#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; template struct array_set { int state[element_size]; // -1 if not in set else index in elems int elems[element_size]; int size = 0; array_set() { memset(state, -1, sizeof(int) * element_size); } void insert(int x) { if (state[x] == -1) { state[x] = size; elems[size] = x; size++; } } bool contains(int x) { return x >= 0 && state[x] != -1; } int* begin() { return elems; } int* end() { return elems + size; } void clear() { while(size) state[elems[--size]] = -1; } void erase(int x) { // not tested int idx = state[x]; if (idx != -1) { state[x] = -1; size--; if (idx != size) { int y = elems[size]; state[y] = idx; elems[idx] = y; } } } }; template struct array_map { int state[element_size]; // -1 if not in set else index in elems pair elems[element_size]; int size = 0; array_map() { memset(state, -1, sizeof(int) * element_size); } bool contains(int x) { return state[x] != -1; } pair* begin() { return elems; } pair* end() { return elems + size; } void clear() { while(size) state[elems[--size].first] = -1; } void erase(int x) { // not tested int idx = state[x]; if (idx != -1) { state[x] = -1; size--; if (idx != size) { int y = elems[size].first; state[y] = idx; elems[idx] = move(elems[size]); } } } T& operator[](int x) { if (state[x] == -1) { state[x] = size; elems[size].first = x; elems[size].second = T(); size++; } return elems[state[x]].second; } }; } int main() { ios::sync_with_stdio(false); cin.tie(0); int tt; cin >> tt; while (tt--) { int n; cin >> n; VI p(n + 1, -1), pos(n + 1, -1); auto ask = [&](int i, int j) { cout << "1 " << i << ' ' << j << endl; int k; cin >> k; return k; }; auto dfs = [&](auto&& self, VI idx) -> void { assert(idx.size() >= 4); int sz = idx.size(); // S:={1, 2, ..., sz} // find a s.t. pa+pb in S in sz/2+1 queries static array_set<10002> st; st.clear(); for (int i : idx) st.insert(i); int a = -1; for (int i = 0; i + 1 < ssize(idx); i += 2) { int k = ask(idx[i], idx[i+1]); if (st.contains(k)) { a = idx[i]; idx.erase(idx.begin() + i); break; } } if (a == -1) { if (sz % 2) { a = idx.back(); idx.pop_back(); } else { // a+b = k+1, c+d = k+1, a,b,c,d distinct // => a+c <= k or b+d <= k int k = ask(idx[0], idx[2]); if (st.contains(k)) { a = idx[0]; idx.erase(idx.begin()); } else { a = idx[1]; idx.erase(idx.begin() + 1); } } } vector

es; for (int i : idx) { int k = ask(i, a); if (st.contains(k)) es.emplace_back(i, k); } static array_map to, indeg; to.clear(), indeg.clear(); for (auto [u, v] : es) to[u] = v, indeg[v]++; vector

heads; for (int i : idx) if (!indeg[i]) { int j = i, l = 0; while (to[j]) l++, j = to[j]; heads.emplace_back(i, l); } assert(heads.size()); if (heads.size() == 1 && heads[0].second == sz - 2) { p[a] = 1; int i = heads[0].first; p[i] = 2; rep(c, sz - 2) i = to[i], p[i] = 3 + c; return; } if (ranges::max_element(heads, {}, &P::second)->second > 1) { heads.erase(ranges::min_element(heads, {}, &P::second)); } else { heads.erase(ranges::remove_if(heads, [](P x) { return x.second == 0; }).begin(), heads.end()); } if (heads.size() == 1) { int i1 = heads[0].first; p[i1] = 1; idx.emplace_back(a); auto dfs = [&](auto&& self, int i) -> void { if (p[i] != -1) return; int ni = ask(i1, i); if (st.contains(ni)) { self(self, ni); p[i] = p[ni] - 1; } else { p[i] = sz; } }; for (int i : idx) dfs(dfs, i); return; } if (heads.size() <= 3) { assert(sz >= 5); int i12a, i12b, i3; if (heads.size() == 2) { i12a = heads[0].first, i12b = heads[1].first; i3 = ask(i12a, i12b); } else { int x = heads[0].first, y = heads[1].first, z = heads[2].first; tie(i12a, i12b, i3) = ask(x, y) == z ? tuple(x, y, z) : ask(y, z) == x ? tuple(y, z, x) : tuple(z, x, y); } int i45a = ask(i12a, i3), i45b = ask(i12b, i3); int i1, i2, i4, i5; tie(i1, i2, i4, i5) = ask(i12a, i45a) == i45b ? tuple(i12a, i12b, i45a, i45b) : tuple(i12b, i12a, i45b, i45a); p[i1] = 1, p[i2] = 2, p[i3] = 3, p[i4] = 4, p[i5] = 5; } else { VI is; for (auto [i, l] : heads) is.emplace_back(i); self(self, is); } idx.emplace_back(a); for (int i : idx) if (p[i] != -1) pos[p[i]] = i; int i1 = pos[1], ix = pos[2], x = 2; assert(i1 != -1 && ix != -1); while (ix != a) { if (pos[x+1] == -1) { int k = ask(i1, ix); p[k] = x + 1; pos[p[k]] = k; } x++; ix = pos[x]; } to.clear(); for (auto [u, v] : es) to[u] = v; ix = pos[2], x = 2; while (x != sz) { if (to[ix]) { int j = to[ix]; p[j] = x + p[a]; pos[p[j]] = j; } if (pos[x+1] == -1) { int k = ask(i1, ix); p[k] = x + 1; pos[p[k]] = k; } x++; ix = pos[x]; } }; VI all_idx; rep(i, n) all_idx.emplace_back(i + 1); dfs(dfs, all_idx); cout << 2; for (int i = 1; i <= n; i++) cout << ' ' << p[i]; cout << endl; } }