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-//: The goal of this skeleton is to make programs more easy to understand and
-//: more malleable, easy to rewrite in radical ways without accidentally
-//: breaking some corner case. Tests further both goals. They help
-//: understandability by letting one make small changes and get feedback. What
-//: if I wrote this line like so? What if I removed this function call, is it
-//: really necessary? Just try it, see if the tests pass. Want to explore
-//: rewriting this bit in this way? Tests put many refactorings on a firmer
-//: footing.
-//:
-//: But the usual way we write tests seems incomplete. Refactorings tend to
-//: work in the small, but don't help with changes to function boundaries. If
-//: you want to extract a new function you have to manually test-drive it to
-//: create tests for it. If you want to inline a function its tests are no
-//: longer valid. In both cases you end up having to reorganize code as well as
-//: tests, an error-prone activity.
-//:
-//: This file tries to fix this problem by supporting domain-driven testing
-//: We try to focus on the domain of inputs the program should work on. All
-//: tests invoke the program in a single way: by calling run() with different
-//: inputs. The program operates on the input and logs _facts_ it deduces to a
-//: trace:
-//:   trace("label") << "fact 1: " << val;
-//:
-//: The tests check for facts:
-//:   :(scenario foo)
-//:   34  # call run() with this input
-//:   +label: fact 1: 34  # trace should have logged this at the end
-//:   -label: fact 1: 35  # trace should never contain such a line
-//:
-//: Since we never call anything but the run() function directly, we never have
-//: to rewrite the tests when we reorganize the internals of the program. We
-//: just have to make sure our rewrite deduces the same facts about the domain,
-//: and that's something we're going to have to do anyway.
-//:
-//: To avoid the combinatorial explosion of integration tests, we organize the
-//: program into different layers, and each fact is logged to the trace with a
-//: specific label. Individual tests can focus on specific labels. In essence,
-//: validating the facts logged with a specific label is identical to calling
-//: some internal subsystem.
-//:
-//: Traces interact salubriously with layers. Thanks to our ordering
-//: directives, each layer can contain its own tests. They may rely on other
-//: layers, but when a test fails its usually due to breakage in the same
-//: layer. When multiple tests fail, it's usually useful to debug the very
-//: first test to fail. This is in contrast with the traditional approach,
-//: where changes can cause breakages in faraway subsystems, and picking the
-//: right test to debug can be an important skill to pick up.
-//:
-//: A final wrinkle is for recursive functions; it's often useful to segment
-//: calls of different depth in the trace:
-//:   +eval/1: => 34  # the topmost call to eval should have logged this line
-//: (look at new_trace_frame below)
-//:
-//: To build robust tests, trace facts about your domain rather than details of
-//: how you computed them.
-//:
-//: More details: http://akkartik.name/blog/tracing-tests
-//:
-//: ---
-//:
-//: Between layers and domain-driven testing, programming starts to look like a
-//: fundamentally different activity. Instead of a) superficial, b) local rules
-//: on c) code [like http://blog.bbv.ch/2013/06/05/clean-code-cheat-sheet],
-//: we allow programmers to engage with the a) deep, b) global structure of the
-//: c) domain. If you can systematically track discontinuities in the domain
-//: you don't care if the code used gotos as long as it passed the tests. If
-//: tests become more robust to run it becomes easier to try out radically
-//: different implementations for the same program. If code is super-easy to
-//: rewrite, it becomes less important what indentation style it uses, or that
-//: the objects are appropriately encapsulated, or that the functions are
-//: referentially transparent.
-//:
-//: Instead of plumbing, programming becomes building and gradually refining a
-//: map of the environment the program must operate under. Whether a program is
-//: 'correct' at a given point in time is a red herring; what matters is
-//: avoiding regression by monotonically nailing down the more 'eventful' parts
-//: of the terrain. It helps readers new and old and rewards curiosity to
-//: organize large programs in self-similar hiearchies of example scenarios
-//: colocated with the code that makes them work.
