
// The cache production process involves first sequentially filling up 32 MB of
// memory, then performing two passes of Sergio Demian Lerner's RandMemoHash
// algorithm from Strict Memory Hard Hashing Functions (2014). The output is a
// set of 524288 64-byte values.
// This method places the result into dest in machine byte order.
func generateCache(dest []uint32, epoch uint64, seed []byte) {
    // Print some debug logs to allow analysis on low end devices
    logger := log.New("epoch", epoch)

    start := time.Now()
    defer func() {
        elapsed := time.Since(start)

        logFn := logger.Debug
        if elapsed > 3*time.Second {
            logFn = logger.Info
        }
        logFn("Generated ethash verification cache", "elapsed", common.PrettyDuration(elapsed))
    }()
    // Convert our destination slice to a byte buffer
    header := *(*reflect.SliceHeader)(unsafe.Pointer(&dest))
    header.Len *= 4
    header.Cap *= 4
    cache := *(*[]byte)(unsafe.Pointer(&header))

    // Calculate the number of theoretical rows (we'll store in one buffer nonetheless)
    size := uint64(len(cache))
    rows := int(size) / hashBytes

    // Start a monitoring goroutine to report progress on low end devices
    var progress uint32

    done := make(chan struct{})
    defer close(done)

    go func() {
        for {
            select {
            case <-done:
                return
            case <-time.After(3 * time.Second):
                logger.Info("Generating ethash verification cache", "percentage", atomic.LoadUint32(&progress)*100/uint32(rows)/4, "elapsed", common.PrettyDuration(time.Since(start)))
            }
        }
    }()
    // Create a hasher to reuse between invocations
    keccak512 := makeHasher(sha3.NewLegacyKeccak512())

    // Sequentially produce the initial dataset
    keccak512(cache, seed)
    for offset := uint64(hashBytes); offset < size; offset += hashBytes {
        keccak512(cache[offset:], cache[offset-hashBytes:offset])
        atomic.AddUint32(&progress, 1)
    }
    // Use a low-round version of randmemohash
    temp := make([]byte, hashBytes)

    for i := 0; i < cacheRounds; i++ {
        for j := 0; j < rows; j++ {
            var (
                srcOff = ((j - 1 + rows) % rows) * hashBytes
                dstOff = j * hashBytes
                xorOff = (binary.LittleEndian.Uint32(cache[dstOff:]) % uint32(rows)) * hashBytes
            )
            bitutil.XORBytes(temp, cache[srcOff:srcOff+hashBytes], cache[xorOff:xorOff+hashBytes])
            keccak512(cache[dstOff:], temp)

            atomic.AddUint32(&progress, 1)
        }
    }
    // Swap the byte order on big endian systems and return
    if !isLittleEndian() {
        swap(cache)
    }
}

// swap changes the byte order of the buffer assuming a uint32 representation.
func swap(buffer []byte) {
    for i := 0; i < len(buffer); i += 4 {
        binary.BigEndian.PutUint32(buffer[i:], binary.LittleEndian.Uint32(buffer[i:]))
    }
}

// fnv is an algorithm inspired by the FNV hash, which in some cases is used as
// a non-associative substitute for XOR. Note that we multiply the prime with
// the full 32-bit input, in contrast with the FNV-1 spec which multiplies the
// prime with one byte (octet) in turn.
func fnv(a, b uint32) uint32 {
    return a*0x01000193 ^ b
}

// fnvHash mixes in data into mix using the ethash fnv method.
func fnvHash(mix []uint32, data []uint32) {
    for i := 0; i < len(mix); i++ {
        mix[i] = mix[i]*0x01000193 ^ data[i]
    }
}

// generateDatasetItem combines data from 256 pseudorandomly selected cache nodes,
// and hashes that to compute a single dataset node.
func generateDatasetItem(cache []uint32, index uint32, keccak512 hasher) []byte {
    // Calculate the number of theoretical rows (we use one buffer nonetheless)
    rows := uint32(len(cache) / hashWords)

    // Initialize the mix
    mix := make([]byte, hashBytes)

    binary.LittleEndian.PutUint32(mix, cache[(index%rows)*hashWords]^index)
    for i := 1; i < hashWords; i++ {
        binary.LittleEndian.PutUint32(mix[i*4:], cache[(index%rows)*hashWords+uint32(i)])
    }
    keccak512(mix, mix)

    // Convert the mix to uint32s to avoid constant bit shifting
    intMix := make([]uint32, hashWords)
    for i := 0; i < len(intMix); i++ {
        intMix[i] = binary.LittleEndian.Uint32(mix[i*4:])
    }
    // fnv it with a lot of random cache nodes based on index
    for i := uint32(0); i < datasetParents; i++ {
        parent := fnv(index^i, intMix[i%16]) % rows
        fnvHash(intMix, cache[parent*hashWords:])
    }
    // Flatten the uint32 mix into a binary one and return
    for i, val := range intMix {
        binary.LittleEndian.PutUint32(mix[i*4:], val)
    }
    keccak512(mix, mix)
    return mix
}

// generateDataset generates the entire ethash dataset for mining.
// This method places the result into dest in machine byte order.
func generateDataset(dest []uint32, epoch uint64, cache []uint32) {
    // Print some debug logs to allow analysis on low end devices
    logger := log.New("epoch", epoch)

    start := time.Now()
    defer func() {
        elapsed := time.Since(start)

        logFn := logger.Debug
        if elapsed > 3*time.Second {
            logFn = logger.Info
        }
        logFn("Generated ethash verification cache", "elapsed", common.PrettyDuration(elapsed))
    }()

    // Figure out whether the bytes need to be swapped for the machine
    swapped := !isLittleEndian()

    // Convert our destination slice to a byte buffer
    header := *(*reflect.SliceHeader)(unsafe.Pointer(&dest))
    header.Len *= 4
    header.Cap *= 4
    dataset := *(*[]byte)(unsafe.Pointer(&header))

    // Generate the dataset on many goroutines since it takes a while
    threads := runtime.NumCPU()
    size := uint64(len(dataset))

    var pend sync.WaitGroup
    pend.Add(threads)

    var progress uint32
    for i := 0; i < threads; i++ {
        go func(id int) {
            defer pend.Done()

            // Create a hasher to reuse between invocations
            keccak512 := makeHasher(sha3.NewLegacyKeccak512())

            // Calculate the data segment this thread should generate
            batch := uint32((size + hashBytes*uint64(threads) - 1) / (hashBytes * uint64(threads)))
            first := uint32(id) * batch
            limit := first + batch
            if limit > uint32(size/hashBytes) {
                limit = uint32(size / hashBytes)
            }
            // Calculate the dataset segment
            percent := uint32(size / hashBytes / 100)
            for index := first; index < limit; index++ {
                item := generateDatasetItem(cache, index, keccak512)
                if swapped {
                    swap(item)
                }
                copy(dataset[index*hashBytes:], item)

                if status := atomic.AddUint32(&progress, 1); status%percent == 0 {
                    logger.Info("Generating DAG in progress", "percentage", uint64(status*100)/(size/hashBytes), "elapsed", common.PrettyDuration(time.Since(start)))
                }
            }
        }(i)
    }
    // Wait for all the generators to finish and return
    pend.Wait()
}

// hashimoto aggregates data from the full dataset in order to produce our final
// value for a particular header hash and nonce.
func hashimoto(hash []byte, nonce uint64, size uint64, lookup func(index uint32) []uint32) ([]byte, []byte) {
    // Calculate the number of theoretical rows (we use one buffer nonetheless)
    rows := uint32(size / mixBytes)

    // Combine header+nonce into a 64 byte seed
    seed := make([]byte, 40)
    copy(seed, hash)
    binary.LittleEndian.PutUint64(seed[32:], nonce)

    seed = crypto.Keccak512(seed)
    seedHead := binary.LittleEndian.Uint32(seed)

    // Start the mix with replicated seed
    mix := make([]uint32, mixBytes/4)
    for i := 0; i < len(mix); i++ {
        mix[i] = binary.LittleEndian.Uint32(seed[i%16*4:])
    }
    // Mix in random dataset nodes
    temp := make([]uint32, len(mix))

    for i := 0; i < loopAccesses; i++ {
        parent := fnv(uint32(i)^seedHead, mix[i%len(mix)]) % rows
        for j := uint32(0); j < mixBytes/hashBytes; j++ {
            copy(temp[j*hashWords:], lookup(2*parent+j))
        }
        fnvHash(mix, temp)
    }
    // Compress mix
    for i := 0; i < len(mix); i += 4 {
        mix[i/4] = fnv(fnv(fnv(mix[i], mix[i+1]), mix[i+2]), mix[i+3])
    }
    mix = mix[:len(mix)/4]

    digest := make([]byte, common.HashLength)
    for i, val := range mix {
        binary.LittleEndian.PutUint32(digest[i*4:], val)
    }
    return digest, crypto.Keccak256(append(seed, digest...))
}

