#include #include using namespace std; using ll = long long; template istream& operator >> (istream& is, vector& vec) { for(T& x : vec) is >> x; return is; } template ostream& operator << (ostream& os, const vector& vec) { if(vec.empty()) return os; os << vec[0]; for(auto it = vec.begin(); ++it != vec.end(); ) os << ' ' << *it; return os; } struct Weighted_dsu { public: Weighted_dsu() : _n(0) {} Weighted_dsu(int n) : _n(n), num_component(n), parent_or_size(n, -1), diff_weight(n) {} bool merge(int a, int b, long long w) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); w += diff_weight[a] - diff_weight[b]; if(x == y) return w == 0; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y), w *= -1; parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; diff_weight[y] = w; num_component--; return true; } long long diff(int a, int b) { assert(same(a, b)); return diff_weight[b] - diff_weight[a]; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; int r = leader(parent_or_size[a]); diff_weight[a] += diff_weight[parent_or_size[a]]; return parent_or_size[a] = r; } int size() { return num_component; } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } private: int _n, num_component; std::vector parent_or_size; std::vector diff_weight; }; #ifdef DBG vector a = {5, 4, 1, 3, 2}; int ask(int v, int u){ int res; cout << "1 " << v + 1 << ' ' << u + 1 << endl; int vl = a[v] + a[u]; for(int i = 0; i < a.size(); i++){ if(a[i] == vl) return i; } return -1; } #else int ask(int v, int u){ int res; cout << "1 " << v + 1 << ' ' << u + 1 << endl; cin >> res; if(res == -1) return -1; return res - 1; } #endif void answer(vector ans){ cout << "2 " << ans << endl; } void solve(){ int n; #ifdef DBG n = a.size(); #else cin >> n; #endif Weighted_dsu uf(n); vector> G; vector cand(n, -1); int mx = 0, npos = -1, pos = 0; auto f = [&](int pos){ atcoder::dsu uf2(n); int cnt = 0; mx = 0; vector> T; for(int v = 0; v < n; v++){ if(v == pos) continue; int u = ask(pos, v); if(u == -1){ cnt++; }else{ uf2.merge(v, u); T.emplace_back(v, u); } } G = uf2.groups(); for(auto &&vec : G){ if(vec.size() > mx){ mx = vec.size(); } } int res = mx >= 3 ? G.size() - 1 : G.size(); cand[pos] = res; for(auto [u, v] : T){ uf.merge(u, v, res); //if(cand[v] != -1) uf.merge(pos, v, cand[v]); } for(auto &&vec : G){ sort(vec.begin(), vec.end(), [&](int u, int v){ return uf.diff(u, v) > 0; }); } return res; }; int cur = f(0); if(cur == 1){ sort(G.begin(), G.end(), [](vector lhs, vector rhs){ return lhs.size() < rhs.size(); }); G[1].insert(G[1].begin(), G[0][0]); vector ans(n); for(int i = 0; i < n; i++){ ans[G[1][i]] = i + 1; } answer(ans); return; } if(cur != n){ // n を見つけに行く vector fst, lst; for(auto &&vec : G){ if(vec.size() != mx) continue; fst.emplace_back(vec[0]); lst.emplace_back(vec.back()); } int li = 0; for(int i = 0; i < fst.size(); i++){ while(ask(fst[i], lst[li]) != -1){ li++; } } npos = fst[li]; }else{ // nが見つかっている場合 npos = 0; pos = 1; cur = f(1); for(auto &&vec : G){ if(count(vec.begin(), vec.end(), 0) >= 1){ npos = vec[0]; break; } } } f(npos); vector ans(n); int mn = 0; for(int i = 0; i < n; i++){ ans[i] = uf.diff(0, i); mn = min(mn, ans[i]); } //cerr << ans << endl; for(int i = 0; i < n; i++) ans[i] -= mn - 1; answer(ans); } int main(){ ios::sync_with_stdio(false); cin.tie(0); int T; cin >> T; while(T--) solve(); }