-//:
-//:   "Programming properly should be regarded as an activity by which
-//:   programmers form a mental model, rather than as production of a program."
-//:   -- Peter Naur (http://alistair.cockburn.us/ASD+book+extract%3A+%22Naur,+Ehn,+Musashi%22)
-
-:(before "int main")
-// End Tracing  // hack to ensure most code in this layer comes before anything else
-
-:(before "End Tracing")
-bool Hide_warnings = false;
-:(before "End Setup")
-//? cerr << "AAA setup\n"; //? 2
-Hide_warnings = false;
-
-:(before "End Tracing")
-struct trace_stream {
-  vector<pair<string, pair<int, string> > > past_lines;  // [(layer label, frame, line)]
-  map<string, int> frame;
-  // accumulator for current line
-  ostringstream* curr_stream;
-  string curr_layer;
-  string dump_layer;
-  trace_stream() :curr_stream(NULL) {}
-  ~trace_stream() { if (curr_stream) delete curr_stream; }
-
-  ostringstream& stream(string layer) {
-    newline();
-    curr_stream = new ostringstream;
-    curr_layer = layer;
-    return *curr_stream;
-  }
-
-  // be sure to call this before messing with curr_stream or curr_layer or frame
-  void newline() {
-    if (!curr_stream) return;
-    string curr_contents = curr_stream->str();
-    curr_contents.erase(curr_contents.find_last_not_of("\r\n")+1);
-    past_lines.push_back(pair<string, pair<int, string> >(curr_layer, pair<int, string>(frame[curr_layer], curr_contents)));
-    if (curr_layer == dump_layer || curr_layer == "dump" || dump_layer == "all" ||
-        (!Hide_warnings && curr_layer == "warn"))
-      cerr << curr_layer << '/' << frame[curr_layer] << ": " << curr_contents << '\n';
-    delete curr_stream;
-    curr_stream = NULL;
-  }
-
-  // Useful for debugging.
-  string readable_contents(string layer) {  // missing layer = everything, frame, hierarchical layers
-    newline();
-    ostringstream output;
-    string real_layer, frame;
-    parse_layer_and_frame(layer, &real_layer, &frame);
-    for (vector<pair<string, pair<int, string> > >::iterator p = past_lines.begin(); p != past_lines.end(); ++p)
-      if (layer.empty() || prefix_match(real_layer, p->first))
-        output << p->first << "/" << p->second.first << ": " << p->second.second << '\n';
-    return output.str();
-  }
-
-  // Useful for a newcomer to visualize the program at work.
-  void dump_browseable_contents(string layer) {
-    ofstream dump("dump");
-    dump << "<div class='frame' frame_index='1'>start</div>\n";
-    for (vector<pair<string, pair<int, string> > >::iterator p = past_lines.begin(); p != past_lines.end(); ++p) {
-      if (p->first != layer) continue;
-      dump << "<div class='frame";
-      if (p->second.first > 1) dump << " hidden";
-      dump << "' frame_index='" << p->second.first << "'>";
-      dump << p->second.second;
-      dump << "</div>\n";
-    }
-    dump.close();
-  }
-};
-
-
-
-trace_stream* Trace_stream = NULL;
-
-// Top-level helper. IMPORTANT: can't nest.
-#define trace(layer)  !Trace_stream ? cerr /*print nothing*/ : Trace_stream->stream(layer)
-// Warnings should go straight to cerr by default since calls to trace() have
-// some unfriendly constraints (they delay printing, they can't nest)
-#define raise  ((!Trace_stream || !Hide_warnings) ? cerr /*do print*/ : Trace_stream->stream("warn"))
-
-// A separate helper for debugging. We should only trace domain-specific
-// facts. For everything else use log.
-#define xlog if (false) log
-// To turn on logging replace 'xlog' with 'log'.
-#define log cerr
-
-:(before "End Types")
-// raise << die exits after printing -- unless Hide_warnings is set.
