#line 1 "/home/maspy/compro/library/my_template.hpp" #if defined(LOCAL) #include #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") #pragma GCC target("avx2,popcnt") #include using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template constexpr T infty = 0; template <> constexpr int infty = 1'000'000'000; template <> constexpr ll infty = ll(infty) * infty * 2; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * infty; template <> constexpr double infty = infty; template <> constexpr long double infty = infty; using pi = pair; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template T POP(deque &que) { T a = que.front(); que.pop_front(); return a; } template T POP(pq &que) { T a = que.top(); que.pop(); return a; } template T POP(pqg &que) { T a = que.top(); que.pop(); return a; } template T POP(vc &que) { T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template vector argsort(const vector &A) { vector ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { vc B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #endif #line 1 "/home/maspy/compro/library/other/io.hpp" #define FASTIO #include // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d: x) rd(d); } template void rd(vc &x) { for (auto &d: x) rd(d); } void read() {} template void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 3 "main.cpp" #line 2 "/home/maspy/compro/library/alg/monoid/add.hpp" template struct Monoid_Add { using X = E; using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return x + y; } static constexpr X inverse(const X &x) noexcept { return -x; } static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; } static constexpr X unit() { return X(0); } static constexpr bool commute = true; }; #line 3 "/home/maspy/compro/library/ds/fenwicktree/fenwicktree.hpp" template struct FenwickTree { using G = Monoid; using E = typename G::value_type; int n; vector dat; E total; FenwickTree() {} FenwickTree(int n) { build(n); } template FenwickTree(int n, F f) { build(n, f); } FenwickTree(const vc& v) { build(v); } void build(int m) { n = m; dat.assign(m, G::unit()); total = G::unit(); } void build(const vc& v) { build(len(v), [&](int i) -> E { return v[i]; }); } template void build(int m, F f) { n = m; dat.clear(); dat.reserve(n); total = G::unit(); FOR(i, n) { dat.eb(f(i)); } for (int i = 1; i <= n; ++i) { int j = i + (i & -i); if (j <= n) dat[j - 1] = G::op(dat[i - 1], dat[j - 1]); } total = prefix_sum(m); } E prod_all() { return total; } E sum_all() { return total; } E sum(int k) { return prefix_sum(k); } E prod(int k) { return prefix_prod(k); } E prefix_sum(int k) { return prefix_prod(k); } E prefix_prod(int k) { chmin(k, n); E ret = G::unit(); for (; k > 0; k -= k & -k) ret = G::op(ret, dat[k - 1]); return ret; } E sum(int L, int R) { return prod(L, R); } E prod(int L, int R) { chmax(L, 0), chmin(R, n); if (L == 0) return prefix_prod(R); assert(0 <= L && L <= R && R <= n); E pos = G::unit(), neg = G::unit(); while (L < R) { pos = G::op(pos, dat[R - 1]), R -= R & -R; } while (R < L) { neg = G::op(neg, dat[L - 1]), L -= L & -L; } return G::op(pos, G::inverse(neg)); } void add(int k, E x) { multiply(k, x); } void multiply(int k, E x) { static_assert(G::commute); total = G::op(total, x); for (++k; k <= n; k += k & -k) dat[k - 1] = G::op(dat[k - 1], x); } template int max_right(const F check, int L = 0) { assert(check(G::unit())); E s = G::unit(); int i = L; // 2^k 進むとダメ int k = [&]() { while (1) { if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; } if (i == 0) { return topbit(n) + 1; } int k = lowbit(i) - 1; if (i + (1 << k) > n) return k; E t = G::op(s, dat[i + (1 << k) - 1]); if (!check(t)) { return k; } s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i; } }(); while (k) { --k; if (i + (1 << k) - 1 < len(dat)) { E t = G::op(s, dat[i + (1 << k) - 1]); if (check(t)) { i += (1 << k), s = t; } } } return i; } // check(i, x) template int max_right_with_index(const F check, int L = 0) { assert(check(L, G::unit())); E s = G::unit(); int i = L; // 2^k 進むとダメ int k = [&]() { while (1) { if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; } if (i == 0) { return topbit(n) + 1; } int k = lowbit(i) - 1; if (i + (1 << k) > n) return k; E t = G::op(s, dat[i + (1 << k) - 1]); if (!check(i + (1 << k), t)) { return