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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")
+Hide_warnings = false;
+
+:(before "End Tracing")
+struct trace_stream {
+  vector<pair<string, pair<int, string> > > past_lines;  // [(layer label, frame, line)]
+  unordered_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, "");
+  size_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();
+  ostringstream output;
+  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) {
+  string::size_type 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) {
+  size_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, "");
+  size_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();
+  ostringstream output;
+  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
+  size_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();
+  ostringstream output;
+  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;
+  string::size_type 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<cstdlib>
+
+#include<vector>
+using std::vector;
+#include<list>
+using std::list;
+#include<utility>
+using std::pair;
+
+#include<tr1/unordered_map>
+using std::tr1::unordered_map;
+#include<tr1/unordered_set>
+using std::tr1::unordered_set;
+#include<algorithm>
+
+#include<iostream>
+using std::istream;
+using std::ostream;
+using std::iostream;
+using std::cin;
+using std::cout;
+using std::cerr;
+
+#include<sstream>
+using std::stringstream;
+using std::istringstream;
+using std::ostringstream;
+
+#include<fstream>
+using std::ifstream;
+using std::ofstream;
+
+#define unused  __attribute__((unused))