diff --git a/src/core/benchmark/fast_cal.cc b/src/core/benchmark/fast_cal.cc
index a2725c0..c7c3c5b 100644
--- a/src/core/benchmark/fast_cal.cc
+++ b/src/core/benchmark/fast_cal.cc
@@ -8,19 +8,24 @@
 
 using klotski::codec::CommonCode;
 
-using klotski::fast_cal::FastCalPro;
+using klotski::fast_cal::FastCal;
 
 static void FastCalBenchmark(benchmark::State &state) {
 
     auto code = CommonCode::unsafe_create(0x1A9BF0C00).to_raw_code();
-//    auto code = CommonCode::unsafe_create(0x4FEA13400).to_raw_code();
+    // auto code = CommonCode::unsafe_create(0x4FEA13400).to_raw_code();
 
     for (auto _ : state) {
-        auto fc = FastCalPro(code);
+        auto fc = FastCal(code);
+
         benchmark::DoNotOptimize(fc.solve());
-//        benchmark::DoNotOptimize(fc.demo());
-        // benchmark::DoNotOptimize(FastCal_demo(code));
-//        auto tmp = klotski::cases::Group_extend(code);
+        // benchmark::DoNotOptimize(fc.solve_multi());
+        // benchmark::DoNotOptimize(fc.furthest());
+        // fc.search([](const klotski::codec::RawCode tmp) {
+        //     return tmp == 0x7F87E0E5BFFF492;
+        //     // return tmp == 0x1FB1E37F9E9F5CA;
+        // });
+        // fc.build_all();
     }
 
 }
diff --git a/src/core/fast_cal/fast_cal.h b/src/core/fast_cal/fast_cal.h
index a11b859..b624c38 100644
--- a/src/core/fast_cal/fast_cal.h
+++ b/src/core/fast_cal/fast_cal.h
@@ -1,42 +1,39 @@
 /// Klotski Engine by Dnomd343 @2024
 
-// TODO: only copy from old implementation, the interfaces will change in future.
-
 #pragma once
 
-#include <vector>
 #include <cstdint>
 #include <functional>
+#include <parallel_hashmap/phmap.h>
 
 #include "mover/mover.h"
 #include "layer_queue.h"
 #include "raw_code/raw_code.h"
 
-#include <parallel_hashmap/phmap.h>
-
 namespace klotski::fast_cal {
 
-class FastCalPro {
+class FastCal {
 public:
-    FastCalPro() = delete;
+    FastCal() = delete;
 
-    explicit FastCalPro(codec::RawCode raw_code);
+    explicit FastCal(codec::RawCode code);
 
     // ------------------------------------------------------------------------------------- //
 
-    // TODO: add global build
-
-    void build();
-
     /// Calculate a minimum-step case.
     std::optional<codec::RawCode> solve();
 
-    /// Calculate all the maximum-step cases.
-    std::vector<codec::RawCode> furthest();
-
     /// Calculate all the minimum-step cases.
     std::vector<codec::RawCode> solve_multi();
 
+    // ------------------------------------------------------------------------------------- //
+
+    /// Calculate all cases.
+    void build_all();
+
+    /// Calculate all the maximum-step cases.
+    std::vector<codec::RawCode> furthest();
+
     /// Calculate the first case that meets the requirement.
     std::optional<codec::RawCode> search(std::function<bool(codec::RawCode)> &&match);
 
@@ -61,16 +58,18 @@ private:
 
     // ------------------------------------------------------------------------------------- //
 
-    // TODO: add invalid RawCode constexpr var
+    /// Using non-existed RawCode value to represent NULL.
+    static constexpr auto nil = codec::RawCode::unsafe_create(0);
+
+    // ------------------------------------------------------------------------------------- //
 
-    struct data_t {
+    struct info_t {
         uint64_t mask;
-        codec::RawCode back;
+        codec::RawCode parent;
     };
 
-    // codec::RawCode root_;
-    LayerQueue<codec::RawCode> codes_;
-    phmap::flat_hash_map<codec::RawCode, data_t> cases_;
+    LayerQueue<codec::RawCode> seeker_;
+    phmap::flat_hash_map<codec::RawCode, info_t> cases_;
 
     // ------------------------------------------------------------------------------------- //
 };
diff --git a/src/core/fast_cal/internal/fast_cal.cc b/src/core/fast_cal/internal/fast_cal.cc
index a118755..eb77df9 100644
--- a/src/core/fast_cal/internal/fast_cal.cc
+++ b/src/core/fast_cal/internal/fast_cal.cc
@@ -1,110 +1,119 @@
-#include "mover/mover.h"
-#include "group/group.h"
+#include "utils/common.h"
 #include "fast_cal/fast_cal.h"
 
