#ifdef LOCAL111 #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #define _USE_MATH_DEFINES #include const int INF = 1e9; using namespace std; template ostream& operator<< (ostream& os, const pair& p) { cout << '(' << p.first << ' ' << p.second << ')'; return os; } #define endl '\n' #define ALL(a) (a).begin(),(a).end() #define SZ(a) int((a).size()) #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) for (int i=(n)-1;i>=0;i--) #ifdef LOCAL111 #define DEBUG(x) cout<<#x<<": "<<(x)< void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} #else #define DEBUG(x) true template void dpite(T a, T b){ return; } #endif #define F first #define S second #define SNP string::npos #define WRC(hoge) cout << "Case #" << (hoge)+1 << ": " template void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} template bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;} template bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;} // 検証しなおしたい //library typedef long long cost_t; // class Edge { // public: // int to = -1, from = -1, rev = -1; // cost_t cost = -1; // Edge(){ // } // Edge(int x,cost_t y){ // to = x; // cost = y; // } // Edge(int x, int y, cost_t z){ // from = x; // to = y; // cost = z; // } // Edge(int x, int y, int r, cost_t z){ // from = x; // to = y; // cost = z; // rev = r; // } // bool operator< (const Edge& x) const { // if(cost != x.cost) return cost < x.cost; // return to < x.to; // } // bool operator> (const Edge& x) const { // if(cost != x.cost) return cost > x.cost; // return to > x.to; // } // }; class Edge { public: int to = -1; cost_t cost = -1; Edge(){ } Edge(int x,cost_t y){ to = x; cost = y; } // Edge(int x, int y, cost_t z){ // // from = x; // to = y; // cost = z; // } // Edge(int x, int y, int r, cost_t z){ // // from = x; // to = y; // cost = z; // // rev = r; // } bool operator< (const Edge& x) const { if(cost != x.cost) return cost < x.cost; return to < x.to; } bool operator> (const Edge& x) const { if(cost != x.cost) return cost > x.cost; return to > x.to; } }; class Graph { private: typedef vector Edges; //const long long int INF = (long long)1e18; vector v; int n; public: Graph(int x){ n = x; v = vector(x); } Graph(){} Edges& operator[](int x){ return v[x]; } const Edges& operator[](int x) const { return v[x]; } int size() const { return n; } void add_edge(int from, const Edge &e){ v[from].push_back(e); } void add_edge(int from, int to, cost_t cost = -1){ add_edge(from,Edge(to,cost)); } // void add_edge(int from, int to, cost_t cost = -1, int rev = -1){ // add_edge(from,Edge(from,to,rev,cost)); // } void add_uedge(int from, int to, cost_t cost = -1){ add_edge(from,to,cost); add_edge(to,from,cost); } }; vector dijkstra(int from, const Graph& v) { vector dist(v.size(),INF); priority_queue,greater> que; que.push(Edge(from,0)); while(!que.empty()){ Edge e = que.top(); que.pop(); if(dist[e.to] == INF){ dist[e.to] = e.cost; for(auto to : v[e.to]){ if(dist[to.to] == INF) que.push(Edge(to.to, e.cost+to.cost)); } } } return dist; } vector bellmanford(int from, const Graph& g) { vector res(g.size(),INF); res[from] = 0; bool conf = true; int cnt = 0; while(conf){ conf = false; for(int i = 0; i < g.size(); i++){ if(res[i] != INF) for(const auto& e : g[i]){ if(res[e.to] > res[i]+e.cost){ conf = true; res[e.to] = res[i]+e.cost; } } } if(cnt > g.size()+5) return vector(); cnt++; } return res; } Graph prim(const Graph g) { using T = tuple; priority_queue, greater> qu; int n = g.size(); assert(n != 0); vector added(n,false); qu.emplace(0,0,0); Graph res(n); while(!qu.empty()){ int from, to; cost_t cost; tie(cost, from, to) = qu.top(); qu.pop(); if(!added[to]){ added[to] = true; res.add_edge(from, to, cost); res.add_edge(to, from, cost); for(const auto &e : g[to]){ if(!added[e.to]){ qu.emplace(e.cost, to, e.to); } } } } return res; } vector getTreeOrder(const Graph &g, int root) { vector res; function func = [&](int p, int pre){ for(auto &e : g[p]){ if(e.to != pre){ func(e.to,p); } } res.push_back(p); }; func(root,-1); return res; } vector getTreePar(const Graph &g, int root) { vector par(g.size(),root); function func = [&](int p, int pre){ par[p] = pre; for(auto &e : g[p]){ if(e.to != pre){ func(e.to,p); } } }; func(root,root); return par; } vector toposort(const