// hashimotoLight aggregates data from the full dataset (using only a small
// in-memory cache) in order to produce our final value for a particular header
// hash and nonce.
func hashimotoLight(size uint64, cache []uint32, hash []byte, nonce uint64) ([]byte, []byte) {
    keccak512 := makeHasher(sha3.NewLegacyKeccak512())

    lookup := func(index uint32) []uint32 {
        rawData := generateDatasetItem(cache, index, keccak512)

        data := make([]uint32, len(rawData)/4)
        for i := 0; i < len(data); i++ {
            data[i] = binary.LittleEndian.Uint32(rawData[i*4:])
        }
        return data
    }
    return hashimoto(hash, nonce, size, lookup)
}

// hashimotoFull aggregates data from the full dataset (using the full in-memory
// dataset) in order to produce our final value for a particular header hash and
// nonce.
func hashimotoFull(dataset []uint32, hash []byte, nonce uint64) ([]byte, []byte) {
    lookup := func(index uint32) []uint32 {
        offset := index * hashWords
        return dataset[offset : offset+hashWords]
    }
    return hashimoto(hash, nonce, uint64(len(dataset))*4, lookup)
}

const maxEpoch = 2048

// datasetSizes is a lookup table for the ethash dataset size for the first 2048
// epochs (i.e. 61440000 blocks).
var datasetSizes = [maxEpoch]uint64{
    1073739904, 1082130304, 1090514816, 1098906752, 1107293056,
    1115684224, 1124070016, 1132461952, 1140849536, 1149232768,
    1157627776, 1166013824, 1174404736, 1182786944, 1191180416,
    1199568512, 1207958912, 1216345216, 1224732032, 1233124736,
    1241513344, 1249902464, 1258290304, 1266673792, 1275067264,
    1283453312, 1291844992, 1300234112, 1308619904, 1317010048,
    1325397376, 1333787776, 1342176128, 1350561664, 1358954368,
    1367339392, 1375731584, 1384118144, 1392507008, 1400897408,
    1409284736, 1417673344, 1426062464, 1434451072, 1442839168,
    1451229056, 1459615616, 1468006016, 1476394112, 1484782976,
    1493171584, 1501559168, 1509948032, 1518337664, 1526726528,
    1535114624, 1543503488, 1551892096, 1560278656, 1568669056,
    1577056384, 1585446272, 1593831296, 1602219392, 1610610304,
    1619000192, 1627386752, 1635773824, 1644164224, 1652555648,
    1660943488, 1669332608, 1677721216, 1686109312, 1694497664,
    1702886272, 1711274624, 1719661184, 1728047744, 1736434816,
    1744829056, 1753218944, 1761606272, 1769995904, 1778382464,
    1786772864, 1795157888, 1803550592, 1811937664, 1820327552,
    1828711552, 1837102976, 1845488768, 1853879936, 1862269312,
    1870656896, 1879048064, 1887431552, 1895825024, 1904212096,
    1912601216, 1920988544, 1929379456, 1937765504, 1946156672,
    1954543232, 1962932096, 1971321728, 1979707264, 1988093056,
    1996487552, 2004874624, 2013262208, 2021653888, 2030039936,
    2038430848, 2046819968, 2055208576, 2063596672, 2071981952,
    2080373632, 2088762752, 2097149056, 2105539712, 2113928576,
    2122315136, 2130700672, 2139092608, 2147483264, 2155872128,
    2164257664, 2172642176, 2181035392, 2189426048, 2197814912,
    2206203008, 2214587264, 2222979712, 2231367808, 2239758208,
    2248145024, 2256527744, 2264922752, 2273312128, 2281701248,
    2290086272, 2298476672, 2306867072, 2315251072, 2323639168,
    2332032128, 2340420224, 2348808064, 2357196416, 2365580416,
    2373966976, 2382363008, 2390748544, 2399139968, 2407530368,
    2415918976, 2424307328, 2432695424, 2441084288, 2449472384,
    2457861248, 2466247808, 2474637184, 2483026816, 2491414144,
    2499803776, 2508191872, 2516582272, 2524970368, 2533359232,
    2541743488, 2550134144, 2558525056, 2566913408, 2575301504,
    2583686528, 2592073856, 2600467328, 2608856192, 2617240448,
    2625631616, 2634022016, 2642407552, 2650796416, 2659188352,
    2667574912, 2675965312, 2684352896, 2692738688, 2701130624,
    2709518464, 2717907328, 2726293376, 2734685056, 2743073152,
    2751462016, 2759851648, 2768232832, 2776625536, 2785017728,
    2793401984, 2801794432, 2810182016, 2818571648, 2826959488,
    2835349376, 2843734144, 2852121472, 2860514432, 2868900992,
    2877286784, 2885676928, 2894069632, 2902451584, 2910843008,
    2919234688, 2927622784, 2936011648, 2944400768, 2952789376,
    2961177728, 2969565568, 2977951616, 2986338944, 2994731392,
    3003120256, 3011508352, 3019895936, 3028287104, 3036675968,
    3045063808, 3053452928, 3061837696, 3070228352, 3078615424,
    3087003776, 3095394944, 3103782272, 3112173184, 3120562048,
    3128944768, 3137339264, 3145725056, 3154109312, 3162505088,
    3170893184, 3179280256, 3187669376, 3196056704, 3204445568,
    3212836736, 3221224064, 3229612928, 3238002304, 3246391168,
    3254778496, 3263165824, 3271556224, 3279944576, 3288332416,
    3296719232, 3305110912, 3313500032, 3321887104, 3330273152,
    3338658944, 3347053184, 3355440512, 3363827072, 3372220288,
    3380608384, 3388997504, 3397384576, 3405774208, 3414163072,
    3422551936, 3430937984, 3439328384, 3447714176, 3456104576,
    3464493952, 3472883584, 3481268864, 3489655168, 3498048896,
    3506434432, 3514826368, 3523213952, 3531603584, 3539987072,
    3548380288, 3556763264, 3565157248, 3573545344, 3581934464,
    3590324096, 3598712704, 3607098752, 3615488384, 3623877248,
    3632265856, 3640646528, 3649043584, 3657430144, 3665821568,
    3674207872, 3682597504, 3690984832, 3699367808, 3707764352,
    3716152448, 3724541056, 3732925568, 3741318016, 3749706368,
    3758091136, 3766481536, 3774872704, 3783260032, 3791650432,
    3800036224, 3808427648, 3816815488, 3825204608, 3833592704,
    3841981568, 3850370432, 3858755968, 3867147904, 3875536256,
    3883920512, 3892313728, 3900702592, 3909087872, 3917478784,
    3925868416, 3934256512, 3942645376, 3951032192, 3959422336,
    3967809152, 3976200064, 3984588416, 3992974976, 4001363584,
    4009751168, 4018141312, 4026530432, 4034911616, 4043308928,
    4051695488, 4060084352, 4068472448, 4076862848, 4085249408,
    4093640576, 4102028416, 4110413696, 4118805632, 4127194496,
    4135583104, 4143971968, 4152360832, 4160746112, 4169135744,
    4177525888, 4185912704, 4194303616, 4202691968, 4211076736,
    4219463552, 4227855488, 4236246656, 4244633728, 4253022848,
    4261412224, 4269799808, 4278184832, 4286578048, 4294962304,
    4303349632, 4311743104, 4320130432, 4328521088, 4336909184,
    4345295488, 4353687424, 4362073472, 4370458496, 4378852736,
    4387238528, 4395630208, 4404019072, 4412407424, 4420790656,
    4429182848, 4437571456, 4445962112, 4454344064, 4462738048,
    4471119232, 4479516544, 4487904128, 4496289664, 4504682368,
    4513068416, 4521459584, 4529846144, 4538232704, 4546619776,
    4555010176, 4563402112, 4571790208, 4580174464, 4588567936,
    4596957056, 4605344896, 4613734016, 4622119808, 4630511488,
    4638898816, 4647287936, 4655675264, 4664065664, 4672451968,
    4680842624, 4689231488, 4697620352, 4706007424, 4714397056,
    4722786176, 4731173248, 4739562368, 4747951744, 4756340608,
    4764727936, 4773114496, 4781504384, 4789894784, 4798283648,
    4806667648, 4815059584, 4823449472, 4831835776, 4840226176,
    4848612224, 4857003392, 4865391488, 4873780096, 4882169728,
