#include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; class range {private: struct I{int x;int operator*(){return x;}bool operator!=(I& lhs){return x ostream& operator<<(ostream& os, const pair& p){ return os << "{" << p.first << ", " << p.second << "}"; } template ostream& operator<<(ostream& os, const vector& obj) { os << "{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } template ostream& operator<<(ostream& os, const set& obj) { os << "set{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } template ostream& operator<<(ostream& os, const map& obj) { os << "map{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } #ifdef ONLINE_JUDGE #define dump(expr) ; #else #define dump(expr) { cerr << "\033[33m#L" << __LINE__ << ": " << expr << "\033[39m" << endl; } #endif // Strongly Connected Components : k := the number of scc, comp_order[id] := its // topological order [0,k). O(N+M) struct E { int fr, to; E(int fr_, int to_) : fr(fr_), to(to_) {} friend ostream &operator<<(ostream &os, const E &e) { os << "(" << e.fr << " -> " << e.to << ")"; return os; } }; typedef vector V; // typedef vector G; // note that each vertex will have both enterning edges & entered edges void add_edge(vector &vg, int fr, int to) { vg[fr].push_back(E(fr, to)); vg[to].push_back(E(fr, to)); } struct StronglyConnectedComponents { vector visited; vector t_order; vector comp; int n_comps; StronglyConnectedComponents() {} // normal topological sort void dfs1(vector &vg, int id, int &k) { visited[id] = true; for (auto it : vg[id]) if (it.fr == id && !visited[it.to]) dfs1(vg, it.to, k); t_order[--k] = id; } // dfs of reverse order void dfs2(vector &vg, int id, int &k) { visited[id] = true; for (auto it : vg[id]) if (it.to == id && !visited[it.fr]) dfs2(vg, it.fr, k); comp[id] = k; // foreach vertex "id", return the topological order } void exec(vector &vg) { int n = (int)vg.size(), k = n; // 1st dfs visited.assign(n, 0); t_order.assign(n, 0); comp.assign(n, 0); for (int j : range(n)) if (!visited[j]) dfs1(vg, j, k); // 2nd dfs visited.assign(n, 0); for (int i : range(n)) { int j = t_order[i]; if (!visited[j]) dfs2(vg, j, k), k++; } n_comps = k; dump(comp); } }; struct TwoSAT { // negative clause ~x[i] should be represented as ~i (i=0,...,n-1) int n; vector vg; StronglyConnectedComponents scc; vector constructed; TwoSAT(int n_) : n(n_), vg(2 * n) {} void imply(int i, int j) { // x[i] => x[j] i = (i >= 0) ? (2 * i) : (2 * (~i) + 1); j = (j >= 0) ? (2 * j) : (2 * (~j) + 1); add_edge(vg, i, j); } void add_or(int i, int j) { // x[i] OR x[j] // <=> // ~x[i] => x[j] AND ~x[j] => x[i] imply(~i, j); imply(~j, i); } bool exec() { scc.exec(vg); for (int i : range(n)) if (scc.comp[2 * i] == scc.comp[2 * i + 1]) return false; constructed.assign(n, 0); for (int i : range(n)) constructed[i] = scc.comp[2 * i] > scc.comp[2 * i + 1]; return true; } }; void solve() { int n; cin >> n; vector vs(n); for (int i : range(n)) cin >> vs[i]; if (n > 100) { cout << "Impossible" << endl; return; } map> mp; for (int i : range(n)) { mp[vs[i].substr(0, 1)].push_back(i); mp[vs[i].substr(1, 2)].push_back(i); mp[vs[i].substr(0, 2)].push_back(~i); mp[vs[i].substr(2, 1)].push_back(~i); } dump(mp); TwoSAT tsat(n); for (auto p : mp) { for (int i : p.second) for (int j : p.second) { if (i == j) break; dump(i << " OR " << j) tsat.add_or(i, j); } } bool res = tsat.exec(); if (!res) cout << "Impossible" << endl; else { for (int i : range(n)) { int k = tsat.constructed[i] + 1; cout << vs[i].substr(0, k) << " " << vs[i].substr(k) << endl; } } } int main() { cout << fixed << setprecision(12); solve(); }