631 lines
18 KiB
C++
631 lines
18 KiB
C++
// Equihash solver
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// Copyright (c) 2016 John Tromp
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// Fix N, K, such that n = N/(k+1) is integer
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// Fix M = 2^{n+1} hashes each of length N bits,
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// H_0, ... , H_{M-1}, generated fom (n+1)-bit indices.
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// Problem: find binary tree on 2^K distinct indices,
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// for which the exclusive-or of leaf hashes is all 0s.
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// Additionally, it should satisfy the Wagner conditions:
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// for each height i subtree, the exclusive-or
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// of its 2^i corresponding hashes starts with i*n 0 bits,
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// and for i>0 the leftmost leaf of its left subtree
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// is less than the leftmost leaf of its right subtree
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// The algorithm below solves this by maintaining the tree
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// in a graph of K layers, each split into buckets
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// with buckets indexed by the first n-RESTBITS bits following
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// the i*n 0s, each bucket having 4 * 2^RESTBITS slots,
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// twice the number of subtrees expected to land there.
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#include "equi.h"
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#include <stdio.h>
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#include <stdlib.h>
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#include <pthread.h>
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#include <assert.h>
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typedef uint16_t u16;
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typedef uint64_t u64;
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#ifdef ATOMIC
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#include <atomic>
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typedef std::atomic<u32> au32;
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#else
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typedef u32 au32;
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#endif
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#ifndef RESTBITS
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#define RESTBITS 8
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#endif
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// 2_log of number of buckets
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#define BUCKBITS (DIGITBITS-RESTBITS)
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#ifndef SAVEMEM
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#if RESTBITS == 4
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// can't save memory in such small buckets
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#define SAVEMEM 1
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#elif RESTBITS >= 8
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// take advantage of law of large numbers (sum of 2^8 random numbers)
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// this reduces (200,9) memory to under 144MB, with negligible discarding
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#define SAVEMEM 9/14
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#endif
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#endif
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// number of buckets
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static const u32 NBUCKETS = 1<<BUCKBITS;
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// 2_log of number of slots per bucket
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static const u32 SLOTBITS = RESTBITS+1+1;
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static const u32 SLOTRANGE = 1<<SLOTBITS;
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static const u32 SLOTMSB = 1<<(SLOTBITS-1);
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// number of slots per bucket
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static const u32 NSLOTS = SLOTRANGE * SAVEMEM;
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// number of per-xhash slots
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static const u32 XFULL = 16;
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// SLOTBITS mask
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static const u32 SLOTMASK = SLOTRANGE-1;
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// number of possible values of xhash (rest of n) bits
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static const u32 NRESTS = 1<<RESTBITS;
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// number of blocks of hashes extracted from single 512 bit blake2b output
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static const u32 NBLOCKS = (NHASHES+HASHESPERBLAKE-1)/HASHESPERBLAKE;
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// nothing larger found in 100000 runs
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static const u32 MAXSOLS = 8;
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// tree node identifying its children as two different slots in
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// a bucket on previous layer with the same rest bits (x-tra hash)
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struct tree {
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u32 bid_s0_s1; // manual bitfields
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tree(const u32 idx) {
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bid_s0_s1 = idx;
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}
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tree(const u32 bid, const u32 s0, const u32 s1) {
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#ifdef SLOTDIFF
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u32 ds10 = (s1 - s0) & SLOTMASK;
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if (ds10 & SLOTMSB) {
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bid_s0_s1 = (((bid << SLOTBITS) | s1) << (SLOTBITS-1)) | (SLOTMASK & ~ds10);
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} else {
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bid_s0_s1 = (((bid << SLOTBITS) | s0) << (SLOTBITS-1)) | (ds10 - 1);
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}