    4890557312, 4898946944, 4907333248, 4915722368, 4924110976,
    4932499328, 4940889728, 4949276032, 4957666432, 4966054784,
    4974438016, 4982831488, 4991221376, 4999607168, 5007998848,
    5016386432, 5024763776, 5033164672, 5041544576, 5049941888,
    5058329728, 5066717056, 5075107456, 5083494272, 5091883904,
    5100273536, 5108662144, 5117048192, 5125436032, 5133827456,
    5142215296, 5150605184, 5158993024, 5167382144, 5175769472,
    5184157568, 5192543872, 5200936064, 5209324928, 5217711232,
    5226102656, 5234490496, 5242877312, 5251263872, 5259654016,
    5268040832, 5276434304, 5284819328, 5293209728, 5301598592,
    5309986688, 5318374784, 5326764416, 5335151488, 5343542144,
    5351929472, 5360319872, 5368706944, 5377096576, 5385484928,
    5393871232, 5402263424, 5410650496, 5419040384, 5427426944,
    5435816576, 5444205952, 5452594816, 5460981376, 5469367936,
    5477760896, 5486148736, 5494536832, 5502925952, 5511315328,
    5519703424, 5528089984, 5536481152, 5544869504, 5553256064,
    5561645696, 5570032768, 5578423936, 5586811264, 5595193216,
    5603585408, 5611972736, 5620366208, 5628750464, 5637143936,
    5645528192, 5653921408, 5662310272, 5670694784, 5679082624,
    5687474048, 5695864448, 5704251008, 5712641408, 5721030272,
    5729416832, 5737806208, 5746194304, 5754583936, 5762969984,
    5771358592, 5779748224, 5788137856, 5796527488, 5804911232,
    5813300608, 5821692544, 5830082176, 5838468992, 5846855552,
    5855247488, 5863636096, 5872024448, 5880411008, 5888799872,
    5897186432, 5905576832, 5913966976, 5922352768, 5930744704,
    5939132288, 5947522432, 5955911296, 5964299392, 5972688256,
    5981074304, 5989465472, 5997851008, 6006241408, 6014627968,
    6023015552, 6031408256, 6039796096, 6048185216, 6056574848,
    6064963456, 6073351808, 6081736064, 6090128768, 6098517632,
    6106906496, 6115289216, 6123680896, 6132070016, 6140459648,
    6148849024, 6157237376, 6165624704, 6174009728, 6182403712,
    6190792064, 6199176064, 6207569792, 6215952256, 6224345216,
    6232732544, 6241124224, 6249510272, 6257899136, 6266287744,
    6274676864, 6283065728, 6291454336, 6299843456, 6308232064,
    6316620928, 6325006208, 6333395584, 6341784704, 6350174848,
    6358562176, 6366951296, 6375337856, 6383729536, 6392119168,
    6400504192, 6408895616, 6417283456, 6425673344, 6434059136,
    6442444672, 6450837376, 6459223424, 6467613056, 6476004224,
    6484393088, 6492781952, 6501170048, 6509555072, 6517947008,
    6526336384, 6534725504, 6543112832, 6551500672, 6559888768,
    6568278656, 6576662912, 6585055616, 6593443456, 6601834112,
    6610219648, 6618610304, 6626999168, 6635385472, 6643777408,
    6652164224, 6660552832, 6668941952, 6677330048, 6685719424,
    6694107776, 6702493568, 6710882176, 6719274112, 6727662976,
    6736052096, 6744437632, 6752825984, 6761213824, 6769604224,
    6777993856, 6786383488, 6794770816, 6803158144, 6811549312,
    6819937664, 6828326528, 6836706176, 6845101696, 6853491328,
    6861880448, 6870269312, 6878655104, 6887046272, 6895433344,
    6903822208, 6912212864, 6920596864, 6928988288, 6937377152,
    6945764992, 6954149248, 6962544256, 6970928768, 6979317376,
    6987709312, 6996093824, 7004487296, 7012875392, 7021258624,
    7029652352, 7038038912, 7046427776, 7054818944, 7063207808,
    7071595136, 7079980928, 7088372608, 7096759424, 7105149824,
    7113536896, 7121928064, 7130315392, 7138699648, 7147092352,
    7155479168, 7163865728, 7172249984, 7180648064, 7189036672,
    7197424768, 7205810816, 7214196608, 7222589824, 7230975104,
    7239367552, 7247755904, 7256145536, 7264533376, 7272921472,
    7281308032, 7289694848, 7298088832, 7306471808, 7314864512,
    7323253888, 7331643008, 7340029568, 7348419712, 7356808832,
    7365196672, 7373585792, 7381973888, 7390362752, 7398750592,
    7407138944, 7415528576, 7423915648, 7432302208, 7440690304,
    7449080192, 7457472128, 7465860992, 7474249088, 7482635648,
    7491023744, 7499412608, 7507803008, 7516192384, 7524579968,
    7532967296, 7541358464, 7549745792, 7558134656, 7566524032,
    7574912896, 7583300992, 7591690112, 7600075136, 7608466816,
    7616854912, 7625244544, 7633629824, 7642020992, 7650410368,
    7658794112, 7667187328, 7675574912, 7683961984, 7692349568,
    7700739712, 7709130368, 7717519232, 7725905536, 7734295424,
    7742683264, 7751069056, 7759457408, 7767849088, 7776238208,
    7784626816, 7793014912, 7801405312, 7809792128, 7818179968,
    7826571136, 7834957184, 7843347328, 7851732352, 7860124544,
    7868512384, 7876902016, 7885287808, 7893679744, 7902067072,
    7910455936, 7918844288, 7927230848, 7935622784, 7944009344,
    7952400256, 7960786048, 7969176704, 7977565312, 7985953408,
    7994339968, 8002730368, 8011119488, 8019508096, 8027896192,
    8036285056, 8044674688, 8053062272, 8061448832, 8069838464,
    8078227328, 8086616704, 8095006592, 8103393664, 8111783552,
    8120171392, 8128560256, 8136949376, 8145336704, 8153726848,
    8162114944, 8170503296, 8178891904, 8187280768, 8195669632,
    8204058496, 8212444544, 8220834176, 8229222272, 8237612672,
    8246000768, 8254389376, 8262775168, 8271167104, 8279553664,
    8287944064, 8296333184, 8304715136, 8313108352, 8321497984,
    8329885568, 8338274432, 8346663296, 8355052928, 8363441536,
    8371828352, 8380217984, 8388606592, 8396996224, 8405384576,
    8413772672, 8422161536, 8430549376, 8438939008, 8447326592,
    8455715456, 8464104832, 8472492928, 8480882048, 8489270656,
    8497659776, 8506045312, 8514434944, 8522823808, 8531208832,
    8539602304, 8547990656, 8556378752, 8564768384, 8573154176,
    8581542784, 8589933952, 8598322816, 8606705024, 8615099264,
    8623487872, 8631876992, 8640264064, 8648653952, 8657040256,
    8665430656, 8673820544, 8682209152, 8690592128, 8698977152,
    8707374464, 8715763328, 8724151424, 8732540032, 8740928384,
    8749315712, 8757704576, 8766089344, 8774480768, 8782871936,
    8791260032, 8799645824, 8808034432, 8816426368, 8824812928,
    8833199488, 8841591424, 8849976448, 8858366336, 8866757248,
    8875147136, 8883532928, 8891923328, 8900306816, 8908700288,
    8917088384, 8925478784, 8933867392, 8942250368, 8950644608,
    8959032704, 8967420544, 8975809664, 8984197504, 8992584064,
    9000976256, 9009362048, 9017752448, 9026141312, 9034530688,
    9042917504, 9051307904, 9059694208, 9068084864, 9076471424,
    9084861824, 9093250688, 9101638528, 9110027648, 9118416512,
    9126803584, 9135188096, 9143581312, 9151969664, 9160356224,
    9168747136, 9177134464, 9185525632, 9193910144, 9202302848,
    9210690688, 9219079552, 9227465344, 9235854464, 9244244864,
    9252633472, 9261021824, 9269411456, 9277799296, 9286188928,
    9294574208, 9302965888, 9311351936, 9319740032, 9328131968,
    9336516736, 9344907392, 9353296768, 9361685888, 9370074752,
    9378463616, 9386849408, 9395239808, 9403629184, 9412016512,
    9420405376, 9428795008, 9437181568, 9445570688, 9453960832,
    9462346624, 9470738048, 9479121536, 9487515008, 9495903616,
    9504289664, 9512678528, 9521067904, 9529456256, 9537843584,
