diff options
author | Avneesh Saluja <asaluja@gmail.com> | 2013-03-28 18:28:16 -0700 |
---|---|---|
committer | Avneesh Saluja <asaluja@gmail.com> | 2013-03-28 18:28:16 -0700 |
commit | 3d8d656fa7911524e0e6885647173474524e0784 (patch) | |
tree | 81b1ee2fcb67980376d03f0aa48e42e53abff222 /training/dtrain/dtrain.cc | |
parent | be7f57fdd484e063775d7abf083b9fa4c403b610 (diff) | |
parent | 96fedabebafe7a38a6d5928be8fff767e411d705 (diff) |
fixed conflicts
Diffstat (limited to 'training/dtrain/dtrain.cc')
-rw-r--r-- | training/dtrain/dtrain.cc | 553 |
1 files changed, 553 insertions, 0 deletions
diff --git a/training/dtrain/dtrain.cc b/training/dtrain/dtrain.cc new file mode 100644 index 00000000..149f87d4 --- /dev/null +++ b/training/dtrain/dtrain.cc @@ -0,0 +1,553 @@ +#include "dtrain.h" + + +bool +dtrain_init(int argc, char** argv, po::variables_map* cfg) +{ + po::options_description ini("Configuration File Options"); + ini.add_options() + ("input", po::value<string>()->default_value("-"), "input file (src)") + ("refs,r", po::value<string>(), "references") + ("output", po::value<string>()->default_value("-"), "output weights file, '-' for STDOUT") + ("input_weights", po::value<string>(), "input weights file (e.g. from previous iteration)") + ("decoder_config", po::value<string>(), "configuration file for cdec") + ("print_weights", po::value<string>(), "weights to print on each iteration") + ("stop_after", po::value<unsigned>()->default_value(0), "stop after X input sentences") + ("keep", po::value<bool>()->zero_tokens(), "keep weights files for each iteration") + ("epochs", po::value<unsigned>()->default_value(10), "# of iterations T (per shard)") + ("k", po::value<unsigned>()->default_value(100), "how many translations to sample") + ("sample_from", po::value<string>()->default_value("kbest"), "where to sample translations from: 'kbest', 'forest'") + ("filter", po::value<string>()->default_value("uniq"), "filter kbest list: 'not', 'uniq'") + ("pair_sampling", po::value<string>()->default_value("XYX"), "how to sample pairs: 'all', 'XYX' or 'PRO'") + ("hi_lo", po::value<float>()->default_value(0.1), "hi and lo (X) for XYX (default 0.1), <= 0.5") + ("pair_threshold", po::value<score_t>()->default_value(0.), "bleu [0,1] threshold to filter pairs") + ("N", po::value<unsigned>()->default_value(4), "N for Ngrams (BLEU)") + ("scorer", po::value<string>()->default_value("stupid_bleu"), "scoring: bleu, stupid_, smooth_, approx_, lc_") + ("learning_rate", po::value<weight_t>()->default_value(1.0), "learning rate") + ("gamma", po::value<weight_t>()->default_value(0.), "gamma for SVM (0 for perceptron)") + ("select_weights", po::value<string>()->default_value("last"), "output best, last, avg weights ('VOID' to throw away)") + ("rescale", po::value<bool>()->zero_tokens(), "rescale weight vector after each input") + ("l1_reg", po::value<string>()->default_value("none"), "apply l1 regularization as in 'Tsuroka et al' (2010) UNTESTED") + ("l1_reg_strength", po::value<weight_t>(), "l1 regularization strength") + ("fselect", po::value<weight_t>()->default_value(-1), "select top x percent (or by threshold) of features after each epoch NOT IMPLEMENTED") // TODO + ("approx_bleu_d", po::value<score_t>()->default_value(0.9), "discount for approx. BLEU") + ("scale_bleu_diff", po::value<bool>()->zero_tokens(), "learning rate <- bleu diff of a misranked pair") + ("loss_margin", po::value<weight_t>()->default_value(0.), "update if no error in pref pair but model scores this near") + ("max_pairs", po::value<unsigned>()->default_value(std::numeric_limits<unsigned>::max()), "max. # of pairs per Sent.") + ("noup", po::value<bool>()->zero_tokens(), "do