#include #include 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 bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template 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; using vvll = vector; using P = pair; using ld = long double; using vld = vector; using vi = vector; using vvi = vector; 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 ostream &operator<<(ostream &o, const pair &v) { o << "(" << v.first << ", " << v.second << ")"; return o; } template struct seq{}; template struct gen_seq : gen_seq{}; template struct gen_seq<0, Is...> : seq{}; template void print_tuple(basic_ostream& os, Tuple const& t, seq){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get(t)), 0)...}; } template auto operator<<(basic_ostream& os, tuple const& t) -> basic_ostream& { os << "("; print_tuple(os, t, gen_seq()); 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 ostream &operator<<(ostream &o, const vector &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; } vector range(const int x, const int y) { vector v(y - x + 1); iota(v.begin(), v.end(), x); return v; } template istream& operator>>(istream& i, vector& 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 ostream &operator<<(ostream &o, const priority_queue &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} o << endl; return o; } template unordered_map counter(vector vec){unordered_map 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

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 { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash{}(x.fi); seed ^= (hash{}(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 struct myhash{ std::size_t operator()(const T& val) const { return (hash{}(val)%mod_key)^hash_key; } }; }; template class uset:public std::unordered_set> { using SET=std::unordered_set>; 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) class SAT { public: ll n; // v in [0, n) x_v = T // v in [n, 2n) x_v = F vvll g; vvll g_rev; vector ret; SAT (ll n_) : n(n_), g(n*2), g_rev(n*2) { } inline ll node(ll 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(ll t1, ll 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(-t1)); g_rev[node(t2)].pb(node(-t2)); } // 従属可能で1を出力 bool solve(void) { vll id; vector visited(g.size()); rep(i, g.size()) { function dfs1 = [&](ll v) { if (visited[v]) return; visited[v] = true; for (auto x : g[v]) { dfs1(x); } id.pb(v); }; dfs1(i); } fill(all(visited), false); vll color(g.size(), -1); for (int i = id.size() - 1; i >= 0; i--) { function dfs2 = [&](ll v) { if (visited[v]) return; visited[v] = true; for (auto x : g[v]) { dfs2(x); } color[v] = i; }; dfs2(i); } ret.resize(0); rep(v, n) if (color[v] == color[v+n]) return 1; ret.resize(n); rep(i, n) ret[i] = color[i] > color[i+n]; return 0; } vector 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; } } }; // 2-SATソルバ // // 使い方 // SAT sat(n); // x_1, ... x_nの変数が確保される。 // addClouseなどは1-index!! 理由は、not Aを-Aとして表現するから! // // sat.addClause({i, j, h}) // x_iもしくはx_jもしくはx_hが成立する // addClause({x_i, x_j})など、2つでもOK // x_iは負だと、「x_iが成立しない」という意味になる // // sat.solve // 0ならSAT, 1ならUNSAT, 2ならエラーなり解を見つけられなかったり // SATなら副作用でsolver.assigns[i]にx_{i+1}の割当結果が得られる // 注意すべきなのは、0がtrueで1がfalseであること int main(void) { ll n; cin >> n; if (n > 26*2) return cout << "Impossible" << endl, 0; vector u(n); cin >> u; SAT sat(n); map 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.solve(); if (ret == 0) { 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; } return 0; }