    9546233728, 9554621312, 9563011456, 9571398784, 9579788672,
    9588178304, 9596567168, 9604954496, 9613343104, 9621732992,
    9630121856, 9638508416, 9646898816, 9655283584, 9663675776,
    9672061312, 9680449664, 9688840064, 9697230464, 9705617536,
    9714003584, 9722393984, 9730772608, 9739172224, 9747561088,
    9755945344, 9764338816, 9772726144, 9781116544, 9789503872,
    9797892992, 9806282624, 9814670464, 9823056512, 9831439232,
    9839833984, 9848224384, 9856613504, 9865000576, 9873391232,
    9881772416, 9890162816, 9898556288, 9906940544, 9915333248,
    9923721088, 9932108672, 9940496512, 9948888448, 9957276544,
    9965666176, 9974048384, 9982441088, 9990830464, 9999219584,
    10007602816, 10015996544, 10024385152, 10032774016, 10041163648,
    10049548928, 10057940096, 10066329472, 10074717824, 10083105152,
    10091495296, 10099878784, 10108272256, 10116660608, 10125049216,
    10133437312, 10141825664, 10150213504, 10158601088, 10166991232,
    10175378816, 10183766144, 10192157312, 10200545408, 10208935552,
    10217322112, 10225712768, 10234099328, 10242489472, 10250876032,
    10259264896, 10267656064, 10276042624, 10284429184, 10292820352,
    10301209472, 10309598848, 10317987712, 10326375296, 10334763392,
    10343153536, 10351541632, 10359930752, 10368318592, 10376707456,
    10385096576, 10393484672, 10401867136, 10410262144, 10418647424,
    10427039104, 10435425664, 10443810176, 10452203648, 10460589952,
    10468982144, 10477369472, 10485759104, 10494147712, 10502533504,
    10510923392, 10519313536, 10527702656, 10536091264, 10544478592,
    10552867712, 10561255808, 10569642368, 10578032768, 10586423168,
    10594805632, 10603200128, 10611588992, 10619976064, 10628361344,
    10636754048, 10645143424, 10653531776, 10661920384, 10670307968,
    10678696832, 10687086464, 10695475072, 10703863168, 10712246144,
    10720639616, 10729026688, 10737414784, 10745806208, 10754190976,
    10762581376, 10770971264, 10779356288, 10787747456, 10796135552,
    10804525184, 10812915584, 10821301888, 10829692288, 10838078336,
    10846469248, 10854858368, 10863247232, 10871631488, 10880023424,
    10888412032, 10896799616, 10905188992, 10913574016, 10921964672,
    10930352768, 10938742912, 10947132544, 10955518592, 10963909504,
    10972298368, 10980687488, 10989074816, 10997462912, 11005851776,
    11014241152, 11022627712, 11031017344, 11039403904, 11047793024,
    11056184704, 11064570752, 11072960896, 11081343872, 11089737856,
    11098128256, 11106514816, 11114904448, 11123293568, 11131680128,
    11140065152, 11148458368, 11156845696, 11165236864, 11173624192,
    11182013824, 11190402688, 11198790784, 11207179136, 11215568768,
    11223957376, 11232345728, 11240734592, 11249122688, 11257511296,
    11265899648, 11274285952, 11282675584, 11291065472, 11299452544,
    11307842432, 11316231296, 11324616832, 11333009024, 11341395584,
    11349782656, 11358172288, 11366560384, 11374950016, 11383339648,
    11391721856, 11400117376, 11408504192, 11416893568, 11425283456,
    11433671552, 11442061184, 11450444672, 11458837888, 11467226752,
    11475611776, 11484003968, 11492392064, 11500780672, 11509169024,
    11517550976, 11525944448, 11534335616, 11542724224, 11551111808,
    11559500672, 11567890304, 11576277376, 11584667008, 11593056128,
    11601443456, 11609830016, 11618221952, 11626607488, 11634995072,
    11643387776, 11651775104, 11660161664, 11668552576, 11676940928,
    11685330304, 11693718656, 11702106496, 11710496128, 11718882688,
    11727273088, 11735660416, 11744050048, 11752437376, 11760824704,
    11769216128, 11777604736, 11785991296, 11794381952, 11802770048,
    11811157888, 11819548544, 11827932544, 11836324736, 11844713344,
    11853100928, 11861486464, 11869879936, 11878268032, 11886656896,
    11895044992, 11903433088, 11911822976, 11920210816, 11928600448,
    11936987264, 11945375872, 11953761152, 11962151296, 11970543488,
    11978928512, 11987320448, 11995708288, 12004095104, 12012486272,
    12020875136, 12029255552, 12037652096, 12046039168, 12054429568,
    12062813824, 12071206528, 12079594624, 12087983744, 12096371072,
    12104759936, 12113147264, 12121534592, 12129924992, 12138314624,
    12146703232, 12155091584, 12163481216, 12171864704, 12180255872,
    12188643968, 12197034112, 12205424512, 12213811328, 12222199424,
    12230590336, 12238977664, 12247365248, 12255755392, 12264143488,
    12272531584, 12280920448, 12289309568, 12297694592, 12306086528,
    12314475392, 12322865024, 12331253632, 12339640448, 12348029312,
    12356418944, 12364805248, 12373196672, 12381580928, 12389969024,
    12398357632, 12406750592, 12415138432, 12423527552, 12431916416,
    12440304512, 12448692352, 12457081216, 12465467776, 12473859968,
    12482245504, 12490636672, 12499025536, 12507411584, 12515801728,
    12524190592, 12532577152, 12540966272, 12549354368, 12557743232,
    12566129536, 12574523264, 12582911872, 12591299456, 12599688064,
    12608074624, 12616463488, 12624845696, 12633239936, 12641631616,
    12650019968, 12658407296, 12666795136, 12675183232, 12683574656,
    12691960192, 12700350592, 12708740224, 12717128576, 12725515904,
    12733906816, 12742295168, 12750680192, 12759071872, 12767460736,
    12775848832, 12784236928, 12792626816, 12801014656, 12809404288,
    12817789312, 12826181504, 12834568832, 12842954624, 12851345792,
    12859732352, 12868122496, 12876512128, 12884901248, 12893289088,
    12901672832, 12910067584, 12918455168, 12926842496, 12935232896,
    12943620736, 12952009856, 12960396928, 12968786816, 12977176192,
    12985563776, 12993951104, 13002341504, 13010730368, 13019115392,
    13027506304, 13035895168, 13044272512, 13052673152, 13061062528,
    13069446272, 13077838976, 13086227072, 13094613632, 13103000192,
    13111393664, 13119782528, 13128157568, 13136559232, 13144945024,
    13153329536, 13161724288, 13170111872, 13178502784, 13186884736,
    13195279744, 13203667072, 13212057472, 13220445824, 13228832128,
    13237221248, 13245610624, 13254000512, 13262388352, 13270777472,
    13279166336, 13287553408, 13295943296, 13304331904, 13312719488,
    13321108096, 13329494656, 13337885824, 13346274944, 13354663808,
    13363051136, 13371439232, 13379825024, 13388210816, 13396605056,
    13404995456, 13413380224, 13421771392, 13430159744, 13438546048,
    13446937216, 13455326848, 13463708288, 13472103808, 13480492672,
    13488875648, 13497269888, 13505657728, 13514045312, 13522435712,
    13530824576, 13539210112, 13547599232, 13555989376, 13564379008,
    13572766336, 13581154432, 13589544832, 13597932928, 13606320512,
    13614710656, 13623097472, 13631477632, 13639874944, 13648264064,
    13656652928, 13665041792, 13673430656, 13681818496, 13690207616,
    13698595712, 13706982272, 13715373184, 13723762048, 13732150144,
    13740536704, 13748926592, 13757316224, 13765700992, 13774090112,
    13782477952, 13790869376, 13799259008, 13807647872, 13816036736,
    13824425344, 13832814208, 13841202304, 13849591424, 13857978752,
    13866368896, 13874754688, 13883145344, 13891533184, 13899919232,