Graph &g) { int n = g.size(); vector res; res.reserve(n); vector used(n,false); function rec = [&](int p){ if(used[p]) return; used[p] = true; for(auto&& e : g[p]) { rec(e.to); } res.push_back(p); }; for(int i = 0; i < n; ++i) { if(!used[i]) rec(i); } reverse(res.begin(), res.end()); return res; } //0からの連結成分をたどる tuple getTreeDiameter(const Graph &g){ using P = pair; function dfs = [&](int p, int par) -> P{ P res = {0,p}; for(auto&& e : g[p]) { if(e.to == par) continue; auto v = dfs(e.to,p); v.first += e.cost; res = max(res,v); } return res; }; auto ap1 = dfs(0,-1); auto ap2 = dfs(ap1.second,-1); return make_tuple(ap2.first,ap2.second,ap1.second); } // res.secondはなければ-1 pair getTreeCenter(const Graph& g){ cost_t di; int x, y; tie(di, x, y) = getTreeDiameter(g); pair res(-1,-1); cost_t mi; function rec = [&](int p, int par) -> cost_t{ if(p == y){ return 0; } cost_t ress = -1; for(auto&& e : g[p]) if(e.to != par){ cost_t v = rec(e.to,p); if(v != -1){ v += e.cost; ress = v; v = max(v, di-(v)); if(mi > v){ mi = v; res = {p,-1}; }else if(mi == v){ res.second = p; } } } return ress; }; rec(x,-1); return res; } //liblary //liblary tuple,int> SCC(const Graph &g) { int n = g.size(); vector used(n,false); vector cmp(g.size()); Graph rg(n); for(int i = 0; i < n; ++i) { for(auto&& e : g[i]) { rg.add_edge(e.to,i,e.cost); } } vector vs; vs.reserve(g.size()); function dfs = [&](int v){ used[v] = true; for(auto&& e : g[v]) { if(!used[e.to]) dfs(e.to); } vs.push_back(v); }; function rdfs = [&](int v, int k){ used[v] = true; cmp[v] = k; for(auto&& e : rg[v]) { if(!used[e.to]) rdfs(e.to,k); } }; for(int v = 0; v < n; ++v) { if(!used[v]) dfs(v); } fill(used.begin(), used.end(), false); int k = 0; for(int i = n-1; i >= 0; --i) { if(!used[vs[i]]) rdfs(vs[i], k++); } return make_tuple(cmp,k); } Graph getSCCGraph(const Graph &g, vector cmp, int k){ Graph res(k); for(int p = 0; p < (int)g.size(); ++p) { for(auto&& e : g[p]) { if(cmp[p] != cmp[e.to]) res.add_edge(cmp[p],Edge(cmp[e.to],-1)); } } return res; } //liblary void vizGraph(const Graph &g, bool with_dir = false, bool with_cap = false){ ofstream ofs("./out.dot"); if(with_dir) ofs << "graph graph_name {" << endl; else ofs << "digraph graph_name {" << endl; for(int i = 0; i < (int)g.size(); i++){ if (!g[i].size()) continue; for(const auto &e : g[i]){ if(with_dir){ if(e.to > i) ofs << " \"" << i << "\" -- \"" << e.to << '"'; }else ofs << " \"" << i << "\" -> \"" << e.to << '"'; if (with_cap) { ofs << " [ label = \"" << (e.cost == INF ? "inf" : to_string(e.cost)) << "\"];"; } if(!with_dir or e.to > i)ofs << endl; } } ofs << "}" << endl; ofs.close(); system("dot -T png out.dot > sample.png"); } //library //Graph, scc に依存 class TwoSATsolver{ private: Graph g; int center; public: TwoSATsolver(int n){ center = n; g = Graph(2*n+1); } int f(int x){ return center+x; } void add_clause(int x, int y){ g.add_edge(f(-y),f(x)); g.add_edge(f(-x),f(y)); } //充足不可能なら空のvectorを返す vector solve(){ vizGraph(g); vector cmp; int k; tie(cmp,k) = SCC(g); Graph retg = getSCCGraph(g,cmp,k); for(int i = 1; i <= center; ++i) { if(cmp[f(i)] == cmp[f(-i)]){ return vector(); } } vector res(center); for(int i = 1; i <= center; ++i) { int cmpi = cmp[f(i)]; int cmpni = cmp[f(-i)]; assert(cmpi != cmpni); if(cmpi < cmpni){ res[i-1] = false; }else{ res[i-1] = true; } } return res; } }; //library typedef long long int LL; typedef unsigned long long ULL; typedef pair P; void ios_init(){ //cout.setf(ios::fixed); //cout.precision(12); #ifdef LOCAL111 return; #endif ios::sync_with_stdio(false); cin.tie(0); } int main() { ios_init(); int n; while(cin >> n) { vector u(n); REP(i,n) cin >> u[i]; if(n > 3000){ cout << "Impossible" << endl; }else{ TwoSATsolver sat(n); REP(i,n) REP(j,i){ REP(ci,2) REP(cj,2){ array ar; ar[0] = u[i].substr(0,ci+1); ar[1] = u[i].substr(ci+1,3-ci-1); ar[2] = u[j].substr(0,cj+1); ar[3] = u[j].substr(cj+1,3-cj-1); dpite(ALL(ar)); REP(a,4) REP(b,a){ if(ar[a] == ar[b]){ int p = i+1, q = j+1; if(ci) p = -p; if(cj) q = -q; DEBUG(p); DEBUG(q); sat.add_clause(p,q); break; } } } } auto res = sat.solve(); if(SZ(res) == 0){ cout << "Impossible" << endl; }else{ REP(i,n){ cout << u[i].substr(0,res[i]+1) << ' '; cout << u[i].substr(res[i]+1,3-res[i]-1) << endl; } } } } return 0; }