-struct die {};
-:(before "End Tracing")
-ostream& operator<<(ostream& os, unused die) {
-  if (Hide_warnings) return os;
-  os << "dying";
-  if (Trace_stream) Trace_stream->newline();
-  exit(1);
-}
-
-#define CLEAR_TRACE  delete Trace_stream, Trace_stream = new trace_stream;
-
-#define DUMP(layer)  if (Trace_stream) cerr << Trace_stream->readable_contents(layer);
-
-// Trace_stream is a resource, lease_tracer uses RAII to manage it.
-string Trace_file;
-static string Trace_dir = ".traces/";
-struct lease_tracer {
-  lease_tracer() { Trace_stream = new trace_stream; }
-  ~lease_tracer() {
-//?     cerr << "write to file? " << Trace_file << "$\n"; //? 2
-    if (!Trace_file.empty()) {
-//?       cerr << "writing\n"; //? 2
-      ofstream fout((Trace_dir+Trace_file).c_str());
-      fout << Trace_stream->readable_contents("");
-      fout.close();
-    }
-    delete Trace_stream, Trace_stream = NULL, Trace_file = "";
-  }
-};
-
-// To transparently save traces, start tests with the TEST() macro.
-#define TEST(name) void test_##name() { Trace_file = #name;
-
-#define START_TRACING_UNTIL_END_OF_SCOPE  lease_tracer leased_tracer;
-:(before "End Test Setup")
-START_TRACING_UNTIL_END_OF_SCOPE
-//? Trace_stream->dump_layer = "all"; //? 1
-
-:(before "End Tracing")
-void trace_all(const string& label, const list<string>& in) {
-  for (list<string>::const_iterator p = in.begin(); p != in.end(); ++p)
-    trace(label) << *p;
-}
-
-bool check_trace_contents(string FUNCTION, string FILE, int LINE, string expected) {  // missing layer == anywhere, frame, hierarchical layers
-  vector<string> expected_lines = split(expected, "");
-  index_t curr_expected_line = 0;
-  while (curr_expected_line < expected_lines.size() && expected_lines[curr_expected_line].empty())
-    ++curr_expected_line;
-  if (curr_expected_line == expected_lines.size()) return true;
-  Trace_stream->newline();
-  string layer, frame, contents;
-  parse_layer_frame_contents(expected_lines[curr_expected_line], &layer, &frame, &contents);
-  for (vector<pair<string, pair<int, string> > >::iterator p = Trace_stream->past_lines.begin(); p != Trace_stream->past_lines.end(); ++p) {
-    if (!layer.empty() && !prefix_match(layer, p->first))
-      continue;
-
-    if (!frame.empty() && strtol(frame.c_str(), NULL, 0) != p->second.first)
-      continue;
-
-    if (contents != p->second.second)
-      continue;
-
-    ++curr_expected_line;
-    while (curr_expected_line < expected_lines.size() && expected_lines[curr_expected_line].empty())
-      ++curr_expected_line;
-    if (curr_expected_line == expected_lines.size()) return true;
-    parse_layer_frame_contents(expected_lines[curr_expected_line], &layer, &frame, &contents);
-  }
-
-  ++Num_failures;
-  cerr << "\nF " << FUNCTION << "(" << FILE << ":" << LINE << "): missing [" << contents << "] in trace:\n";
-  DUMP(layer);
-  Passed = false;
-  return false;
-}
-
-void parse_layer_frame_contents(const string& orig, string* layer, string* frame, string* contents) {
-  string layer_and_frame;
-  parse_contents(orig, ": ", &layer_and_frame, contents);
-  parse_layer_and_frame(layer_and_frame, layer, frame);
-}
-
-void parse_contents(const string& s, const string& delim, string* prefix, string* contents) {
-  index_t pos = s.find(delim);
-  if (pos == NOT_FOUND) {
-    *prefix = "";
-    *contents = s;
-  }
-  else {
-    *prefix = s.substr(0, pos);
-    *contents = s.substr(pos+delim.size());
-  }
-}
-
-void parse_layer_and_frame(const string& orig, string* layer, string* frame) {