    13908311168, 13916692096, 13925085056, 13933473152, 13941866368,
    13950253696, 13958643584, 13967032192, 13975417216, 13983807616,
    13992197504, 14000582272, 14008973696, 14017363072, 14025752192,
    14034137984, 14042528384, 14050918016, 14059301504, 14067691648,
    14076083584, 14084470144, 14092852352, 14101249664, 14109635968,
    14118024832, 14126407552, 14134804352, 14143188608, 14151577984,
    14159968384, 14168357248, 14176741504, 14185127296, 14193521024,
    14201911424, 14210301824, 14218685056, 14227067264, 14235467392,
    14243855488, 14252243072, 14260630144, 14269021568, 14277409408,
    14285799296, 14294187904, 14302571392, 14310961792, 14319353728,
    14327738752, 14336130944, 14344518784, 14352906368, 14361296512,
    14369685376, 14378071424, 14386462592, 14394848128, 14403230848,
    14411627392, 14420013952, 14428402304, 14436793472, 14445181568,
    14453569664, 14461959808, 14470347904, 14478737024, 14487122816,
    14495511424, 14503901824, 14512291712, 14520677504, 14529064832,
    14537456768, 14545845632, 14554234496, 14562618496, 14571011456,
    14579398784, 14587789184, 14596172672, 14604564608, 14612953984,
    14621341312, 14629724288, 14638120832, 14646503296, 14654897536,
    14663284864, 14671675264, 14680061056, 14688447616, 14696835968,
    14705228416, 14713616768, 14722003328, 14730392192, 14738784128,
    14747172736, 14755561088, 14763947648, 14772336512, 14780725376,
    14789110144, 14797499776, 14805892736, 14814276992, 14822670208,
    14831056256, 14839444352, 14847836032, 14856222848, 14864612992,
    14872997504, 14881388672, 14889775744, 14898165376, 14906553472,
    14914944896, 14923329664, 14931721856, 14940109696, 14948497024,
    14956887424, 14965276544, 14973663616, 14982053248, 14990439808,
    14998830976, 15007216768, 15015605888, 15023995264, 15032385152,
    15040768384, 15049154944, 15057549184, 15065939072, 15074328448,
    15082715008, 15091104128, 15099493504, 15107879296, 15116269184,
    15124659584, 15133042304, 15141431936, 15149824384, 15158214272,
    15166602368, 15174991232, 15183378304, 15191760512, 15200154496,
    15208542592, 15216931712, 15225323392, 15233708416, 15242098048,
    15250489216, 15258875264, 15267265408, 15275654528, 15284043136,
    15292431488, 15300819584, 15309208192, 15317596544, 15325986176,
    15334374784, 15342763648, 15351151744, 15359540608, 15367929728,
    15376318336, 15384706432, 15393092992, 15401481856, 15409869952,
    15418258816, 15426649984, 15435037568, 15443425664, 15451815296,
    15460203392, 15468589184, 15476979328, 15485369216, 15493755776,
    15502146944, 15510534272, 15518924416, 15527311232, 15535699072,
    15544089472, 15552478336, 15560866688, 15569254528, 15577642624,
    15586031488, 15594419072, 15602809472, 15611199104, 15619586432,
    15627975296, 15636364928, 15644753792, 15653141888, 15661529216,
    15669918848, 15678305152, 15686696576, 15695083136, 15703474048,
    15711861632, 15720251264, 15728636288, 15737027456, 15745417088,
    15753804928, 15762194048, 15770582656, 15778971008, 15787358336,
    15795747712, 15804132224, 15812523392, 15820909696, 15829300096,
    15837691264, 15846071936, 15854466944, 15862855808, 15871244672,
    15879634816, 15888020608, 15896409728, 15904799104, 15913185152,
    15921577088, 15929966464, 15938354816, 15946743424, 15955129472,
    15963519872, 15971907968, 15980296064, 15988684928, 15997073024,
    16005460864, 16013851264, 16022241152, 16030629248, 16039012736,
    16047406976, 16055794816, 16064181376, 16072571264, 16080957824,
    16089346688, 16097737856, 16106125184, 16114514816, 16122904192,
    16131292544, 16139678848, 16148066944, 16156453504, 16164839552,
    16173236096, 16181623424, 16190012032, 16198401152, 16206790528,
    16215177344, 16223567744, 16231956352, 16240344704, 16248731008,
    16257117824, 16265504384, 16273898624, 16282281856, 16290668672,
    16299064192, 16307449216, 16315842176, 16324230016, 16332613504,
    16341006464, 16349394304, 16357783168, 16366172288, 16374561664,
    16382951296, 16391337856, 16399726208, 16408116352, 16416505472,
    16424892032, 16433282176, 16441668224, 16450058624, 16458448768,
    16466836864, 16475224448, 16483613056, 16492001408, 16500391808,
    16508779648, 16517166976, 16525555328, 16533944192, 16542330752,
    16550719616, 16559110528, 16567497088, 16575888512, 16584274816,
    16592665472, 16601051008, 16609442944, 16617832064, 16626218624,
    16634607488, 16642996096, 16651385728, 16659773824, 16668163712,
    16676552576, 16684938112, 16693328768, 16701718144, 16710095488,
    16718492288, 16726883968, 16735272832, 16743661184, 16752049792,
    16760436608, 16768827008, 16777214336, 16785599104, 16793992832,
    16802381696, 16810768768, 16819151744, 16827542656, 16835934848,
    16844323712, 16852711552, 16861101952, 16869489536, 16877876864,
    16886265728, 16894653056, 16903044736, 16911431296, 16919821696,
    16928207488, 16936592768, 16944987776, 16953375616, 16961763968,
    16970152832, 16978540928, 16986929536, 16995319168, 17003704448,
    17012096896, 17020481152, 17028870784, 17037262208, 17045649536,
    17054039936, 17062426496, 17070814336, 17079205504, 17087592064,
    17095978112, 17104369024, 17112759424, 17121147776, 17129536384,
    17137926016, 17146314368, 17154700928, 17163089792, 17171480192,
    17179864192, 17188256896, 17196644992, 17205033856, 17213423488,
    17221811072, 17230198912, 17238588032, 17246976896, 17255360384,
    17263754624, 17272143232, 17280530048, 17288918912, 17297309312,
    17305696384, 17314085504, 17322475136, 17330863744, 17339252096,
    17347640192, 17356026496, 17364413824, 17372796544, 17381190016,
    17389583488, 17397972608, 17406360704, 17414748544, 17423135872,
    17431527296, 17439915904, 17448303232, 17456691584, 17465081728,
    17473468288, 17481857408, 17490247552, 17498635904, 17507022464,
    17515409024, 17523801728, 17532189824, 17540577664, 17548966016,
    17557353344, 17565741184, 17574131584, 17582519168, 17590907008,
    17599296128, 17607687808, 17616076672, 17624455808, 17632852352,
    17641238656, 17649630848, 17658018944, 17666403968, 17674794112,
    17683178368, 17691573376, 17699962496, 17708350592, 17716739968,
    17725126528, 17733517184, 17741898112, 17750293888, 17758673024,
    17767070336, 17775458432, 17783848832, 17792236928, 17800625536,
    17809012352, 17817402752, 17825785984, 17834178944, 17842563968,
    17850955648, 17859344512, 17867732864, 17876119424, 17884511872,
    17892900224, 17901287296, 17909677696, 17918058112, 17926451072,
    17934843776, 17943230848, 17951609216, 17960008576, 17968397696,
    17976784256, 17985175424, 17993564032, 18001952128, 18010339712,
    18018728576, 18027116672, 18035503232, 18043894144, 18052283264,
    18060672128, 18069056384, 18077449856, 18085837184, 18094225792,
    18102613376, 18111004544, 18119388544, 18127781248, 18136170368,
    18144558976, 18152947328, 18161336192, 18169724288, 18178108544,
    18186498944, 18194886784, 18203275648, 18211666048, 18220048768,
    18228444544, 18236833408, 18245220736}