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#else
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bid_s0_s1 = (((bid << SLOTBITS) | s0) << SLOTBITS) | s1;
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#endif
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}
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u32 getindex() const {
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return bid_s0_s1;
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}
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u32 bucketid() const {
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#ifdef SLOTDIFF
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return bid_s0_s1 >> (2 * SLOTBITS - 1);
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#else
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return bid_s0_s1 >> (2 * SLOTBITS);
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#endif
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}
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u32 slotid0() const {
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#ifdef SLOTDIFF
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return (bid_s0_s1 >> (SLOTBITS-1)) & SLOTMASK;
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#else
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return (bid_s0_s1 >> SLOTBITS) & SLOTMASK;
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#endif
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}
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u32 slotid1() const {
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#ifdef SLOTDIFF
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return (slotid0() + 1 + (bid_s0_s1 & (SLOTMASK>>1))) & SLOTMASK;
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#else
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return bid_s0_s1 & SLOTMASK;
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#endif
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}
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};
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union htunit {
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tree tag;
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u32 word;
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uchar bytes[sizeof(u32)];
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};
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#define WORDS(bits) ((bits + 31) / 32)
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#define HASHWORDS0 WORDS(WN - DIGITBITS + RESTBITS)
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#define HASHWORDS1 WORDS(WN - 2*DIGITBITS + RESTBITS)
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// A slot is up to HASHWORDS0 hash units followed by a tag
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typedef htunit slot0[HASHWORDS0+1];
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typedef htunit slot1[HASHWORDS1+1];
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// a bucket is NSLOTS treenodes
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typedef slot0 bucket0[NSLOTS];
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typedef slot1 bucket1[NSLOTS];
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// the N-bit hash consists of K+1 n-bit "digits"
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// each of which corresponds to a layer of NBUCKETS buckets
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typedef bucket0 digit0[NBUCKETS];
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typedef bucket1 digit1[NBUCKETS];
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typedef au32 bsizes[NBUCKETS];
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u32 min(const u32 a, const u32 b) {
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return a < b ? a : b;
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}
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// size (in bytes) of hash in round 0 <= r < WK
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u32 hashsize(const u32 r) {
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const u32 hashbits = WN - (r+1) * DIGITBITS + RESTBITS;
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return (hashbits + 7) / 8;
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}
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u32 hashwords(u32 bytes) {
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return (bytes + 3) / 4;
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}
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// manages hash and tree data
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struct htalloc {
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bucket0 *heap0;
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bucket1 *heap1;
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u32 alloced;
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htalloc() {
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alloced = 0;
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}
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void alloctrees() {
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// optimize xenoncat's fixed memory layout, avoiding any waste
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// digit hashes tree hashes tree
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// 0 A A A A A A 0 . . . . . .
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// 1 A A A A A A 0 B B B B B 1
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// 2 C C C C C 2 0 B B B B B 1
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// 3 C C C C C 2 0 D D D D 3 1
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// 4 E E E E 4 2 0 D D D D 3 1
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// 5 E E E E 4 2 0 F F F 5 3 1
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// 6 G G 6 . 4 2 0 F F F 5 3 1
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// 7 G G 6 . 4 2 0 H H 7 5 3 1
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// 8 I 8 6 . 4 2 0 H H 7 5 3 1
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assert(DIGITBITS >= 16); // ensures hashes shorten by 1 unit every 2 digits
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heap0 = (bucket0 *)alloc(NBUCKETS, sizeof(bucket0));
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heap1 = (bucket1 *)alloc(NBUCKETS, sizeof(bucket1));
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}
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void dealloctrees() {
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free(heap0);
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free(heap1);
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}