-  index_t last_slash = orig.rfind('/');
-  if (last_slash == NOT_FOUND
-      || orig.find_last_not_of("0123456789") != last_slash) {
-    *layer = orig;
-    *frame = "";
-  }
-  else {
-    *layer = orig.substr(0, last_slash);
-    *frame = orig.substr(last_slash+1);
-  }
-}
-
-
-
-bool check_trace_contents(string FUNCTION, string FILE, int LINE, string layer, string expected) {  // empty layer == everything, multiple layers, hierarchical layers
-  vector<string> expected_lines = split(expected, "");
-  index_t curr_expected_line = 0;
-  while (curr_expected_line < expected_lines.size() && expected_lines[curr_expected_line].empty())
-    ++curr_expected_line;
-  if (curr_expected_line == expected_lines.size()) return true;
-  Trace_stream->newline();
-  vector<string> layers = split(layer, ",");
-  for (vector<pair<string, pair<int, string> > >::iterator p = Trace_stream->past_lines.begin(); p != Trace_stream->past_lines.end(); ++p) {
-    if (!layer.empty() && !any_prefix_match(layers, p->first))
-      continue;
-    if (p->second.second != expected_lines[curr_expected_line])
-      continue;
-    ++curr_expected_line;
-    while (curr_expected_line < expected_lines.size() && expected_lines[curr_expected_line].empty())
-      ++curr_expected_line;
-    if (curr_expected_line == expected_lines.size()) return true;
-  }
-
-  ++Num_failures;
-  cerr << "\nF " << FUNCTION << "(" << FILE << ":" << LINE << "): missing [" << expected_lines[curr_expected_line] << "] in trace:\n";
-  DUMP(layer);
-  Passed = false;
-  return false;
-}
-
-#define CHECK_TRACE_CONTENTS(...)  check_trace_contents(__FUNCTION__, __FILE__, __LINE__, __VA_ARGS__)
-
-int trace_count(string layer) {
-  return trace_count(layer, "");
-}
-
-int trace_count(string layer, string line) {
-  Trace_stream->newline();
-  long result = 0;
-  vector<string> layers = split(layer, ",");
-  for (vector<pair<string, pair<int, string> > >::iterator p = Trace_stream->past_lines.begin(); p != Trace_stream->past_lines.end(); ++p) {
-    if (any_prefix_match(layers, p->first))
-      if (line == "" || p->second.second == line)
-        ++result;
-  }
-  return result;
-}
-
-int trace_count(string layer, int frame, string line) {
-  Trace_stream->newline();
-  long result = 0;
-  vector<string> layers = split(layer, ",");
-  for (vector<pair<string, pair<int, string> > >::iterator p = Trace_stream->past_lines.begin(); p != Trace_stream->past_lines.end(); ++p) {
-    if (any_prefix_match(layers, p->first) && p->second.first == frame)
-      if (line == "" || p->second.second == line)
-        ++result;
-  }
-  return result;
-}
-
-#define CHECK_TRACE_WARNS()  CHECK(trace_count("warn") > 0)
-#define CHECK_TRACE_DOESNT_WARN() \
-  if (trace_count("warn") > 0) { \
-    ++Num_failures; \
-    cerr << "\nF " << __FUNCTION__ << "(" << __FILE__ << ":" << __LINE__ << "): unexpected warnings\n"; \
-    DUMP("warn"); \
-    Passed = false; \
-    return; \
-  }
-
-bool trace_doesnt_contain(string layer, string line) {
-  return trace_count(layer, line) == 0;
-}
-
-bool trace_doesnt_contain(string expected) {
-  vector<string> tmp = split(expected, ": ");
-  return trace_doesnt_contain(tmp[0], tmp[1]);
-}
-
-bool trace_doesnt_contain(string layer, int frame, string line) {
-  return trace_count(layer, frame, line) == 0;
-}
-
-#define CHECK_TRACE_DOESNT_CONTAIN(...)  CHECK(trace_doesnt_contain(__VA_ARGS__))
-
-
-
-// manage layer counts in Trace_stream using RAII
-struct lease_trace_frame {
-  string layer;