// cacheSizes is a lookup table for the ethash verification cache size for the
// first 2048 epochs (i.e. 61440000 blocks).
var cacheSizes = [maxEpoch]uint64{
    16776896, 16907456, 17039296, 17170112, 17301056, 17432512, 17563072,
    17693888, 17824192, 17955904, 18087488, 18218176, 18349504, 18481088,
    18611392, 18742336, 18874304, 19004224, 19135936, 19267264, 19398208,
    19529408, 19660096, 19791424, 19922752, 20053952, 20184896, 20315968,
    20446912, 20576576, 20709184, 20840384, 20971072, 21102272, 21233216,
    21364544, 21494848, 21626816, 21757376, 21887552, 22019392, 22151104,
    22281536, 22412224, 22543936, 22675264, 22806464, 22935872, 23068096,
    23198272, 23330752, 23459008, 23592512, 23723968, 23854912, 23986112,
    24116672, 24247616, 24378688, 24509504, 24640832, 24772544, 24903488,
    25034432, 25165376, 25296704, 25427392, 25558592, 25690048, 25820096,
    25951936, 26081728, 26214208, 26345024, 26476096, 26606656, 26737472,
    26869184, 26998208, 27131584, 27262528, 27393728, 27523904, 27655744,
    27786688, 27917888, 28049344, 28179904, 28311488, 28441792, 28573504,
    28700864, 28835648, 28966208, 29096768, 29228608, 29359808, 29490752,
    29621824, 29752256, 29882816, 30014912, 30144448, 30273728, 30406976,
    30538432, 30670784, 30799936, 30932672, 31063744, 31195072, 31325248,
    31456192, 31588288, 31719232, 31850432, 31981504, 32110784, 32243392,
    32372672, 32505664, 32636608, 32767808, 32897344, 33029824, 33160768,
    33289664, 33423296, 33554368, 33683648, 33816512, 33947456, 34076992,
    34208704, 34340032, 34471744, 34600256, 34734016, 34864576, 34993984,
    35127104, 35258176, 35386688, 35518528, 35650624, 35782336, 35910976,
    36044608, 36175808, 36305728, 36436672, 36568384, 36699968, 36830656,
    36961984, 37093312, 37223488, 37355072, 37486528, 37617472, 37747904,
    37879232, 38009792, 38141888, 38272448, 38403392, 38535104, 38660672,
    38795584, 38925632, 39059264, 39190336, 39320768, 39452096, 39581632,
    39713984, 39844928, 39974848, 40107968, 40238144, 40367168, 40500032,
    40631744, 40762816, 40894144, 41023552, 41155904, 41286208, 41418304,
    41547712, 41680448, 41811904, 41942848, 42073792, 42204992, 42334912,
    42467008, 42597824, 42729152, 42860096, 42991552, 43122368, 43253696,
    43382848, 43515712, 43646912, 43777088, 43907648, 44039104, 44170432,
    44302144, 44433344, 44564288, 44694976, 44825152, 44956864, 45088448,
    45219008, 45350464, 45481024, 45612608, 45744064, 45874496, 46006208,
    46136768, 46267712, 46399424, 46529344, 46660672, 46791488, 46923328,
    47053504, 47185856, 47316928, 47447872, 47579072, 47710144, 47839936,
    47971648, 48103232, 48234176, 48365248, 48496192, 48627136, 48757312,
    48889664, 49020736, 49149248, 49283008, 49413824, 49545152, 49675712,
    49807168, 49938368, 50069056, 50200256, 50331584, 50462656, 50593472,
    50724032, 50853952, 50986048, 51117632, 51248576, 51379904, 51510848,
    51641792, 51773248, 51903296, 52035136, 52164032, 52297664, 52427968,
    52557376, 52690112, 52821952, 52952896, 53081536, 53213504, 53344576,
    53475776, 53608384, 53738816, 53870528, 54000832, 54131776, 54263744,
    54394688, 54525248, 54655936, 54787904, 54918592, 55049152, 55181248,
    55312064, 55442752, 55574336, 55705024, 55836224, 55967168, 56097856,
    56228672, 56358592, 56490176, 56621888, 56753728, 56884928, 57015488,
    57146816, 57278272, 57409216, 57540416, 57671104, 57802432, 57933632,
    58064576, 58195264, 58326976, 58457408, 58588864, 58720192, 58849984,
    58981696, 59113024, 59243456, 59375552, 59506624, 59637568, 59768512,
    59897792, 60030016, 60161984, 60293056, 60423872, 60554432, 60683968,
    60817216, 60948032, 61079488, 61209664, 61341376, 61471936, 61602752,
    61733696, 61865792, 61996736, 62127808, 62259136, 62389568, 62520512,
    62651584, 62781632, 62910784, 63045056, 63176128, 63307072, 63438656,
    63569216, 63700928, 63831616, 63960896, 64093888, 64225088, 64355392,
    64486976, 64617664, 64748608, 64879424, 65009216, 65142464, 65273792,
    65402816, 65535424, 65666752, 65797696, 65927744, 66060224, 66191296,
    66321344, 66453056, 66584384, 66715328, 66846656, 66977728, 67108672,
    67239104, 67370432, 67501888, 67631296, 67763776, 67895104, 68026304,
    68157248, 68287936, 68419264, 68548288, 68681408, 68811968, 68942912,
    69074624, 69205568, 69337024, 69467584, 69599168, 69729472, 69861184,
    69989824, 70122944, 70253888, 70385344, 70515904, 70647232, 70778816,
    70907968, 71040832, 71171648, 71303104, 71432512, 71564992, 71695168,
    71826368, 71958464, 72089536, 72219712, 72350144, 72482624, 72613568,
    72744512, 72875584, 73006144, 73138112, 73268672, 73400128, 73530944,
    73662272, 73793344, 73924544, 74055104, 74185792, 74316992, 74448832,
    74579392, 74710976, 74841664, 74972864, 75102784, 75233344, 75364544,
    75497024, 75627584, 75759296, 75890624, 76021696, 76152256, 76283072,
    76414144, 76545856, 76676672, 76806976, 76937792, 77070016, 77200832,
    77331392, 77462464, 77593664, 77725376, 77856448, 77987776, 78118336,
    78249664, 78380992, 78511424, 78642496, 78773056, 78905152, 79033664,
    79166656, 79297472, 79429568, 79560512, 79690816, 79822784, 79953472,
    80084672, 80214208, 80346944, 80477632, 80608576, 80740288, 80870848,
    81002048, 81133504, 81264448, 81395648, 81525952, 81657536, 81786304,
    81919808, 82050112, 82181312, 82311616, 82443968, 82573376, 82705984,
    82835776, 82967744, 83096768, 83230528, 83359552, 83491264, 83622464,
    83753536, 83886016, 84015296, 84147776, 84277184, 84409792, 84540608,
    84672064, 84803008, 84934336, 85065152, 85193792, 85326784, 85458496,
    85589312, 85721024, 85851968, 85982656, 86112448, 86244416, 86370112,
    86506688, 86637632, 86769344, 86900672, 87031744, 87162304, 87293632,
    87424576, 87555392, 87687104, 87816896, 87947968, 88079168, 88211264,
    88341824, 88473152, 88603712, 88735424, 88862912, 88996672, 89128384,
    89259712, 89390272, 89521984, 89652544, 89783872, 89914816, 90045376,
    90177088, 90307904, 90438848, 90569152, 90700096, 90832832, 90963776,
    91093696, 91223744, 91356992, 91486784, 91618496, 91749824, 91880384,
    92012224, 92143552, 92273344, 92405696, 92536768, 92666432, 92798912,
    92926016, 93060544, 93192128, 93322816, 93453632, 93583936, 93715136,
    93845056, 93977792, 94109504, 94240448, 94371776, 94501184, 94632896,
    94764224, 94895552, 95023424, 95158208, 95287744, 95420224, 95550016,
    95681216, 95811904, 95943872, 96075328, 96203584, 96337856, 96468544,
    96599744, 96731072, 96860992, 96992576, 97124288, 97254848, 97385536,
    97517248, 97647808, 97779392, 97910464, 98041408, 98172608, 98303168,
    98434496, 98565568, 98696768, 98827328, 98958784, 99089728, 99220928,
    99352384, 99482816, 99614272, 99745472, 99876416, 100007104,
    100138048, 100267072, 100401088, 100529984, 100662592, 100791872,
    100925248, 101056064, 101187392, 101317952, 101449408, 101580608,
    101711296, 101841728, 101973824, 102104896, 102235712, 102366016,
    102498112, 102628672, 102760384, 102890432, 103021888, 103153472,
    103284032, 103415744, 103545152, 103677248, 103808576, 103939648,
    104070976, 104201792, 104332736, 104462528, 104594752, 104725952,
    104854592, 104988608, 105118912, 105247808, 105381184, 105511232,
    105643072, 105774784, 105903296, 106037056, 106167872, 106298944,
    106429504, 106561472, 106691392, 106822592, 106954304, 107085376,
    107216576, 107346368, 107478464, 107609792, 107739712, 107872192,
    108003136, 108131392, 108265408, 108396224, 108527168, 108657344,
    108789568, 108920384, 109049792, 109182272, 109312576, 109444928,
    109572928, 109706944, 109837888, 109969088, 110099648, 110230976,