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void *alloc(const u32 n, const u32 sz) {
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void *mem = calloc(n, sz);
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assert(mem);
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alloced += n * sz;
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return mem;
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}
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};
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struct equi {
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blake2b_state blake_ctx;
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htalloc hta;
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bsizes *nslots; // PUT IN BUCKET STRUCT
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proof *sols;
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au32 nsols;
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u32 nthreads;
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u32 xfull;
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u32 hfull;
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u32 bfull;
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pthread_barrier_t barry;
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equi(const u32 n_threads) {
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assert(sizeof(htunit) == 4);
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nthreads = n_threads;
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const int err = pthread_barrier_init(&barry, NULL, nthreads);
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assert(!err);
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hta.alloctrees();
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nslots = (bsizes *)hta.alloc(2 * NBUCKETS, sizeof(au32));
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sols = (proof *)hta.alloc(MAXSOLS, sizeof(proof));
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}
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~equi() {
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hta.dealloctrees();
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free(nslots);
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free(sols);
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}
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void setnonce(const char *header, const u32 headerlen, const u32 nonce) {
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setheader(&blake_ctx, header, headerlen, nonce);
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memset(nslots, 0, NBUCKETS * sizeof(au32)); // only nslots[0] needs zeroing
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nsols = 0;
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}
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u32 getslot(const u32 r, const u32 bucketi) {
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#ifdef ATOMIC
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return std::atomic_fetch_add_explicit(&nslots[r&1][bucketi], 1U, std::memory_order_relaxed);
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#else
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return nslots[r&1][bucketi]++;
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#endif
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}
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u32 getnslots(const u32 r, const u32 bid) { // SHOULD BE METHOD IN BUCKET STRUCT
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au32 &nslot = nslots[r&1][bid];
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const u32 n = min(nslot, NSLOTS);
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nslot = 0;
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return n;
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}
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void orderindices(u32 *indices, u32 size) {
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if (indices[0] > indices[size]) {
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for (u32 i=0; i < size; i++) {
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const u32 tmp = indices[i];
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indices[i] = indices[size+i];
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indices[size+i] = tmp;
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}
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}
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}
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void listindices0(u32 r, const tree t, u32 *indices) {
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if (r == 0) {
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*indices = t.getindex(); // TRY INTEGRATE PROBDUPE TEST HERE
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return;
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}
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const slot1 *buck = hta.heap1[t.bucketid()];
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const u32 size = 1 << --r;
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u32 *indices1 = indices + size;
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u32 tagi = hashwords(hashsize(r));
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listindices1(r, buck[t.slotid0()][tagi].tag, indices);
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listindices1(r, buck[t.slotid1()][tagi].tag, indices1);
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orderindices(indices, size);
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}
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void listindices1(u32 r, const tree t, u32 *indices) {
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const slot0 *buck = hta.heap0[t.bucketid()];
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const u32 size = 1 << --r;
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u32 *indices1 = indices + size;
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u32 tagi = hashwords(hashsize(r));
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listindices0(r, buck[t.slotid0()][tagi].tag, indices);
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listindices0(r, buck[t.slotid1()][tagi].tag, indices1);
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orderindices(indices, size);
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}
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void candidate(const tree t) {
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proof prf;
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listindices1(WK, t, prf); // assume WK odd
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qsort(prf, PROOFSIZE, sizeof(u32), &compu32);