not update weights"); + po::options_description cl("Command Line Options"); + cl.add_options() + ("config,c", po::value<string>(), "dtrain config file") + ("quiet,q", po::value<bool>()->zero_tokens(), "be quiet") + ("verbose,v", po::value<bool>()->zero_tokens(), "be verbose"); + cl.add(ini); + po::store(parse_command_line(argc, argv, cl), *cfg); + if (cfg->count("config")) { + ifstream ini_f((*cfg)["config"].as<string>().c_str()); + po::store(po::parse_config_file(ini_f, ini), *cfg); + } + po::notify(*cfg); + if (!cfg->count("decoder_config")) { + cerr << cl << endl; + return false; + } + if ((*cfg)["sample_from"].as<string>() != "kbest" + && (*cfg)["sample_from"].as<string>() != "forest") { + cerr << "Wrong 'sample_from' param: '" << (*cfg)["sample_from"].as<string>() << "', use 'kbest' or 'forest'." << endl; + return false; + } + if ((*cfg)["sample_from"].as<string>() == "kbest" && (*cfg)["filter"].as<string>() != "uniq" && + (*cfg)["filter"].as<string>() != "not") { + cerr << "Wrong 'filter' param: '" << (*cfg)["filter"].as<string>() << "', use 'uniq' or 'not'." << endl; + return false; + } + if ((*cfg)["pair_sampling"].as<string>() != "all" && (*cfg)["pair_sampling"].as<string>() != "XYX" && + (*cfg)["pair_sampling"].as<string>() != "PRO") { + cerr << "Wrong 'pair_sampling' param: '" << (*cfg)["pair_sampling"].as<string>() << "'." << endl; + return false; + } + if(cfg->count("hi_lo") && (*cfg)["pair_sampling"].as<string>() != "XYX") { + cerr << "Warning: hi_lo only works with pair_sampling XYX." << endl; + } + if((*cfg)["hi_lo"].as<float>() > 0.5 || (*cfg)["hi_lo"].as<float>() < 0.01) { + cerr << "hi_lo must lie in [0.01, 0.5]" << endl; + return false; + } + if ((*cfg)["pair_threshold"].as<score_t>() < 0) { + cerr << "The threshold must be >= 0!" << endl; + return false; + } + if ((*cfg)["select_weights"].as<string>() != "last" && (*cfg)["select_weights"].as<string>() != "best" && + (*cfg)["select_weights"].as<string>() != "avg" && (*cfg)["select_weights"].as<string>() != "VOID") { + cerr << "Wrong 'select_weights' param: '" << (*cfg)["select_weights"].as<string>() << "', use 'last' or 'best'." << endl; + return false; + } + return true; +} + +int +main(int argc, char** argv) +{ + // handle most parameters + po::variables_map cfg; + if (!dtrain_init(argc, argv, &cfg)) exit(1); // something is wrong + bool quiet = false; + if (cfg.count("quiet")) quiet = true; + bool verbose = false; + if (cfg.count("verbose")) verbose = true; + bool noup = false; + if (cfg.count("noup")) noup = true; + bool rescale = false; + if (cfg.count("rescale")) rescale = true; + bool keep = false; + if (cfg.count("keep")) keep = true; + + const unsigned k = cfg["k"].as<unsigned>(); + const unsigned N = cfg["N"].as<unsigned>(); + const unsigned T = cfg["epochs"].as<unsigned>(); + const unsigned stop_after = cfg["stop_after"].as<unsigned>(); + const string filter_type = cfg["filter"].as<string>(); + const string sample_from = cfg["sample_from"].as<string>(); + const string pair_sampling = cfg["pair_sampling"].as<string>(); + const score_t pair_threshold = cfg["pair_threshold"].as<score_t>(); + const string select_weights = cfg["select_weights"].as<string>(); + const float hi_lo = cfg["hi_lo"].as<float>(); + const score_t approx_bleu_d = cfg["approx_bleu_d"].as<score_t>(); + const unsigned max_pairs = cfg["max_pairs"].as<unsigned>(); + weight_t loss_margin = cfg["loss_margin"].as<weight_t>(); + if (loss_margin > 9998.) loss_margin = std::numeric_limits<float>::max(); + bool scale_bleu_diff = false; + if (cfg.count("scale_bleu_diff")) scale_bleu_diff = true; + bool average = false; + if (select_weights == "avg") + average = true; + vector<string> print_weights; + if (cfg.count("print_weights")) + boost::split(print_weights, cfg["print_weights"].as<string>(), boost::is_any_of(" ")); + + + // setup decoder + register_feature_functions(); + SetSilent(true); + ReadFile ini_rf(cfg["decoder_config"].as<string>()); + if (!quiet) + cerr << setw(25) << "cdec cfg " << "'" << cfg["decoder_config"].as<string>() << "'" << endl; + Decoder decoder(ini_rf.stream()); + + // scoring metric/scorer + string scorer_str = cfg["scorer"].as<string>(); + LocalScorer* scorer; + if (scorer_str == "bleu") { + scorer = dynamic_cast<BleuScorer*>(new BleuScorer); + } else if (scorer_str == "stupid_bleu") { + scorer = dynamic_cast<StupidBleuScorer*>(new StupidBleuScorer); + } else if (scorer_str == "fixed_stupid_bleu") { + scorer = dynamic_cast<FixedStupidBleuScorer*>(new FixedStupidBleuScorer); + } else if (scorer_str == "smooth_bleu") { + scorer = dynamic_cast<SmoothBleuScorer*>(new SmoothBleuScorer); + } else if (scorer_str == "sum_bleu") { + scorer = dynamic_cast<SumBleuScorer*>(new SumBleuScorer); + } else if (scorer_str == "sumexp_bleu") { + scorer = dynamic_cast<SumExpBleuScorer*>(new SumExpBleuScorer); + } else if (scorer_str == "sumwhatever_bleu") { + scorer = dynamic_cast<SumWhateverBleuScorer*>(new SumWhateverBleuScorer); + } else if (scorer_str == "approx_bleu") { + scorer = dynamic_cast<ApproxBleuScorer*>(new ApproxBleuScorer(N, approx_bleu_d)); + } else if (scorer_str == "lc_bleu") { + scorer = dynamic_cast<LinearBleuScorer*>(new LinearBleuScorer(N)); + } else { + cerr << "Don't know scoring metric: '" << scorer_str << "', exiting." << endl; + exit(1); + } + vector<score_t> bleu_weights; + scorer->Init(N, bleu_weights); + + // setup decoder observer + MT19937 rng; // random number generator, only for forest sampling + HypSampler* observer; + if (sample_from == "kbest") + observer = dynamic_cast<KBestGetter*>(new KBestGetter(k, filter_type)); + else + observer = dynamic_cast<KSampler*>(new KSampler(k, &rng)); + observer->SetScorer(scorer); + + // init weights + vector<weight_t>& dense_weights = decoder.CurrentWeightVector(); + SparseVector<weight_t> lambdas, cumulative_penalties, w_average; + if (cfg.count("input_weights")) Weights::InitFromFile(cfg["input_weights"].as<string>(), &dense_weights); + Weights::InitSparseVector(dense_weights, &lambdas); + + // meta params for perceptron, SVM + weight_t eta = cfg["learning_rate"].as<weight_t>(); + weight_t gamma = cfg["gamma"].as<weight_t>(); + + // faster perceptron: consider only misranked pairs, see + // DO NOT ENABLE WITH SVM (gamma > 0) OR loss_margin! + bool faster_perceptron = false; + if (gamma==0 && loss_margin==0) faster_perceptron = true; + + // l1 regularization + bool l1naive = false; + bool l1clip = false; + bool l1cumul = false; + weight_t l1_reg = 0; + if (cfg["l1_reg"].as<string>() != "none") { + string s = cfg["l1_reg"].as<string>(); + if (s == "naive") l1naive = true; + else if (s == "clip") l1clip = true; + else if (s == "cumul") l1cumul = true; + l1_reg = cfg["l1_reg_strength"].as<weight_t>(); + } + + // output + string output_fn = cfg["output"].as<string>(); + // input + string input_fn = cfg["input"].as<string>(); + ReadFile input(input_fn); + // buffer input for t > 0 + vector<string> src_str_buf; // source strings (decoder takes only strings) + vector<vector<WordID> > ref_ids_buf; // references as WordID vecs + string refs_fn = cfg["refs"].as<string>(); + ReadFile refs(refs_fn); + + unsigned in_sz = std::numeric_limits<unsigned>::max(); // input index, input size + vector<pair<score_t, score_t> > all_scores; + score_t max_score = 0.; + unsigned best_it = 0; + float overall_time = 0.; + + // output cfg + if (!quiet) { + cerr << _p5; + cerr << endl << "dtrain" << endl << "Parameters:" << endl; + cerr << setw(25) << "k " << k << endl; + cerr << setw(25) << "N " << N << endl; + cerr << setw(25) << "T " << T << endl; + cerr << setw(26) << "scorer '" << scorer_str << "'" << endl; + if (scorer_str == "approx_bleu") + cerr << setw(25) << "approx. B discount " << approx_bleu_d << endl; + cerr << setw(25) << "sample from " << "'" << sample_from << "'" << endl; + if (sample_from == "kbest") + cerr << setw(25) << "filter " << "'" << filter_type << "'" << endl; + if (!scale_bleu_diff) cerr << setw(25) << "learning rate " << eta << endl; + else cerr << setw(25) << "learning rate " << "bleu diff" << endl; + cerr << setw(25) << "gamma " << gamma << endl; + cerr << setw(25) << "loss margin " << loss_margin << endl; + cerr << setw(25) << "faster perceptron " << faster_perceptron << endl; + cerr << setw(25) << "pairs " << "'" << pair_sampling << "'" << endl; + if (pair_sampling == "XYX") + cerr << setw(25) << "hi lo " << hi_lo << endl; + cerr << setw(25) << "pair threshold " << pair_threshold << endl; + cerr << setw(25) << "select weights " << "'" << select_weights << "'" << endl; + if (cfg.count("l1_reg")) + cerr << setw(25) << "l1 reg " << l1_reg << " '" << cfg["l1_reg"].as<string>() << "'" << endl; + if (rescale) + cerr << setw(25) << "rescale " << rescale << endl; + cerr << setw(25) << "max pairs " << max_pairs << endl; + cerr << setw(25) << "cdec cfg " << "'" << cfg["decoder_config"].as<string>() << "'" << endl; + cerr << setw(25) << "input " << "'" << input_fn << "'" << endl; + cerr << setw(25) << "refs " << "'" << refs_fn << "'" << endl; + cerr << setw(25) << "output " << "'" << output_fn << "'" << endl; + if (cfg.count("input_weights")) + cerr << setw(25) << "weights in " << "'" << cfg["input_weights"].as<string>() << "'" << endl; + if (stop_after > 0) + cerr << setw(25) << "stop_after " << stop_after << endl; + if (!verbose) cerr << "(a dot represents " << DTRAIN_DOTS << " inputs)" << endl; + } + + + for (unsigned t = 0; t < T; t++) // T epochs + { + + time_t start, end; + time(&start); + score_t score_sum = 0.; + score_t model_sum(0); + unsigned ii = 0, rank_errors = 0, margin_violations = 0, npairs = 0, f_count = 0, list_sz = 0; + if (!quiet) cerr << "Iteration #" << t+1 << " of " << T << "." << endl; + + while(true) + { + + string in; + bool next = false, stop = false; // next iteration or premature stop + if (t == 0) { + if(!getline(*input, in)) next = true; + } else { + if (ii == in_sz) next = true; // stop if we reach the end of our input + } + // stop after X sentences (but still go on for those) + if (stop_after > 0 && stop_after == ii && !next) stop = true; + + // produce some pretty output + if (!quiet && !verbose) { + if (ii == 0) cerr << " "; + if ((ii+1) % (DTRAIN_DOTS) == 0) { + cerr << "."; + cerr.flush(); + } + if ((ii+1) % (20*DTRAIN_DOTS) == 0) { + cerr << " " << ii+1 << endl; + if (!next && !stop) cerr << " "; + } + if (stop) { + if (ii % (20*DTRAIN_DOTS) != 0) cerr << " " << ii << endl; + cerr << "Stopping after " << stop_after << " input sentences." << endl; + } else { + if (next) { + if (ii % (20*DTRAIN_DOTS) != 0) cerr << " " << ii << endl; + } + } + } + + // next iteration + if (next || stop) break; + + // weights + lambdas.init_vector(&dense_weights); + + // getting input + vector<WordID> ref_ids; // reference as vector<WordID> + if (t == 0) { + string r_; + getline(*refs, r_); + vector<string> ref_tok; + boost::split(ref_tok, r_, boost::is_any_of(" ")); + register_and_convert(ref_tok, ref_ids); + ref_ids_buf.push_back(ref_ids); + src_str_buf.push_back(in); + } else { + ref_ids = ref_ids_buf[ii]; + } + observer->SetRef(ref_ids); + if (t == 0) + decoder.Decode(in, observer); + else + decoder.Decode(src_str_buf[ii], observer); + + // get (scored) samples + vector<ScoredHyp>* samples = observer->GetSamples(); + + if (verbose) { + cerr << "--- ref for " << ii << ": "; + if (t > 0) printWordIDVec(ref_ids_buf[ii]); + else printWordIDVec(ref_ids); + cerr << endl; + for (unsigned u = 0; u < samples->size(); u++) { + cerr << _p2 << _np << "[" << u << ". '"; + printWordIDVec((*samples)[u].w); + cerr << "'" << endl; + cerr << "SCORE=" << (*samples)[u].score << ",model="<< (*samples)[u].model << endl; + cerr << "F{" << (*samples)[u].f << "} ]" << endl << endl; + } + } + + score_sum += (*samples)[0].score; // stats for 1best + model_sum += (*samples)[0].model; + + f_count += observer->get_f_count(); + list_sz += observer->get_sz(); + + // weight updates + if (!noup) { + // get pairs + vector<pair<ScoredHyp,ScoredHyp> > pairs; + if (pair_sampling == "all") + all_pairs(samples, pairs, pair_threshold, max_pairs, faster_perceptron); + if (pair_sampling == "XYX") + partXYX(samples, pairs, pair_threshold, max_pairs, faster_perceptron, hi_lo); + if (pair_sampling == "PRO") + PROsampling(samples, pairs, pair_threshold, max_pairs); + npairs += pairs.size(); + + for (vector<pair<ScoredHyp,ScoredHyp> >::iterator it = pairs.begin(); + it != pairs.end(); it++) { + bool rank_error; + score_t margin; + if (faster_perceptron) { // we only have considering misranked pairs + rank_error = true; // pair sampling already did this for us + margin = std::numeric_limits<float>::max(); + } else { + rank_error = it->first.model <= it->second.model; + margin = fabs(fabs(it->first.model) - fabs(it->second.model)); + if (!rank_error && margin < loss_margin) margin_violations++; + } + if (rank_error) rank_errors++; + if (scale_bleu_diff) eta = it->first.score - it->second.score; + if (rank_error || margin < loss_margin) { + SparseVector<weight_t> diff_vec = it->first.f - it->second.f; + lambdas.plus_eq_v_times_s(diff_vec, eta); + if (gamma) + lambdas.plus_eq_v_times_s(lambdas, -2*gamma*eta*(1./npairs)); + } + } + + // l1 regularization + // please note that this penalizes _all_ weights + // (contrary to only the ones changed by the last update) + // after a _sentence_ (not after each example/pair) + if (l1naive) { + FastSparseVector<weight_t>::iterator it = lambdas.begin(); + for (; it != lambdas.end(); ++it) { + it->second -= sign(it->second) * l1_reg; + } + } else if (l1clip) { + FastSparseVector<weight_t>::iterator it = lambdas.begin(); + for (; it != lambdas.end(); ++it) { + if (it->second != 0) { + weight_t v = it->second; + if (v > 0) { + it->second = max(0., v - l1_reg); + } else { + it->second = min(0., v + l1_reg); + } + } + } + } else if (l1cumul) { + weight_t acc_penalty = (ii+1) * l1_reg; // ii is the index of the current input + FastSparseVector<weight_t>::iterator it = lambdas.begin(); + for (; it != lambdas.end(); ++it) { + if (it->second != 0) { + weight_t v = it->second; + weight_t penalized = 0.; + if (v > 0) { + penalized = max(0., v-(acc_penalty + cumulative_penalties.get(it->first))); + } else { + penalized = min(0., v+(acc_penalty - cumulative_penalties.get(it->first))); + } + it->second = penalized; + cumulative_penalties.set_value(it->first, cumulative_penalties.get(it->first)+penalized); + } + } + } + + } + + if (rescale) lambdas /= lambdas.l2norm(); + + ++ii; + + } // input loop + + if (average) w_average += lambdas; + + if (scorer_str == "approx_bleu" || scorer_str == "lc_bleu") scorer->Reset(); + + if (t == 0) { + in_sz = ii; // remember size