    110362432, 110492992, 110624704, 110755264, 110886208, 111017408,
    111148864, 111279296, 111410752, 111541952, 111673024, 111803456,
    111933632, 112066496, 112196416, 112328512, 112457792, 112590784,
    112715968, 112852672, 112983616, 113114944, 113244224, 113376448,
    113505472, 113639104, 113770304, 113901376, 114031552, 114163264,
    114294592, 114425536, 114556864, 114687424, 114818624, 114948544,
    115080512, 115212224, 115343296, 115473472, 115605184, 115736128,
    115867072, 115997248, 116128576, 116260288, 116391488, 116522944,
    116652992, 116784704, 116915648, 117046208, 117178304, 117308608,
    117440192, 117569728, 117701824, 117833024, 117964096, 118094656,
    118225984, 118357312, 118489024, 118617536, 118749632, 118882112,
    119012416, 119144384, 119275328, 119406016, 119537344, 119668672,
    119798464, 119928896, 120061376, 120192832, 120321728, 120454336,
    120584512, 120716608, 120848192, 120979136, 121109056, 121241408,
    121372352, 121502912, 121634752, 121764416, 121895744, 122027072,
    122157632, 122289088, 122421184, 122550592, 122682944, 122813888,
    122945344, 123075776, 123207488, 123338048, 123468736, 123600704,
    123731264, 123861952, 123993664, 124124608, 124256192, 124386368,
    124518208, 124649024, 124778048, 124911296, 125041088, 125173696,
    125303744, 125432896, 125566912, 125696576, 125829056, 125958592,
    126090304, 126221248, 126352832, 126483776, 126615232, 126746432,
    126876608, 127008704, 127139392, 127270336, 127401152, 127532224,
    127663552, 127794752, 127925696, 128055232, 128188096, 128319424,
    128449856, 128581312, 128712256, 128843584, 128973632, 129103808,
    129236288, 129365696, 129498944, 129629888, 129760832, 129892288,
    130023104, 130154048, 130283968, 130416448, 130547008, 130678336,
    130807616, 130939456, 131071552, 131202112, 131331776, 131464384,
    131594048, 131727296, 131858368, 131987392, 132120256, 132250816,
    132382528, 132513728, 132644672, 132774976, 132905792, 133038016,
    133168832, 133299392, 133429312, 133562048, 133692992, 133823296,
    133954624, 134086336, 134217152, 134348608, 134479808, 134607296,
    134741056, 134872384, 135002944, 135134144, 135265472, 135396544,
    135527872, 135659072, 135787712, 135921472, 136052416, 136182848,
    136313792, 136444864, 136576448, 136707904, 136837952, 136970048,
    137099584, 137232064, 137363392, 137494208, 137625536, 137755712,
    137887424, 138018368, 138149824, 138280256, 138411584, 138539584,
    138672832, 138804928, 138936128, 139066688, 139196864, 139328704,
    139460032, 139590208, 139721024, 139852864, 139984576, 140115776,
    140245696, 140376512, 140508352, 140640064, 140769856, 140902336,
    141032768, 141162688, 141294016, 141426496, 141556544, 141687488,
    141819584, 141949888, 142080448, 142212544, 142342336, 142474432,
    142606144, 142736192, 142868288, 142997824, 143129408, 143258944,
    143392448, 143523136, 143653696, 143785024, 143916992, 144045632,
    144177856, 144309184, 144440768, 144570688, 144701888, 144832448,
    144965056, 145096384, 145227584, 145358656, 145489856, 145620928,
    145751488, 145883072, 146011456, 146144704, 146275264, 146407232,
    146538176, 146668736, 146800448, 146931392, 147062336, 147193664,
    147324224, 147455936, 147586624, 147717056, 147848768, 147979456,
    148110784, 148242368, 148373312, 148503232, 148635584, 148766144,
    148897088, 149028416, 149159488, 149290688, 149420224, 149551552,
    149683136, 149814976, 149943616, 150076352, 150208064, 150338624,
    150470464, 150600256, 150732224, 150862784, 150993088, 151125952,
    151254976, 151388096, 151519168, 151649728, 151778752, 151911104,
    152042944, 152174144, 152304704, 152435648, 152567488, 152698816,
    152828992, 152960576, 153091648, 153222976, 153353792, 153484096,
    153616192, 153747008, 153878336, 154008256, 154139968, 154270912,
    154402624, 154533824, 154663616, 154795712, 154926272, 155057984,
    155188928, 155319872, 155450816, 155580608, 155712064, 155843392,
    155971136, 156106688, 156237376, 156367424, 156499264, 156630976,
    156761536, 156892352, 157024064, 157155008, 157284416, 157415872,
    157545536, 157677248, 157810496, 157938112, 158071744, 158203328,
    158334656, 158464832, 158596288, 158727616, 158858048, 158988992,
    159121216, 159252416, 159381568, 159513152, 159645632, 159776192,
    159906496, 160038464, 160169536, 160300352, 160430656, 160563008,
    160693952, 160822208, 160956352, 161086784, 161217344, 161349184,
    161480512, 161611456, 161742272, 161873216, 162002752, 162135872,
    162266432, 162397888, 162529216, 162660032, 162790976, 162922048,
    163052096, 163184576, 163314752, 163446592, 163577408, 163707968,
    163839296, 163969984, 164100928, 164233024, 164364224, 164494912,
    164625856, 164756672, 164887616, 165019072, 165150016, 165280064,
    165412672, 165543104, 165674944, 165805888, 165936832, 166067648,
    166198336, 166330048, 166461248, 166591552, 166722496, 166854208,
    166985408, 167116736, 167246656, 167378368, 167508416, 167641024,
    167771584, 167903168, 168034112, 168164032, 168295744, 168427456,
    168557632, 168688448, 168819136, 168951616, 169082176, 169213504,
    169344832, 169475648, 169605952, 169738048, 169866304, 169999552,
    170131264, 170262464, 170393536, 170524352, 170655424, 170782016,
    170917696, 171048896, 171179072, 171310784, 171439936, 171573184,
    171702976, 171835072, 171966272, 172097216, 172228288, 172359232,
    172489664, 172621376, 172747712, 172883264, 173014208, 173144512,
    173275072, 173407424, 173539136, 173669696, 173800768, 173931712,
    174063424, 174193472, 174325696, 174455744, 174586816, 174718912,
    174849728, 174977728, 175109696, 175242688, 175374272, 175504832,
    175636288, 175765696, 175898432, 176028992, 176159936, 176291264,
    176422592, 176552512, 176684864, 176815424, 176946496, 177076544,
    177209152, 177340096, 177470528, 177600704, 177731648, 177864256,
    177994816, 178126528, 178257472, 178387648, 178518464, 178650176,
    178781888, 178912064, 179044288, 179174848, 179305024, 179436736,
    179568448, 179698496, 179830208, 179960512, 180092608, 180223808,
    180354752, 180485696, 180617152, 180748096, 180877504, 181009984,
    181139264, 181272512, 181402688, 181532608, 181663168, 181795136,
    181926592, 182057536, 182190016, 182320192, 182451904, 182582336,
    182713792, 182843072, 182976064, 183107264, 183237056, 183368384,
    183494848, 183631424, 183762752, 183893824, 184024768, 184154816,
    184286656, 184417984, 184548928, 184680128, 184810816, 184941248,
    185072704, 185203904, 185335616, 185465408, 185596352, 185727296,
    185859904, 185989696, 186121664, 186252992, 186383552, 186514112,
    186645952, 186777152, 186907328, 187037504, 187170112, 187301824,
    187429184, 187562048, 187693504, 187825472, 187957184, 188087104,
    188218304, 188349376, 188481344, 188609728, 188743616, 188874304,
    189005248, 189136448, 189265088, 189396544, 189528128, 189660992,
    189791936, 189923264, 190054208, 190182848, 190315072, 190447424,
    190577984, 190709312, 190840768, 190971328, 191102656, 191233472,
    191364032, 191495872, 191626816, 191758016, 191888192, 192020288,
    192148928, 192282176, 192413504, 192542528, 192674752, 192805952,
    192937792, 193068608, 193198912, 193330496, 193462208, 193592384,
    193723456, 193854272, 193985984, 194116672, 194247232, 194379712,
    194508352, 194641856, 194772544, 194900672, 195035072, 195166016,
    195296704, 195428032, 195558592, 195690304, 195818176, 195952576,
    196083392, 196214336, 196345792, 196476736, 196607552, 196739008,
    196869952, 197000768, 197130688, 197262784, 197394368, 197523904,
