#237522 (C++11) No.470 Inverse S+T Problem

• 問題: No.470 Inverse S+T Problem
• ユーザー: はむこ
• 提出日時: 2018-02-21 11:31:40
• 言語: C++11 (gcc 11.4.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 22,263 bytes
• コンパイル時間: 2,227 ms
• コンパイル使用メモリ: 224,076 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-06-01 22:54:30
• 合計ジャッジ時間: 3,330 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	1 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	1 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	1 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	1 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	2 ms; 5,376 KB

コンパイルメッセージ

main.cpp: In function ‘void vizGraph(vvll&, int, std::string)’:
main.cpp:43:425: warning: ignoring return value of ‘int system(const char*)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   43 | void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set<P> memo; rep(i, g.size())  rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << "    " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl;  } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); }
      |                                                                                                                                                                                                                                                                                                                                                                                                                                   ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

ソースコード

#include <bits/stdc++.h>
#include <sys/time.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
#define ZERO(a) memset(a,0,sizeof(a))
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
#define exists find_if
#define forall all_of

using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>;
using ld = long double;  using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }

inline void input(int &v){ v=0;char c=0;int p=1; while(c<'0' || c>'9'){if(c=='-')p=-1;c=getchar();} while(c>='0' && c<='9'){v=(v<<3)+(v<<1)+c-'0';c=getchar();} v*=p; }
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const unordered_set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U, typename V>  ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; }
template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;}
string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); reverse(all(s)); return s; }
template <typename T> ostream &operator<<(ostream &o, const priority_queue<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} o << endl; return o; }

template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;};
string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); }
void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set<P> memo; rep(i, g.size())  rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << "    " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl;  } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); }

size_t random_seed; namespace std { using argument_type = P; template<> struct hash<argument_type> { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash<ll>{}(x.fi); seed ^= (hash<ll>{}(x.se) << 1); return seed; } }; }; // hash for various class
namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template <typename T> struct myhash{ std::size_t operator()(const T& val) const { return (hash<T>{}(val)%mod_key)^hash_key; } }; };
template <typename T> class uset:public std::unordered_set<T,myhash::myhash<T>> { using SET=std::unordered_set<T,myhash::myhash<T>>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} };
uint32_t randxor() { static uint32_t x=1+(uint32_t)random_seed,y=362436069,z=521288629,w=88675123; uint32_t t; t=(x^(x<<11));x=y;y=z;z=w; return( w=(w^(w>>19))^(t^(t>>8)) ); }
struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; }
struct init_{init_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); struct timeval myTime; struct tm *time_st; gettimeofday(&myTime, NULL); time_st = localtime(&myTime.tv_sec); srand(myTime.tv_usec); random_seed = RAND_MAX / 2 + rand() / 2; }} init__;
#define rand randxor

static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;
#define ldout fixed << setprecision(40) 



// https://github.com/togasakih/Togasat
namespace togasat {
using Var = int;
using CRef = int;
using lbool = int;
const CRef CRef_Undef = INT32_MAX;
class Solver {

private:
  const lbool l_True = 0;
  const lbool l_False = 1;
  const lbool l_Undef = 2;

  const int var_Undef = -1;

  // Literal
  struct Lit {
    int x;
    inline bool operator==(Lit p) const { return x == p.x; }
    inline bool operator!=(Lit p) const { return x != p.x; }
    inline bool operator<(Lit p) const { return x < p.x; }
    inline Lit operator~() {
      Lit q;
      q.x = x ^ 1;
      return q;
    }
  };

  inline Lit mkLit(Var var, bool sign) {
    Lit p;
    p.x = var + var + sign;
    return p;
  };
  inline bool sign(Lit p) const { return p.x & 1; }
  inline int var(Lit p) const { return p.x >> 1; }
  inline int toInt(Var v) { return v; }
  inline int toInt(Lit p) { return p.x; }
  inline Lit toLit(int x) {
    Lit p;
    p.x = x;
    return p;
  }
  const Lit lit_Undef = {-2};
  const Lit lit_Error = {-1};