-  lease_trace_frame(string l) :layer(l) {
-    if (!Trace_stream) return;
-    Trace_stream->newline();
-    ++Trace_stream->frame[layer];
-  }
-  ~lease_trace_frame() {
-    if (!Trace_stream) return;
-    Trace_stream->newline();
-    --Trace_stream->frame[layer];
-  }
-};
-#define new_trace_frame(layer)  lease_trace_frame leased_frame(layer);
-
-bool check_trace_contents(string FUNCTION, string FILE, int LINE, string layer, int frame, string expected) {  // multiple layers, hierarchical layers
-  vector<string> expected_lines = split(expected, "");  // hack: doesn't handle newlines in embedded in lines
-  index_t curr_expected_line = 0;
-  while (curr_expected_line < expected_lines.size() && expected_lines[curr_expected_line].empty())
-    ++curr_expected_line;
-  if (curr_expected_line == expected_lines.size()) return true;
-  Trace_stream->newline();
-  vector<string> layers = split(layer, ",");
-  for (vector<pair<string, pair<int, string> > >::iterator p = Trace_stream->past_lines.begin(); p != Trace_stream->past_lines.end(); ++p) {
-    if (!layer.empty() && !any_prefix_match(layers, p->first))
-      continue;
-    if (p->second.first != frame)
-      continue;
-    if (p->second.second != expected_lines[curr_expected_line])
-      continue;
-    ++curr_expected_line;
-    while (curr_expected_line < expected_lines.size() && expected_lines[curr_expected_line].empty())
-      ++curr_expected_line;
-    if (curr_expected_line == expected_lines.size()) return true;
-  }
-
-  ++Num_failures;
-  cerr << "\nF " << FUNCTION << "(" << FILE << ":" << LINE << "): missing [" << expected_lines[curr_expected_line] << "] in trace/" << frame << ":\n";
-  DUMP(layer);
-  Passed = false;
-  return false;
-}
-
-#define CHECK_TRACE_TOP(layer, expected)  CHECK_TRACE_CONTENTS(layer, 1, expected)
-
-
-
-vector<string> split(string s, string delim) {
-  vector<string> result;
-  index_t begin=0, end=s.find(delim);
-  while (true) {
-    if (end == NOT_FOUND) {
-      result.push_back(string(s, begin, NOT_FOUND));
-      break;
-    }
-    result.push_back(string(s, begin, end-begin));
-    begin = end+delim.size();
-    end = s.find(delim, begin);
-  }
-  return result;
-}
-
-bool any_prefix_match(const vector<string>& pats, const string& needle) {
-  if (pats.empty()) return false;
-  if (*pats[0].rbegin() != '/')
-    // prefix match not requested
-    return find(pats.begin(), pats.end(), needle) != pats.end();
-  // first pat ends in a '/'; assume all pats do.
-  for (vector<string>::const_iterator p = pats.begin(); p != pats.end(); ++p)
-    if (headmatch(needle, *p)) return true;
-  return false;
-}
-
-bool prefix_match(const string& pat, const string& needle) {
-  if (*pat.rbegin() != '/')
-    // prefix match not requested
-    return pat == needle;
-  return headmatch(needle, pat);
-}
-
-bool headmatch(const string& s, const string& pat) {
-  if (pat.size() > s.size()) return false;
-  return std::mismatch(pat.begin(), pat.end(), s.begin()).first == pat.end();
-}
-
-:(before "End Includes")
-#include<vector>
-using std::vector;
-#include<list>
-using std::list;
-#include<utility>
-using std::pair;
-#include<map>
-using std::map;
-#include<set>
-using std::set;
-#include<algorithm>
-
-#include<iostream>
-using std::istream;
-using std::ostream;
-using std::cin;
-using std::cout;
-using std::cerr;
-
-#include<sstream>
-using std::istringstream;
-using std::ostringstream;
-
-#include<fstream>
-using std::ifstream;
-using std::ofstream;
-
-#define unused  __attribute__((unused))