    197656384, 197787584, 197916608, 198049472, 198180544, 198310208,
    198442432, 198573632, 198705088, 198834368, 198967232, 199097792,
    199228352, 199360192, 199491392, 199621696, 199751744, 199883968,
    200014016, 200146624, 200276672, 200408128, 200540096, 200671168,
    200801984, 200933312, 201062464, 201194944, 201326144, 201457472,
    201588544, 201719744, 201850816, 201981632, 202111552, 202244032,
    202374464, 202505152, 202636352, 202767808, 202898368, 203030336,
    203159872, 203292608, 203423296, 203553472, 203685824, 203816896,
    203947712, 204078272, 204208192, 204341056, 204472256, 204603328,
    204733888, 204864448, 204996544, 205125568, 205258304, 205388864,
    205517632, 205650112, 205782208, 205913536, 206044736, 206176192,
    206307008, 206434496, 206569024, 206700224, 206831168, 206961856,
    207093056, 207223616, 207355328, 207486784, 207616832, 207749056,
    207879104, 208010048, 208141888, 208273216, 208404032, 208534336,
    208666048, 208796864, 208927424, 209059264, 209189824, 209321792,
    209451584, 209582656, 209715136, 209845568, 209976896, 210106432,
    210239296, 210370112, 210501568, 210630976, 210763712, 210894272,
    211024832, 211156672, 211287616, 211418176, 211549376, 211679296,
    211812032, 211942592, 212074432, 212204864, 212334016, 212467648,
    212597824, 212727616, 212860352, 212991424, 213120832, 213253952,
    213385024, 213515584, 213645632, 213777728, 213909184, 214040128,
    214170688, 214302656, 214433728, 214564544, 214695232, 214826048,
    214956992, 215089088, 215219776, 215350592, 215482304, 215613248,
    215743552, 215874752, 216005312, 216137024, 216267328, 216399296,
    216530752, 216661696, 216790592, 216923968, 217054528, 217183168,
    217316672, 217448128, 217579072, 217709504, 217838912, 217972672,
    218102848, 218233024, 218364736, 218496832, 218627776, 218759104,
    218888896, 219021248, 219151936, 219281728, 219413056, 219545024,
    219675968, 219807296, 219938624, 220069312, 220200128, 220331456,
    220461632, 220592704, 220725184, 220855744, 220987072, 221117888,
    221249216, 221378368, 221510336, 221642048, 221772736, 221904832,
    222031808, 222166976, 222297536, 222428992, 222559936, 222690368,
    222820672, 222953152, 223083968, 223213376, 223345984, 223476928,
    223608512, 223738688, 223869376, 224001472, 224132672, 224262848,
    224394944, 224524864, 224657344, 224788288, 224919488, 225050432,
    225181504, 225312704, 225443776, 225574592, 225704768, 225834176,
    225966784, 226097216, 226229824, 226360384, 226491712, 226623424,
    226754368, 226885312, 227015104, 227147456, 227278528, 227409472,
    227539904, 227669696, 227802944, 227932352, 228065216, 228196288,
    228326464, 228457792, 228588736, 228720064, 228850112, 228981056,
    229113152, 229243328, 229375936, 229505344, 229636928, 229769152,
    229894976, 230030272, 230162368, 230292416, 230424512, 230553152,
    230684864, 230816704, 230948416, 231079616, 231210944, 231342016,
    231472448, 231603776, 231733952, 231866176, 231996736, 232127296,
    232259392, 232388672, 232521664, 232652608, 232782272, 232914496,
    233043904, 233175616, 233306816, 233438528, 233569984, 233699776,
    233830592, 233962688, 234092224, 234221888, 234353984, 234485312,
    234618304, 234749888, 234880832, 235011776, 235142464, 235274048,
    235403456, 235535936, 235667392, 235797568, 235928768, 236057152,
    236190272, 236322752, 236453312, 236583616, 236715712, 236846528,
    236976448, 237108544, 237239104, 237371072, 237501632, 237630784,
    237764416, 237895232, 238026688, 238157632, 238286912, 238419392,
    238548032, 238681024, 238812608, 238941632, 239075008, 239206336,
    239335232, 239466944, 239599168, 239730496, 239861312, 239992384,
    240122816, 240254656, 240385856, 240516928, 240647872, 240779072,
    240909632, 241040704, 241171904, 241302848, 241433408, 241565248,
    241696192, 241825984, 241958848, 242088256, 242220224, 242352064,
    242481856, 242611648, 242744896, 242876224, 243005632, 243138496,
    243268672, 243400384, 243531712, 243662656, 243793856, 243924544,
    244054592, 244187072, 244316608, 244448704, 244580032, 244710976,
    244841536, 244972864, 245104448, 245233984, 245365312, 245497792,
    245628736, 245759936, 245889856, 246021056, 246152512, 246284224,
    246415168, 246545344, 246675904, 246808384, 246939584, 247070144,
    247199552, 247331648, 247463872, 247593536, 247726016, 247857088,
    247987648, 248116928, 248249536, 248380736, 248512064, 248643008,
    248773312, 248901056, 249036608, 249167552, 249298624, 249429184,
    249560512, 249692096, 249822784, 249954112, 250085312, 250215488,
    250345792, 250478528, 250608704, 250739264, 250870976, 251002816,
    251133632, 251263552, 251395136, 251523904, 251657792, 251789248,
    251919424, 252051392, 252182464, 252313408, 252444224, 252575552,
    252706624, 252836032, 252968512, 253099712, 253227584, 253361728,
    253493056, 253623488, 253754432, 253885504, 254017216, 254148032,
    254279488, 254410432, 254541376, 254672576, 254803264, 254933824,
    255065792, 255196736, 255326528, 255458752, 255589952, 255721408,
    255851072, 255983296, 256114624, 256244416, 256374208, 256507712,
    256636096, 256768832, 256900544, 257031616, 257162176, 257294272,
    257424448, 257555776, 257686976, 257818432, 257949632, 258079552,
    258211136, 258342464, 258473408, 258603712, 258734656, 258867008,
    258996544, 259127744, 259260224, 259391296, 259522112, 259651904,
    259784384, 259915328, 260045888, 260175424, 260308544, 260438336,
    260570944, 260700992, 260832448, 260963776, 261092672, 261226304,
    261356864, 261487936, 261619648, 261750592, 261879872, 262011968,
    262143424, 262274752, 262404416, 262537024, 262667968, 262799296,
    262928704, 263061184, 263191744, 263322944, 263454656, 263585216,
    263716672, 263847872, 263978944, 264108608, 264241088, 264371648,
    264501184, 264632768, 264764096, 264895936, 265024576, 265158464,
    265287488, 265418432, 265550528, 265681216, 265813312, 265943488,
    266075968, 266206144, 266337728, 266468032, 266600384, 266731072,
    266862272, 266993344, 267124288, 267255616, 267386432, 267516992,
    267648704, 267777728, 267910592, 268040512, 268172096, 268302784,
    268435264, 268566208, 268696256, 268828096, 268959296, 269090368,
    269221312, 269352256, 269482688, 269614784, 269745856, 269876416,
    270007616, 270139328, 270270272, 270401216, 270531904, 270663616,
    270791744, 270924736, 271056832, 271186112, 271317184, 271449536,
    271580992, 271711936, 271843136, 271973056, 272105408, 272236352,
    272367296, 272498368, 272629568, 272759488, 272891456, 273022784,
    273153856, 273284672, 273415616, 273547072, 273677632, 273808448,
    273937088, 274071488, 274200896, 274332992, 274463296, 274595392,
    274726208, 274857536, 274988992, 275118656, 275250496, 275382208,
    275513024, 275643968, 275775296, 275906368, 276037184, 276167872,
    276297664, 276429376, 276560576, 276692672, 276822976, 276955072,
    277085632, 277216832, 277347008, 277478848, 277609664, 277740992,
    277868608, 278002624, 278134336, 278265536, 278395328, 278526784,
    278657728, 278789824, 278921152, 279052096, 279182912, 279313088,
    279443776, 279576256, 279706048, 279838528, 279969728, 280099648,
    280230976, 280361408, 280493632, 280622528, 280755392, 280887104,
    281018176, 281147968, 281278912, 281411392, 281542592, 281673152,
    281803712, 281935552, 282066496, 282197312, 282329024, 282458816,
    282590272, 282720832, 282853184, 282983744, 283115072, 283246144,
    283377344, 283508416, 283639744, 283770304, 283901504, 284032576,
    284163136, 284294848, 284426176, 284556992, 284687296, 284819264,
    284950208, 285081536}