-using klotski::codec::RawCode;
-using klotski::codec::CommonCode;
-using klotski::cases::RangesUnion;
+using klotski::BLOCK_MSK;
+using klotski::BLOCK_CE_2x2;
 
+using klotski::codec::RawCode;
 using klotski::mover::MaskMover;
-using klotski::cases::GroupUnion;
+using klotski::fast_cal::FastCal;
+
+// ----------------------------------------------------------------------------------------- //
+
+void FastCal::build_all() {
+    auto mover = MaskMover([this](const RawCode code, const uint64_t mask) {
+        try_emplace(code, mask);
+    });
+    while (!seeker_.is_ending()) {
+        spawn_next(mover);
+    }
+}
 
-using klotski::fast_cal::FastCalPro;
+std::vector<RawCode> FastCal::furthest() {
+    if (!seeker_.is_ending()) {
+        build_all();
+    }
+    return seeker_.last_layer();
+}
 
-static KLSK_INLINE bool is_solved(RawCode raw_code) {
-    return ((raw_code.unwrap() >> 39) & 0b111) == 0b100;
+// ----------------------------------------------------------------------------------------- //
+
+std::vector<std::vector<RawCode>> FastCal::exports() const {
+    return seeker_.all_layers();
 }
 
-std::optional<RawCode> FastCalPro::solve() {
-    // if (is_solved(root_.unwrap())) {
-    //     return root_;
-    // }
+std::vector<RawCode> FastCal::backtrack(RawCode code) const {
+    if (const auto match = cases_.find(code); match == cases_.end()) {
+        return {}; // case not found
+    }
+    std::vector<RawCode> path;
+    while (code != 0) {
+        path.emplace_back(code);
+        code = cases_.find(code)->second.parent;
+    }
+    std::reverse(path.begin(), path.end());
+    return path;
+}
+
+// ----------------------------------------------------------------------------------------- //
+
+static KLSK_INLINE bool is_solved(const RawCode raw_code) {
+    return ((raw_code.unwrap() >> 39) & BLOCK_MSK) == BLOCK_CE_2x2;
+}
+
+std::optional<RawCode> FastCal::solve() {
+    if (is_solved(seeker_.current())) {
+        return seeker_.current(); // root case solved
+    }
 
-    uint64_t solution = 0;
-    auto mover = MaskMover([this, &solution](RawCode code, uint64_t mask) {
+    RawCode solution {nil};
+    auto mover = MaskMover([this, &solution](const RawCode code, const uint64_t mask) {
         if (try_emplace(code, mask) && is_solved(code)) {
-            solution = code.unwrap();
+            solution = code;
         }
     });
-    while (!codes_.is_ending()) {
+
+    while (!seeker_.is_ending()) {
         spawn_next(mover);
-        if (solution != 0) {
-            return RawCode::unsafe_create(solution);
+        if (solution != nil) {
+            return solution;
         }
     }
     return std::nullopt;
 }
 
-std::optional<RawCode> FastCalPro::search(std::function<bool(RawCode)> &&match) {
-    // TODO: check root case
+std::optional<RawCode> FastCal::search(std::function<bool(RawCode)> &&match) {
+    if (match(seeker_.current())) {
+        return seeker_.current(); // root case matched
+    }
 
-    uint64_t target = 0;
-    auto mover = MaskMover([this, &target, match = std::move(match)](RawCode code, uint64_t mask) {
+    RawCode target {nil};
+    auto mover = MaskMover([this, &target, match = std::move(match)](const RawCode code, const uint64_t mask) {
         if (try_emplace(code, mask) && match(code)) {
-            target = code.unwrap();
+            target = code;
         }
     });
-    while (!codes_.is_ending()) {
+
+    while (!seeker_.is_ending()) {
         spawn_next(mover);
-        if (target != 0) {
-            return RawCode::unsafe_create(target);
+        if (target != nil) {
+            return target;
         }
     }
     return std::nullopt;
 }
 
-std::vector<RawCode> FastCalPro::solve_multi() {
-    // TODO: check root case
+std::vector<RawCode> FastCal::solve_multi() {
+    if (is_solved(seeker_.current())) {
+        return {seeker_.current()}; // root case solved
+    }
 
     bool stop_flag = false;
     std::vector<RawCode> results {};
-
-    auto mover = MaskMover([this, &stop_flag, &results](RawCode code, uint64_t mask) {
+    auto mover = MaskMover([this, &stop_flag, &results](const RawCode code, const uint64_t mask) {
         if (try_emplace(code, mask) && is_solved(code)) {
             stop_flag = true;
             results.emplace_back(code);
         }
     });
 