  // lifted boolean
  // VarData
  struct VarData {
    CRef reason;
    int level;
  };
  inline VarData mkVarData(CRef cr, int l) {
    VarData d = {cr, l};
    return d;
  }
  // Watcher
  struct Watcher {
    CRef cref;
    Lit blocker;
    Watcher() {}
    Watcher(CRef cr, Lit p) : cref(cr), blocker(p) {}
    bool operator==(const Watcher &w) const { return cref == w.cref; }
    bool operator!=(const Watcher &w) const { return cref != w.cref; }
  };

  // Clause
  class Clause {
  public:
    struct {
      bool learnt;
      int size;
    } header;
    std::vector<Lit> data; //(x1 v x2 v not x3)
    Clause() {}
    Clause(const std::vector<Lit> &ps, bool learnt) {
      header.learnt = learnt;
      header.size = ps.size();
      for (int i = 0; i < ps.size(); i++) {
        data.push_back(ps[i]);
      }
    }

    int size() const { return header.size; }
    bool learnt() const { return header.learnt; }
    Lit &operator[](int i) { return data[i]; }
    Lit operator[](int i) const { return data[i]; }
  };

  CRef alloc_clause(const std::vector<Lit> &ps, bool learnt = false) {
    static CRef res = 0;
    ca[res] = Clause(ps, learnt);
    return res++;
  }

  Var newVar(bool sign = true, bool dvar = true) {
    int v = nVars();

    assigns.push_back(l_Undef);
    vardata.push_back(mkVarData(CRef_Undef, 0));
    activity.push_back(0.0);
    seen.push_back(false);
    polarity.push_back(sign);
    decision.push_back(0);
    setDecisionVar(v, dvar);
    return v;
  }

  bool addClause_(std::vector<Lit> &ps) {
    std::sort(ps.begin(), ps.end());
    // empty clause
    if (ps.size() == 0) {
      return false;
    } else if (ps.size() == 1) {
      uncheckedEnqueue(ps[0]);
    } else {
      CRef cr = alloc_clause(ps, false);
      clauses.insert(cr);
      attachClause(cr);
    }

    return true;
  }
  void attachClause(CRef cr) {
    const Clause &c = ca[cr];

    assert(c.size() > 1);

    watches[(~c[0]).x].push_back(Watcher(cr, c[1]));
    watches[(~c[1]).x].push_back(Watcher(cr, c[0]));
  }

  // Input
  void readClause(const std::string &line, std::vector<Lit> &lits) {
    lits.clear();
    int parsed_lit, var;
    parsed_lit = var = 0;
    bool neg = false;
    std::stringstream ss(line);
    while (ss) {
      int val;
      ss >> val;
      if (val == 0)
        break;
      var = abs(val) - 1;
      while (var >= nVars()) {
        newVar();
      }
      lits.push_back(val > 0 ? mkLit(var, false) : mkLit(var, true));
    }
  }

  std::unordered_map<CRef, Clause> ca; // store clauses
  std::unordered_set<CRef> clauses;    // original problem;
  std::unordered_set<CRef> learnts;
  std::unordered_map<int, std::vector<Watcher>> watches;
  std::vector<VarData> vardata; // store reason and level for each variable
  std::vector<bool> polarity;   // The preferred polarity of each variable
  std::vector<bool> decision;
  std::vector<bool> seen;
  // Todo
  int qhead = 0;
  std::vector<Lit> trail;
  std::vector<int> trail_lim;
  // Todo rename(not heap)
  std::set<std::pair<double, Var>> order_heap;
  std::vector<double> activity;
  double var_inc;
  std::vector<Lit> model;
  std::vector<Lit> conflict;
  int nVars() const { return vardata.size(); }
  int decisionLevel() const { return trail_lim.size(); }
  void newDecisionLevel() { trail_lim.push_back(trail.size()); }

  inline CRef reason(Var x) const { return vardata[x].reason; }
  inline int level(Var x) const { return vardata[x].level; }
  inline void varBumpActivity(Var v){
    std::pair<double, Var> p = std::make_pair(activity[v], v);
    activity[v] += var_inc;
    if (order_heap.erase(p) == 1){
      order_heap.emplace(std::make_pair(activity[v], v));
    }
    
    if (activity[v] > 1e100){
      //Rescale
      std::set<std::pair<double,Var>> tmp_order;
      tmp_order = order_heap;
      order_heap.clear();
      for (int i = 0; i < nVars(); i++){
  activity[i] *= 1e-100;
      }
      for (auto &val : tmp_order){
  order_heap.emplace(std::make_pair(activity[val.first], val.first));
      }
      var_inc *= 1e-100;
    }

