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author | Péter Szilágyi <peterke@gmail.com> | 2017-04-05 06:16:29 +0800 |
---|---|---|
committer | Felix Lange <fjl@users.noreply.github.com> | 2017-04-05 06:16:29 +0800 |
commit | 09777952ee476ff80d4b6e63b5041ff5ca0e441b (patch) | |
tree | e85320f88f548201e3476b3e7095e96fd071617b /pow/ethash_algo.go | |
parent | e50a5b77712d891ff409aa942a5cbc24e721b332 (diff) | |
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core, consensus: pluggable consensus engines (#3817)
This commit adds pluggable consensus engines to go-ethereum. In short, it
introduces a generic consensus interface, and refactors the entire codebase to
use this interface.
Diffstat (limited to 'pow/ethash_algo.go')
-rw-r--r-- | pow/ethash_algo.go | 1103 |
1 files changed, 0 insertions, 1103 deletions
diff --git a/pow/ethash_algo.go b/pow/ethash_algo.go deleted file mode 100644 index 1e996785f..000000000 --- a/pow/ethash_algo.go +++ /dev/null @@ -1,1103 +0,0 @@ -// 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 pow - -import ( - "encoding/binary" - "hash" - "reflect" - "runtime" - "sync" - "sync/atomic" - "time" - "unsafe" - - "github.com/ethereum/go-ethereum/common" - "github.com/ethereum/go-ethereum/crypto" - "github.com/ethereum/go-ethereum/crypto/sha3" - "github.com/ethereum/go-ethereum/log" -) - -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 -) - -// 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 { - return func(dest []byte, data []byte) { - h.Write(data) - h.Sum(dest[:0]) - h.Reset() - } -} - -// 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.NewKeccak256()) - 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 thoretical 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.NewKeccak512()) - - // 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 - ) - 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:])) - } -} - -// prepare converts an ethash cache or dataset from a byte stream into the internal -// int representation. All ethash methods work with ints to avoid constant byte to -// int conversions as well as to handle both little and big endian systems. -func prepare(dest []uint32, src []byte) { - for i := 0; i < len(dest); i++ { - dest[i] = binary.LittleEndian.Uint32(src[i*4:]) - } -} - -// 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 thoretical 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.NewKeccak512()) - - // 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 thoretical 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.NewKeccak512()) - - 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) -} - -// datasetSizes is a lookup table for the ethash dataset size for the first 2048 -// epochs (i.e. 61440000 blocks). -var datasetSizes = []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, - 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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 = []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, - 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