-    while (!codes_.is_ending()) {
+    while (!seeker_.is_ending()) {
         spawn_next(mover);
-        if (stop_flag && (codes_.is_new_layer() || codes_.is_ending())) {
+        if (stop_flag && (seeker_.is_new_layer() || seeker_.is_ending())) {
             return results;
         }
-
     }
     return {};
 }
 
-void FastCalPro::build() {
-    auto mover = MaskMover([this](RawCode code, uint64_t mask) {
-        try_emplace(code, mask);
-    });
-    while (!codes_.is_ending()) {
-        spawn_next(mover);
-    }
-}
-
-std::vector<RawCode> FastCalPro::furthest() {
-    if (!codes_.is_ending()) {
-        build();
-    }
-    return codes_.last_layer();
-}
-
-std::vector<RawCode> FastCalPro::backtrack(RawCode code) const {
-    if (const auto match = cases_.find(code); match == cases_.end()) {
-        return {}; // case not found
-    }
-    std::vector<RawCode> path;
-    while (code != 0) {
-        path.emplace_back(code);
-        code = cases_.find(code)->second.back;
-    }
-    std::reverse(path.begin(), path.end());
-    return path;
-}
-
-std::vector<std::vector<RawCode>> FastCalPro::exports() const {
-    return codes_.all_layers();
-}
+// ----------------------------------------------------------------------------------------- //
diff --git a/src/core/fast_cal/internal/fast_cal.inl b/src/core/fast_cal/internal/fast_cal.inl
index 4aee075..0173f0b 100644
--- a/src/core/fast_cal/internal/fast_cal.inl
+++ b/src/core/fast_cal/internal/fast_cal.inl
@@ -4,30 +4,30 @@
 
 namespace klotski::fast_cal {
 
-inline FastCalPro::FastCalPro(codec::RawCode raw_code)
-        : codes_({raw_code}, cases::GroupUnion::from_raw_code(raw_code).max_group_size()) {
-    const auto reserve = cases::GroupUnion::from_raw_code(raw_code).max_group_size();
+inline FastCal::FastCal(const codec::RawCode code)
+        : seeker_({code}, cases::GroupUnion::from_raw_code(code).max_group_size()) {
+    const auto reserve = cases::GroupUnion::from_raw_code(code).max_group_size();
     cases_.reserve(static_cast<size_t>(reserve * 1.56));
-    cases_.emplace(raw_code, data_t {0, codec::RawCode::unsafe_create(0)}); // without mask
+    cases_.emplace(code, info_t {0, nil}); // without mask
 }
 
-inline KLSK_INLINE bool FastCalPro::try_emplace(codec::RawCode code, uint64_t mask) {
+inline KLSK_INLINE bool FastCal::try_emplace(const codec::RawCode code, const uint64_t mask) {
     if (const auto match = cases_.find(code); match != cases_.end()) {
         match->second.mask |= mask; // update mask
         return false;
     }
-    cases_.emplace(code, data_t {
+    cases_.emplace(code, info_t {
         .mask = mask,
-        .back = codes_.current(),
+        .parent = seeker_.current(),
     });
-    codes_.emplace(code);
+    seeker_.emplace(code);
     return true;
 }
 
-inline KLSK_INLINE void FastCalPro::spawn_next(mover::MaskMover &mover) {
-    auto curr = codes_.current();
+inline KLSK_INLINE void FastCal::spawn_next(mover::MaskMover &mover) {
+    auto curr = seeker_.current();
     mover.next_cases(curr, cases_.find(curr)->second.mask);
-    codes_.next();
+    seeker_.next();
 }
 
 } // namespace klotski::fast_cal
diff --git a/src/core/fast_cal/internal/layer_queue.inl b/src/core/fast_cal/internal/layer_queue.inl
index d71ec1e..ae17276 100644
--- a/src/core/fast_cal/internal/layer_queue.inl
+++ b/src/core/fast_cal/internal/layer_queue.inl
@@ -10,7 +10,7 @@ LayerQueue<T>::LayerQueue(std::initializer_list<T> first_layer, const size_t max
     for (const auto node : first_layer) {
         emplace(node);
     }
-    layer_offset_.reserve(139); // TODO: confirm the max layer number
+    layer_offset_.reserve(232); // TODO: confirm the max layer number
     layer_offset_.emplace_back(layer_end_);
 }
 