  }
  bool satisfied(const Clause &c) const {
    for (int i = 0; i < c.size(); i++) {
      if (value(c[i]) == l_True) {
        return true;
      }
    }
    return false;
  }
  lbool value(Var p) const { return assigns[p]; }
  lbool value(Lit p) const {
    if (assigns[var(p)] == l_Undef) {
      return l_Undef;
    }
    return assigns[var(p)] ^ sign(p);
  }
  void setDecisionVar(Var v, bool b) {
    decision[v] = b;
    order_heap.emplace(std::make_pair(0.0, v));
  }
  void uncheckedEnqueue(Lit p, CRef from = CRef_Undef) {
    assert(value(p) == l_Undef);
    assigns[var(p)] = sign(p);
    vardata[var(p)] = mkVarData(from, decisionLevel());
    trail.push_back(p);
  }
  // decision
  Lit pickBranchLit() {
    Var next = var_Undef;
    while (next == var_Undef or value(next) != l_Undef) {
      if (order_heap.empty()) {
        next = var_Undef;
        break;
      } else {
  auto p = *order_heap.rbegin();
        next = p.second;
        order_heap.erase(p);
      }
    }
    return next == var_Undef ? lit_Undef : mkLit(next, polarity[next]);
  }
  // clause learning
  void analyze(CRef confl, std::vector<Lit> &out_learnt, int &out_btlevel) {
    int pathC = 0;
    Lit p = lit_Undef;
    int index = trail.size() - 1;
    out_learnt.push_back(mkLit(0, false));
    do {
      assert(confl != CRef_Undef);
      Clause &c = ca[confl];
      for (int j = (p == lit_Undef) ? 0 : 1; j < c.size(); j++) {
        Lit q = c[j];
        if (not seen[var(q)] and level(var(q)) > 0) {
    varBumpActivity(var(q));
          seen[var(q)] = 1;
          if (level(var(q)) >= decisionLevel()) {
            pathC++;
          } else {
            out_learnt.push_back(q);
          }
        }
      }
      while (not seen[var(trail[index--])])
        ;
      p = trail[index + 1];
      confl = reason(var(p));
      seen[var(p)] = 0;
      pathC--;
    } while (pathC > 0);

    out_learnt[0] = ~p;

    // unit clause
    if (out_learnt.size() == 1) {
      out_btlevel = 0;
    } else {
      int max_i = 1;
      for (int i = 2; i < out_learnt.size(); i++) {
        if (level(var(out_learnt[i])) > level(var(out_learnt[max_i]))) {
          max_i = i;
        }
      }

      Lit p = out_learnt[max_i];
      out_learnt[max_i] = out_learnt[1];
      out_learnt[1] = p;
      out_btlevel = level(var(p));
    }

    for (int i = 0; i < out_learnt.size(); i++) {
      seen[var(out_learnt[i])] = false;
    }
  }

  // backtrack
  void cancelUntil(int level) {
    if (decisionLevel() > level) {
      for (int c = trail.size() - 1; c >= trail_lim[level]; c--) {
        Var x = var(trail[c]);
        assigns[x] = l_Undef;
        polarity[x] = sign(trail[c]);
        order_heap.emplace(std::make_pair(activity[x], x));
      }
      qhead = trail_lim[level];
      trail.erase(trail.end() - (trail.size() - trail_lim[level]), trail.end());
      trail_lim.erase(trail_lim.end() - (trail_lim.size() - level),
                      trail_lim.end());
    }
  }
  CRef propagate() {
    CRef confl = CRef_Undef;
    int num_props = 0;
    while (qhead < trail.size()) {
      Lit p = trail[qhead++]; // 'p' is enqueued fact to propagate.
      std::vector<Watcher> &ws = watches[p.x];
      std::vector<Watcher>::iterator i, j, end;
      num_props++;

      for (i = j = ws.begin(), end = i + ws.size(); i != end;) {
        // Try to avoid inspecting the clause:
        Lit blocker = i->blocker;
        if (value(blocker) == l_True) {
          *j++ = *i++;
          continue;
        }