of input (# lines) + } + + // print some stats + score_t score_avg = score_sum/(score_t)in_sz; + score_t model_avg = model_sum/(score_t)in_sz; + score_t score_diff, model_diff; + if (t > 0) { + score_diff = score_avg - all_scores[t-1].first; + model_diff = model_avg - all_scores[t-1].second; + } else { + score_diff = score_avg; + model_diff = model_avg; + } + + unsigned nonz = 0; + if (!quiet) nonz = (unsigned)lambdas.num_nonzero(); + + if (!quiet) { + cerr << _p5 << _p << "WEIGHTS" << endl; + for (vector<string>::iterator it = print_weights.begin(); it != print_weights.end(); it++) { + cerr << setw(18) << *it << " = " << lambdas.get(FD::Convert(*it)) << endl; + } + cerr << " ---" << endl; + cerr << _np << " 1best avg score: " << score_avg; + cerr << _p << " (" << score_diff << ")" << endl; + cerr << _np << " 1best avg model score: " << model_avg; + cerr << _p << " (" << model_diff << ")" << endl; + cerr << " avg # pairs: "; + cerr << _np << npairs/(float)in_sz; + if (faster_perceptron) cerr << " (meaningless)"; + cerr << endl; + cerr << " avg # rank err: "; + cerr << rank_errors/(float)in_sz << endl; + cerr << " avg # margin viol: "; + cerr << margin_violations/(float)in_sz << endl; + cerr << " non0 feature count: " << nonz << endl; + cerr << " avg list sz: " << list_sz/(float)in_sz << endl; + cerr << " avg f count: " << f_count/(float)list_sz << endl; + } + + pair<score_t,score_t> remember; + remember.first = score_avg; + remember.second = model_avg; + all_scores.push_back(remember); + if (score_avg > max_score) { + max_score = score_avg; + best_it = t; + } + time (&end); + float time_diff = difftime(end, start); + overall_time += time_diff; + if (!quiet) { + cerr << _p2 << _np << "(time " << time_diff/60. << " min, "; + cerr << time_diff/in_sz << " s/S)" << endl; + } + if (t+1 != T && !quiet) cerr << endl; + + if (noup) break; + + // write weights to file + if (select_weights == "best" || keep) { + lambdas.init_vector(&dense_weights); + string w_fn = "weights." + boost::lexical_cast<string>(t) + ".gz"; + Weights::WriteToFile(w_fn, dense_weights, true); + } + + } // outer loop + + if (average) w_average /= (weight_t)T; + + if (!noup) { + if (!quiet) cerr << endl << "Writing weights file to '" << output_fn << "' ..." << endl; + if (select_weights == "last" || average) { // last, average + WriteFile of(output_fn); // works with '-' + ostream& o = *of.stream(); + o.precision(17); + o << _np; + if (average) { + for (SparseVector<weight_t>::iterator it = w_average.begin(); it != w_average.end(); ++it) { + if (it->second == 0) continue; + o << FD::Convert(it->first) << '\t' << it->second << endl; + } + } else { + for (SparseVector<weight_t>::iterator it = lambdas.begin(); it != lambdas.end(); ++it) { + if (it->second == 0) continue; + o << FD::Convert(it->first) << '\t' << it->second << endl; + } + } + } else if (select_weights == "VOID") { // do nothing with the weights + } else { // best + if (output_fn != "-") { + CopyFile("weights."+boost::lexical_cast<string>(best_it)+".gz", output_fn); + } else { + ReadFile bestw("weights."+boost::lexical_cast<string>(best_it)+".gz"); + string o; + cout.precision(17); + cout << _np; + while(getline(*bestw, o)) cout << o << endl; + } + if (!keep) { + for (unsigned i = 0; i < T; i++) { + string s = "weights." + boost::lexical_cast<string>(i) + ".gz"; + unlink(s.c_str()); + } + } + } + if (!quiet) cerr << "done" << endl; + } + + if (!quiet) { + cerr << _p5 << _np << endl << "---" << endl << "Best iteration: "; + cerr << best_it+1 << " [SCORE '" << scorer_str << "'=" << max_score << "]." << endl; + cerr << "This took " << overall_time/60. << " min." << endl; + } +} + |