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for (u32 i=1; i<PROOFSIZE; i++)
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if (prf[i] <= prf[i-1])
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return;
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#ifdef ATOMIC
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u32 soli = std::atomic_fetch_add_explicit(&nsols, 1U, std::memory_order_relaxed);
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#else
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u32 soli = nsols++;
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#endif
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if (soli < MAXSOLS)
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listindices1(WK, t, sols[soli]); // assume WK odd
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}
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void showbsizes(u32 r) {
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#if defined(HIST) || defined(SPARK) || defined(LOGSPARK)
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u32 binsizes[65];
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memset(binsizes, 0, 65 * sizeof(u32));
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for (u32 bucketid = 0; bucketid < NBUCKETS; bucketid++) {
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u32 bsize = min(nslots[r&1][bucketid], NSLOTS) >> (SLOTBITS-6);
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binsizes[bsize]++;
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}
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for (u32 i=0; i < 65; i++) {
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#ifdef HIST
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printf(" %d:%d", i, binsizes[i]);
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#else
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#ifdef SPARK
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u32 sparks = binsizes[i] / SPARKSCALE;
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#else
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u32 sparks = 0;
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for (u32 bs = binsizes[i]; bs; bs >>= 1) sparks++;
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sparks = sparks * 7 / SPARKSCALE;
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#endif
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printf("\342\226%c", '\201' + sparks);
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#endif
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}
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printf("\n");
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#endif
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}
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struct htlayout {
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htalloc hta;
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u32 prevhtunits;
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u32 nexthtunits;
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u32 dunits;
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u32 prevbo;
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htlayout(equi *eq, u32 r): hta(eq->hta), prevhtunits(0), dunits(0) {
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u32 nexthashbytes = hashsize(r);
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nexthtunits = hashwords(nexthashbytes);
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prevbo = 0;
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if (r) {
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u32 prevhashbytes = hashsize(r-1);
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prevhtunits = hashwords(prevhashbytes);
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prevbo = prevhtunits * sizeof(htunit) - prevhashbytes; // 0-3
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dunits = prevhtunits - nexthtunits;
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}
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}
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u32 getxhash0(const htunit* slot) const {
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#if WN == 200 && RESTBITS == 4
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return slot->bytes[prevbo] >> 4;
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#elif WN == 200 && RESTBITS == 8
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return (slot->bytes[prevbo] & 0xf) << 4 | slot->bytes[prevbo+1] >> 4;
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#elif WN == 200 && RESTBITS == 9
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return (slot->bytes[prevbo] & 0x1f) << 4 | slot->bytes[prevbo+1] >> 4;
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#elif WN == 144 && RESTBITS == 4
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return slot->bytes[prevbo] & 0xf;
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#else
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#error non implemented
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#endif
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}
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u32 getxhash1(const htunit* slot) const {
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#if WN == 200 && RESTBITS == 4
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return slot->bytes[prevbo] & 0xf;
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#elif WN == 200 && RESTBITS == 8
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return slot->bytes[prevbo];
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#elif WN == 200 && RESTBITS == 9
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return (slot->bytes[prevbo]&1) << 8 | slot->bytes[prevbo+1];
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#elif WN == 144 && RESTBITS == 4
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return slot->bytes[prevbo] & 0xf;
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#else
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#error non implemented
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#endif
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}
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bool equal(const htunit *hash0, const htunit *hash1) const {
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return hash0[prevhtunits-1].word == hash1[prevhtunits-1].word;
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}
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};
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struct collisiondata {
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#ifdef XBITMAP
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#if NSLOTS > 64
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#error cant use XBITMAP with more than 64 slots