        CRef cr = i->cref;
        Clause &c = ca[cr];
        Lit false_lit = ~p;
        if (c[0] == false_lit)
          c[0] = c[1], c[1] = false_lit;
        assert(c[1] == false_lit);
        i++;

        Lit first = c[0];
        Watcher w = Watcher(cr, first);
        if (first != blocker && value(first) == l_True) {
          *j++ = w;
          continue;
        }

        // Look for new watch:
        for (int k = 2; k < c.size(); k++)
          if (value(c[k]) != l_False) {
            c[1] = c[k];
            c[k] = false_lit;
            watches[(~c[1]).x].push_back(w);
            goto NextClause;
          }
        *j++ = w;
        if (value(first) == l_False) { // conflict
          confl = cr;
          qhead = trail.size();
          while (i < end)
            *j++ = *i++;
        } else {
          uncheckedEnqueue(first, cr);
        }
      NextClause:;
      }
      int size = i - j;
      ws.erase(ws.end() - size, ws.end());
    }
    return confl;
  }

  static double luby(double y, int x) {

    // Find the finite subsequence that contains index 'x', and the
    // size of that subsequence:
    int size, seq;
    for (size = 1, seq = 0; size < x + 1; seq++, size = 2 * size + 1)
      ;

    while (size - 1 != x) {
      size = (size - 1) >> 1;
      seq--;
      x = x % size;
    }

    return pow(y, seq);
  }

  lbool search(int nof_conflicts) {
    int backtrack_level;
    std::vector<Lit> learnt_clause;
    learnt_clause.push_back(mkLit(-1, false));
    int conflictC = 0;
    while (true) {
      CRef confl = propagate();

      if (confl != CRef_Undef) {
        // CONFLICT
        conflictC++;
        if (decisionLevel() == 0)
          return l_False;
        learnt_clause.clear();
        analyze(confl, learnt_clause, backtrack_level);
        cancelUntil(backtrack_level);
        if (learnt_clause.size() == 1) {
          uncheckedEnqueue(learnt_clause[0]);
        } else {
          CRef cr = alloc_clause(learnt_clause, true);
          learnts.insert(cr);
          attachClause(cr);
          uncheckedEnqueue(learnt_clause[0], cr);
        }
  //varDecay
  var_inc *= 1.05;
      } else {
        // NO CONFLICT
        if ((nof_conflicts >= 0 and conflictC >= nof_conflicts)) {
          cancelUntil(0);
          return l_Undef;
        }
        Lit next = pickBranchLit();

        if (next == lit_Undef) {
          return l_True;
        }
        newDecisionLevel();
        uncheckedEnqueue(next);
      }
    }
  };

public:
  std::vector<lbool> assigns; // The current assignments (ex assigns[0] = 0 ->
                              // X1 = True, assigns[1] = 1 -> X2 = False)
  lbool answer;               // SATISFIBLE 0 UNSATISFIBLE 1 UNKNOWN 2
  Solver() { }
  Solver(int n) { for (int i = 0; i < n; i++) { vector<int> tmp = {i+1, -(i+1)}; addClause(tmp); } }
  void parse_dimacs_problem(std::string problem_name) {
    std::vector<Lit> lits;
    int vars = 0;
    int clauses = 0;
    std::string line;
    std::ifstream ifs(problem_name, std::ios_base::in);
    while (ifs.good()) {
      getline(ifs, line);
      if (line.size() > 0) {
        if (line[0] == 'p') {
          sscanf(line.c_str(), "p cnf %d %d", &vars, &clauses);
        } else if (line[0] == 'c' or line[0] == 'p') {
          continue;
        } else {
          readClause(line, lits);
          if (lits.size() > 0)
            addClause_(lits);
        }
      }
    }
    ifs.close();
  }
  lbool solve() {
    model.clear();
    conflict.clear();
    lbool status = l_Undef;
    answer = l_Undef;
    var_inc = 1.01;
    int curr_restarts = 0;
    double restart_inc = 2;
    double restart_first = 100;
    while (status == l_Undef) {
      double rest_base = luby(restart_inc, curr_restarts);
      status = search(rest_base * restart_first);
      curr_restarts++;
    }
    answer = status;
    return status;
  };