k; } s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i; } }(); while (k) { --k; if (i + (1 << k) - 1 < len(dat)) { E t = G::op(s, dat[i + (1 << k) - 1]); if (check(i + (1 << k), t)) { i += (1 << k), s = t; } } } return i; } template int min_left(const F check, int R) { assert(check(G::unit())); E s = G::unit(); int i = R; // false になるところまで戻る int k = 0; while (i > 0 && check(s)) { s = G::op(s, dat[i - 1]); k = lowbit(i); i -= i & -i; } if (check(s)) { assert(i == 0); return 0; } // 2^k 進むと ok になる // false を維持して進む while (k) { --k; E t = G::op(s, G::inverse(dat[i + (1 << k) - 1])); if (!check(t)) { i += (1 << k), s = t; } } return i + 1; } int kth(E k, int L = 0) { return max_right([&k](E x) -> bool { return x <= k; }, L); } }; #line 2 "/home/maspy/compro/library/ds/fenwicktree/fenwicktree_01.hpp" struct FenwickTree_01 { int N, n; vc dat; FenwickTree> bit; FenwickTree_01() {} FenwickTree_01(int n) { build(n); } template FenwickTree_01(int n, F f) { build(n, f); } void build(int m) { N = m; n = ceil(N + 1, 64); dat.assign(n, u64(0)); bit.build(n); } template void build(int m, F f) { N = m; n = ceil(N + 1, 64); dat.assign(n, u64(0)); FOR(i, N) { dat[i / 64] |= u64(f(i)) << (i % 64); } bit.build(n, [&](int i) -> int { return popcnt(dat[i]); }); } int sum_all() { return bit.sum_all(); } int sum(int k) { return prefix_sum(k); } int prefix_sum(int k) { int ans = bit.sum(k / 64); ans += popcnt(dat[k / 64] & ((u64(1) << (k % 64)) - 1)); return ans; } int sum(int L, int R) { if (L == 0) return prefix_sum(R); int ans = 0; ans -= popcnt(dat[L / 64] & ((u64(1) << (L % 64)) - 1)); ans += popcnt(dat[R / 64] & ((u64(1) << (R % 64)) - 1)); ans += bit.sum(L / 64, R / 64); return ans; } void add(int k, int x) { if (x == 1) add(k); if (x == -1) remove(k); } void add(int k) { dat[k / 64] |= u64(1) << (k % 64); bit.add(k / 64, 1); } void remove(int k) { dat[k / 64] &= ~(u64(1) << (k % 64)); bit.add(k / 64, -1); } int kth(int k, int L = 0) { if (k >= sum_all()) return N; k += popcnt(dat[L / 64] & ((u64(1) << (L % 64)) - 1)); L /= 64; int mid = 0; auto check = [&](auto e) -> bool { if (e <= k) chmax(mid, e); return e <= k; }; int idx = bit.max_right(check, L); if (idx == n) return N; k -= mid; u64 x = dat[idx]; int p = popcnt(x); if (p <= k) return N; k = binary_search([&](int n) -> bool { return (p - popcnt(x >> n)) <= k; }, 0, 64, 0); return 64 * idx + k; } int next(int k) { int idx = k / 64; k %= 64; u64 x = dat[idx] & ~((u64(1) << k) - 1); if (x) return 64 * idx + lowbit(x); idx = bit.kth(0, idx + 1); if (idx == n || !dat[idx]) return N; return 64 * idx + lowbit(dat[idx]); } int prev(int k) { if (k == N) --k; int idx = k / 64; k %= 64; u64 x = dat[idx]; if (k < 63) x &= (u64(1) << (k + 1)) - 1; if (x) return 64 * idx + topbit(x); idx = bit.min_left([&](auto e) -> bool { return e <= 0; }, idx) - 1; if (idx == -1) return -1; return 64 * idx + topbit(dat[idx]); } }; #line 3 "/home/maspy/compro/library/seq/inversion.hpp" template ll inversion(vc A) { int N = len(A); if (A.empty()) return 0; ll ANS = 0; FenwickTree_01 bit(N); auto I = argsort(A); for (auto& i: I) { ANS += bit.sum_all() - bit.sum(i); bit.add(i, 1); } return ANS; } // i 番目:A_i が先頭になるように rotate したときの転倒数 template vi inversion_rotate(vc& A) { const int N = len(A); if (!SMALL) { auto key = A; UNIQUE(key); for (auto&& x: A) x = LB(key, x); } ll K = MAX(A) + 1; ll ANS = 0; FenwickTree> bit(K); for (auto&& x: A) { ANS += bit.sum(x + 1, K); bit.add(x, 1); } vi res(N); FOR(i, N) { res[i] = ANS; ll x = A[i]; ANS = ANS + bit.sum(x + 1, K) - bit.prefix_sum(x); } return res; } // inv[i][j] = inversion A[i:j) であるような (N+1, N+1) テーブル template vvc all_range_inversion(vc& A) { int N = len(A); vv(int, dp, N + 1, N + 1); FOR_R(L, N + 1) FOR(R, L + 2, N + 1) { dp[L][R] = dp[L][R - 1] + dp[L + 1][R] - dp[L + 1][R - 1]; if (A[L] > A[R - 1]) ++dp[L][R]; } return dp; } #line 5 "main.cpp" void solve() { LL(N); VEC(int, A, N); FenwickTree_01 bit(N + 1); deque ANS; for (auto& x: A) { ll lo = bit.sum(0, x); ll hi = bit.sum(x, N + 1); if (lo < hi) { ANS.push_front(x); } elif (lo > hi) { ANS.push_back(x); } else { if (ANS.empty()) { ANS.push_back(x); } else { if (ANS[0] > x) { ANS.push_front(x); } else { ANS.push_back(x); } } } bit.add(x); } vc X; while (len(ANS)) X.eb(POP(ANS)); print(inversion(X)); print(X); } signed main() { INT(T); FOR(T) solve(); return 0; }