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#endif
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u64 xhashmap[NRESTS];
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u64 xmap;
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#else
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#if RESTBITS <= 6
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typedef uchar xslot;
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#else
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typedef u16 xslot;
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#endif
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xslot nxhashslots[NRESTS];
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xslot xhashslots[NRESTS][XFULL];
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xslot *xx;
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u32 n0;
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u32 n1;
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#endif
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u32 s0;
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void clear() {
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#ifdef XBITMAP
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memset(xhashmap, 0, NRESTS * sizeof(u64));
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#else
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memset(nxhashslots, 0, NRESTS * sizeof(xslot));
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#endif
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}
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bool addslot(u32 s1, u32 xh) {
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#ifdef XBITMAP
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xmap = xhashmap[xh];
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xhashmap[xh] |= (u64)1 << s1;
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s0 = -1;
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return true;
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#else
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n1 = (u32)nxhashslots[xh]++;
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if (n1 >= XFULL)
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return false;
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xx = xhashslots[xh];
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xx[n1] = s1;
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n0 = 0;
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return true;
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#endif
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}
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bool nextcollision() const {
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#ifdef XBITMAP
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return xmap != 0;
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#else
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return n0 < n1;
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#endif
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}
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u32 slot() {
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#ifdef XBITMAP
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const u32 ffs = __builtin_ffsll(xmap);
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s0 += ffs; xmap >>= ffs;
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return s0;
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#else
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return (u32)xx[n0++];
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#endif
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}
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};
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void digit0(const u32 id) {
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uchar hash[HASHOUT];
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blake2b_state state;
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htlayout htl(this, 0);
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const u32 hashbytes = hashsize(0);
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for (u32 block = id; block < NBLOCKS; block += nthreads) {
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state = blake_ctx;
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u32 leb = htole32(block);
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blake2b_update(&state, (uchar *)&leb, sizeof(u32));
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blake2b_final(&state, hash, HASHOUT);
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for (u32 i = 0; i<HASHESPERBLAKE; i++) {
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const uchar *ph = hash + i * WN/8;
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#if BUCKBITS == 16 && RESTBITS == 4
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const u32 bucketid = ((u32)ph[0] << 8) | ph[1];
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#elif BUCKBITS == 12 && RESTBITS == 8
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const u32 bucketid = ((u32)ph[0] << 4) | ph[1] >> 4;
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#elif BUCKBITS == 11 && RESTBITS == 9
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const u32 bucketid = ((u32)ph[0] << 3) | ph[1] >> 5;
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#elif BUCKBITS == 20 && RESTBITS == 4
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const u32 bucketid = ((((u32)ph[0] << 8) | ph[1]) << 4) | ph[2] >> 4;
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#elif BUCKBITS == 12 && RESTBITS == 4
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const u32 bucketid = ((u32)ph[0] << 4) | ph[1] >> 4;
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const u32 xhash = ph[1] & 0xf;
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#else
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#error not implemented
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#endif
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const u32 slot = getslot(0, bucketid);
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if (slot >= NSLOTS) {
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bfull++;
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continue;
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}
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htunit *s = hta.heap0[bucketid][slot] + htl.nexthtunits;
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memcpy(s->bytes-hashbytes, ph+WN/8-hashbytes, hashbytes);
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s->tag = tree(block * HASHESPERBLAKE + i);