  void addClause(std::vector<int> &clause) {
    std::vector<Lit> lits;
    for (int i = 0; i < clause.size(); i++) {
      int var = abs(clause[i]) - 1;
      while (var >= nVars())
        newVar();
      lits.push_back(clause[i] > 0 ? mkLit(var, false) : mkLit(var, true));
    }
    addClause_(lits);
  }
  void print_answer() {
    if (answer == 0) {
      std::cout << "SAT" << std::endl;
      for (int i = 0; i < assigns.size(); i++) {
        if (assigns[i] == 0) {
          std::cout << (i + 1) << " ";
        } else {
          std::cout << -(i + 1) << " ";
        }
      }
      std::cout << "0" << std::endl;
    } else {
      std::cout << "UNSAT" << std::endl;
    }
  }
};
}

class SAT {
public:
    int n;
    // v in [0, n)      x_v = T
    // v in [n, 2n)     x_v = F
    vector<vector<int>> g, g_rev;
    vector<bool> ret;
    SAT (int n_) : n(n_), g(n*2), g_rev(n*2) { }
    inline int node(int t) {
        return (t > 0 ? t-1 : n+(-t)-1);
    }

    // and (sign(t1) x_|t1| or sign(t2) t2)を論理式に加える。
    // ただし、sign(t)はt>0で何もなし、t<0でnot
    //
    // 1 <= |t1| <= n
    // 1 <= |t2| <= n
    void addClause(int t1, int t2) {
        assert(1 <= abs(t1) && abs(t1) <= n);
        assert(1 <= abs(t2) && abs(t2) <= n);
        g[node(-t1)].pb(node(t2));
        g[node(-t2)].pb(node(t1));
        g_rev[node(t1)].pb(node(-t2));
        g_rev[node(t2)].pb(node(-t1));
    }

    // 従属可能で1を出力
    bool isSAT(void) {
        // SCC
        vector<int> color(g.size(), -1); // color[i] == color[j]ならばiとjは同じ連結成分
        {
            vector<int> id;
            vector<bool> visited(g.size());
            rep(i, g.size()) {
                function<void(int)> dfs1 = [&](int v) {
                    if (visited[v]) return;
                    visited[v] = true;
                    for (auto x : g[v]) dfs1(x);
                    id.pb(v);
                };
                dfs1(i);
            }
            fill(all(visited), false);
            for (int i = id.size() - 1; i >= 0; i--) {
                function<void(int)> dfs2 = [&](int v) {
                    if (visited[v]) return;
                    visited[v] = true;
                    for (auto x : g_rev[v]) dfs2(x);
                    color[v] = i;
                };
                dfs2(id[i]);
            }
        }

        ret.resize(0);
        rep(v, n) if (color[v] == color[v+n]) return 0;
        ret.resize(n);
        rep(i, n) ret[i] = color[i] > color[i+n];
        return 1;
    }

    // 解ありの場合、x_i = ret[i]がSATを与える。
    // 解なしの場合、ret.size() == 0である
    vector<bool> getAnswer(void) { return ret; }
    void print_answer(void) {
        if (ret.size()) {
            cout << "SAT : "; rep(i, n) cout << ret[i] << " "; cout << endl;
        } else {
            cout << "UNSAT" << endl;
        }
    }
};

int main(void) {
    ll n; cin >> n;
    if (n > 26*2) return cout << "Impossible" << endl, 0;

    vector<string> u(n); cin >> u;
    SAT sat(n);

    map<string, vll> memo;
    rep(i, n) {
        memo[u[i].substr(0, 1)].pb(i+1);
        memo[u[i].substr(1, 2)].pb(i+1);
        memo[u[i].substr(0, 2)].pb(-i-1);
        memo[u[i].substr(2, 1)].pb(-i-1);
    }

    for (auto&& x : memo) {
        auto&& v = x.se;
        for (auto i : v) for (auto j : v) if (i != j) {
            sat.addClause(-i, -j);
        }
    }

    ll ret = sat.isSAT();
    if (ret) {
        rep(i, n) {
            if (sat.ret[i] == 0) 
                cout << u[i].substr(0, 1) << " " << u[i].substr(1, 2) << endl;
            else 
                cout << u[i].substr(0, 2) << " " << u[i].substr(2, 1) << endl;
        }
    } else {
        cout << "Impossible" << endl;
    }
}