@@ -66,9 +66,12 @@ template <typename T>
 requires std::is_trivial_v<T>
 std::vector<std::vector<T>> LayerQueue<T>::all_layers() const {
     std::vector<std::vector<T>> result;
+    result.reserve(layer_offset_.size() - 1);
     for (size_t i = 0; i < layer_offset_.size() - 1; ++i) {
-        std::vector<T> layer {data_ + layer_offset_[i], data_ + layer_offset_[i + 1]};
-        result.emplace_back(layer);
+        result.emplace_back(std::vector<T> {
+            data_ + layer_offset_[i],
+            data_ + layer_offset_[i + 1]
+        });
     }
     return result;
 }
diff --git a/src/core/main.cc b/src/core/main.cc
index bdca255..0e87a05 100644
--- a/src/core/main.cc
+++ b/src/core/main.cc
@@ -19,6 +19,7 @@
 #include "../../third_party/thread-pool/include/BS_thread_pool.hpp"
 
 using klotski::mover::MaskMover;
+using klotski::fast_cal::FastCal;
 
 using klotski::cases::AllCases;
 using klotski::cases::BasicRanges;
@@ -48,24 +49,25 @@ int main() {
 
     const auto start = std::chrono::system_clock::now();
 
-    auto code = CommonCode::unsafe_create(0x1A9BF0C00).to_raw_code();
-    klotski::fast_cal::FastCalPro fc {code};
+    // const auto code = CommonCode::unsafe_create(0x1A9BF0C00).to_raw_code();
+    const auto code = CommonCode::unsafe_create(0x4FEA13400).to_raw_code();
+    FastCal fc {code};
 
-    std::cout << fc.solve().value() << std::endl;
+    // std::cout << fc.solve().value() << std::endl;
 
-    // for (auto x : fc.solve_multi()) {
-    //     std::cout << x << std::endl;
-    // }
+    for (const auto x : fc.solve_multi()) {
+        std::cout << x.to_common_code() << std::endl;
+    }
 
-    // for (auto x : fc.furthest()) {
-    //     std::cout << x.to_common_code() << std::endl;
-    // }
+    for (const auto x : fc.furthest()) {
+        std::cout << x.to_common_code() << std::endl;
+    }
 
-    // fc.furthest();
-    // for (const auto &layer : fc.exports()) {
-    //     std::cout << layer.size() << std::endl;
-    // }
-    // std::cout << "layer num: " << fc.exports().size() << std::endl;
+    fc.build_all();
+    for (const auto &layer : fc.exports()) {
+        std::cout << layer.size() << std::endl;
+    }
+    std::cout << "layer num: " << fc.exports().size() << std::endl;
 
 //    for (int i = 0; i < 10000000; ++i) {
 //        MaskMover mover([](uint64_t code, uint64_t mask) {
diff --git a/src/core/raw_code/internal/raw_code.inl b/src/core/raw_code/internal/raw_code.inl
index 17d6756..f7e62c8 100644
--- a/src/core/raw_code/internal/raw_code.inl
+++ b/src/core/raw_code/internal/raw_code.inl
@@ -10,7 +10,7 @@ inline RawCode::RawCode(const CommonCode common_code) {
     code_ = extract(common_code.unwrap());
 }
 
-inline RawCode RawCode::unsafe_create(const uint64_t raw_code) {
+constexpr RawCode RawCode::unsafe_create(const uint64_t raw_code) {
     return std::bit_cast<RawCode>(raw_code); // init directly
 }
 
diff --git a/src/core/raw_code/raw_code.h b/src/core/raw_code/raw_code.h
index ce5b71c..ff5f8e9 100644
--- a/src/core/raw_code/raw_code.h
+++ b/src/core/raw_code/raw_code.h
@@ -80,7 +80,7 @@ public:
     explicit RawCode(CommonCode common_code);
 
     /// Create RawCode without any check.
-    static RawCode unsafe_create(uint64_t raw_code);
+    static constexpr RawCode unsafe_create(uint64_t raw_code);
 
     /// Create RawCode with validity check.
     static std::optional<RawCode> create(uint64_t raw_code);
diff --git a/src/core/utils/common.h b/src/core/utils/common.h
index 4d46012..a47e18e 100644
--- a/src/core/utils/common.h
+++ b/src/core/utils/common.h
@@ -21,6 +21,19 @@
 
 // TODO: using constexpr
 
+namespace klotski {
+
+// TODO: remove `CE` tag
+constexpr uint_fast8_t BLOCK_SPC    {0b000}; // space
+constexpr uint_fast8_t BLOCK_FIL    {0b111}; // fill
+constexpr uint_fast8_t BLOCK_CE_1x2 {0b001};
+constexpr uint_fast8_t BLOCK_CE_2x1 {0b010};
+constexpr uint_fast8_t BLOCK_CE_1x1 {0b011};
+constexpr uint_fast8_t BLOCK_CE_2x2 {0b100};
+constexpr uint_fast8_t BLOCK_MSK    {0b111}; // mask
+
+} // namespace klotski
+
 /// NOTE: 0b101 and 0b110 are reserved
 #define BLOCK_space 0b000
 #define BLOCK_fill  0b111