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}
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}
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}
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void digitodd(const u32 r, const u32 id) {
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htlayout htl(this, r);
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collisiondata cd;
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for (u32 bucketid=id; bucketid < NBUCKETS; bucketid += nthreads) {
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cd.clear();
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slot0 *buck = htl.hta.heap0[bucketid];
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u32 bsize = getnslots(r-1, bucketid);
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for (u32 s1 = 0; s1 < bsize; s1++) {
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const htunit *slot1 = buck[s1];
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if (!cd.addslot(s1, htl.getxhash0(slot1))) {
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xfull++;
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continue;
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}
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for (; cd.nextcollision(); ) {
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const u32 s0 = cd.slot();
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const htunit *slot0 = buck[s0];
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if (htl.equal(slot0, slot1)) {
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hfull++;
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continue;
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}
|
|
u32 xorbucketid;
|
|
const uchar *bytes0 = slot0->bytes, *bytes1 = slot1->bytes;
|
|
#if WN == 200 && BUCKBITS == 12 && RESTBITS == 8
|
|
xorbucketid = (((u32)(bytes0[htl.prevbo+1] ^ bytes1[htl.prevbo+1]) & 0xf) << 8)
|
|
| (bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2]);
|
|
#elif WN == 200 && BUCKBITS == 11 && RESTBITS == 9
|
|
xorbucketid = (((u32)(bytes0[htl.prevbo+1] ^ bytes1[htl.prevbo+1]) & 0xf) << 7)
|
|
| (bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2]) >> 1;
|
|
#elif WN == 144 && BUCKBITS == 20 && RESTBITS == 4
|
|
xorbucketid = ((((u32)(bytes0[htl.prevbo+1] ^ bytes1[htl.prevbo+1]) << 8)
|
|
| (bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2])) << 4)
|
|
| (bytes0[htl.prevbo+3] ^ bytes1[htl.prevbo+3]) >> 4;
|
|
#elif WN == 96 && BUCKBITS == 12 && RESTBITS == 4
|
|
xorbucketid = ((u32)(bytes0[htl.prevbo+1] ^ bytes1[htl.prevbo+1]) << 4)
|
|
| (bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2]) >> 4;
|
|
#else
|
|
#error not implemented
|
|
#endif
|
|
const u32 xorslot = getslot(r, xorbucketid);
|
|
if (xorslot >= NSLOTS) {
|
|
bfull++;
|
|
continue;
|
|
}
|
|
htunit *xs = htl.hta.heap1[xorbucketid][xorslot];
|
|
for (u32 i=htl.dunits; i < htl.prevhtunits; i++)
|
|
xs++->word = slot0[i].word ^ slot1[i].word;
|
|
xs->tag = tree(bucketid, s0, s1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void digiteven(const u32 r, const u32 id) {
|
|
htlayout htl(this, r);
|
|
collisiondata cd;
|
|
for (u32 bucketid=id; bucketid < NBUCKETS; bucketid += nthreads) {
|
|
cd.clear();
|
|
slot1 *buck = htl.hta.heap1[bucketid];
|
|
u32 bsize = getnslots(r-1, bucketid);
|
|
for (u32 s1 = 0; s1 < bsize; s1++) {
|
|
const htunit *slot1 = buck[s1];
|
|
if (!cd.addslot(s1, htl.getxhash1(slot1))) {
|
|
xfull++;
|
|
continue;
|
|
}
|
|
for (; cd.nextcollision(); ) {
|
|
const u32 s0 = cd.slot();
|
|
const htunit *slot0 = buck[s0];
|
|
if (htl.equal(slot0, slot1)) {
|
|
hfull++;
|
|
continue;
|
|
}
|
|
u32 xorbucketid;
|
|
const uchar *bytes0 = slot0->bytes, *bytes1 = slot1->bytes;
|
|
#if WN == 200 && BUCKBITS == 12 && RESTBITS == 8
|
|
xorbucketid = ((u32)(bytes0[htl.prevbo+1] ^ bytes1[htl.prevbo+1]) << 4)
|
|
| (bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2]) >> 4;
|
|
#elif WN == 200 && BUCKBITS == 11 && RESTBITS == 9
|
|
xorbucketid = ((u32)(bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2]) << 3)
|
|
| (bytes0[htl.prevbo+3] ^ bytes1[htl.prevbo+3]) >> 5;
|
|
#elif WN == 144 && BUCKBITS == 20 && RESTBITS == 4
|
|
xorbucketid = ((((u32)(bytes0[htl.prevbo+1] ^ bytes1[htl.prevbo+1]) << 8)
|
|
| (bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2])) << 4)
|
|
| (bytes0[htl.prevbo+3] ^ bytes1[htl.prevbo+3]) >> 4;
|
|
#elif WN == 96 && BUCKBITS == 12 && RESTBITS == 4
|
|
xorbucketid = ((u32)(bytes0[htl.prevbo+1] ^ bytes1[htl.prevbo+1]) << 4)
|
|
| (bytes0[htl.prevbo+2] ^ bytes1[htl.prevbo+2]) >> 4;
|
|
#else
|
|
#error not implemented
|
|
#endif
|
|
const u32 xorslot = getslot(r, xorbucketid);
|
|
if (xorslot >= NSLOTS) {
|
|
bfull++;
|
|
continue;
|
|
}
|
|
htunit *xs = htl.hta.heap0[xorbucketid][xorslot];
|
|
for (u32 i=htl.dunits; i < htl.prevhtunits; i++)
|
|
xs++->word = slot0[i].word ^ slot1[i].word;
|
|
xs->tag = tree(bucketid, s0, s1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void digitK(const u32 id) {
|
|
collisiondata cd;
|
|
htlayout htl(this, WK);
|
|
u32 nc = 0;
|
|
for (u32 bucketid = id; bucketid < NBUCKETS; bucketid += nthreads) {
|
|
cd.clear();
|
|
slot0 *buck = htl.hta.heap0[bucketid];
|
|
u32 bsize = getnslots(WK-1, bucketid);
|
|
for (u32 s1 = 0; s1 < bsize; s1++) {
|
|
const htunit *slot1 = buck[s1];
|
|
if (!cd.addslot(s1, htl.getxhash0(slot1))) // assume WK odd
|
|
continue;
|
|
for (; cd.nextcollision(); ) {
|
|
const u32 s0 = cd.slot();
|
|
if (htl.equal(buck[s0], slot1))
|
|
nc++, candidate(tree(bucketid, s0, s1));
|
|
}
|
|
}
|
|
}
|
|
printf(" %d candidates ", nc);
|
|
}
|
|
};
|
|
|
|
typedef struct {
|
|
u32 id;
|
|
pthread_t thread;
|
|
equi *eq;
|
|
} thread_ctx;
|
|
|
|
void barrier(pthread_barrier_t *barry) {
|
|
const int rc = pthread_barrier_wait(barry);
|
|
if (rc != 0 && rc != PTHREAD_BARRIER_SERIAL_THREAD) {
|
|
printf("Could not wait on barrier\n");
|
|
pthread_exit(NULL);
|
|
}
|
|
}
|
|
|
|
void *worker(void *vp) {
|
|
thread_ctx *tp = (thread_ctx *)vp;
|
|
equi *eq = tp->eq;
|
|
|
|
if (tp->id == 0)
|
|
printf("Digit 0\n");
|
|
barrier(&eq->barry);
|
|
eq->digit0(tp->id);
|
|
barrier(&eq->barry);
|
|
if (tp->id == 0) {
|
|
eq->xfull = eq->bfull = eq->hfull = 0;
|
|
eq->showbsizes(0);
|
|
}
|
|
barrier(&eq->barry);
|
|
for (u32 r = 1; r < WK; r++) {
|
|
if (tp->id == 0)
|
|
printf("Digit %d", r);
|
|
barrier(&eq->barry);
|
|
r&1 ? eq->digitodd(r, tp->id) : eq->digiteven(r, tp->id);
|
|
barrier(&eq->barry);
|
|
if (tp->id == 0) {
|
|
printf(" x%d b%d h%d\n", eq->xfull, eq->bfull, eq->hfull);
|
|
eq->xfull = eq->bfull = eq->hfull = 0;
|
|
eq->showbsizes(r);
|
|
}
|
|
barrier(&eq->barry);
|
|
}
|
|
if (tp->id == 0)
|
|
printf("Digit %d\n", WK);
|
|
eq->digitK(tp->id);
|
|
barrier(&eq->barry);
|
|
pthread_exit(NULL);
|
|
return 0;
|
|
}
|