diff --git a/src/core/all_cases/internal/all_cases.cc b/src/core/all_cases/internal/all_cases.cc
index b9be571..5f82087 100644
--- a/src/core/all_cases/internal/all_cases.cc
+++ b/src/core/all_cases/internal/all_cases.cc
@@ -65,7 +65,7 @@ void AllCases::build() {
         x = range_reverse(x);
     }
     for (const auto head : get_heads()) {
-        build_cases(ranges, reversed, get_cases()[head], head);
+        build_cases(ranges, reversed, get_cases().ranges(head), head);
     }
     available_ = true;
     KLSK_MEM_BARRIER;
@@ -92,7 +92,7 @@ void AllCases::build_async(Executor &&executor, Notifier &&callback) {
     Worker worker {executor};
     for (const auto head : get_heads()) {
         worker.post([head, reversed] {
-            build_cases(BasicRanges::instance().fetch(), *reversed, get_cases()[head], head);
+            build_cases(BasicRanges::instance().fetch(), *reversed, get_cases().ranges(head), head);
         });
     }
 
diff --git a/src/core/benchmark/ranges.cc b/src/core/benchmark/ranges.cc
index 3c9cfc5..e2f90c4 100644
--- a/src/core/benchmark/ranges.cc
+++ b/src/core/benchmark/ranges.cc
@@ -31,8 +31,34 @@ static void RangesUnionExport(benchmark::State &state) {
     }
 }
 
-BENCHMARK(SpawnRanges)->Unit(benchmark::kMillisecond);
+static void RangesSize(benchmark::State &state) {
+    auto &all_cases = AllCases::instance().fetch();
+    // std::cout << all_cases.size() << std::endl;
+    for (auto _ : state) {
+        volatile auto k1 = all_cases.size();
+        volatile auto k2 = all_cases.size();
+        volatile auto k3 = all_cases.size();
+        volatile auto k4 = all_cases.size();
+        volatile auto k5 = all_cases.size();
+        volatile auto k6 = all_cases.size();
+        volatile auto k7 = all_cases.size();
+        volatile auto k8 = all_cases.size();
+
+        volatile auto p1 = all_cases.size();
+        volatile auto p2 = all_cases.size();
+        volatile auto p3 = all_cases.size();
+        volatile auto p4 = all_cases.size();
+        volatile auto p5 = all_cases.size();
+        volatile auto p6 = all_cases.size();
+        volatile auto p7 = all_cases.size();
+        volatile auto p8 = all_cases.size();
+    }
+}
+
+// BENCHMARK(SpawnRanges)->Unit(benchmark::kMillisecond);
 
 // BENCHMARK(RangesUnionExport)->Unit(benchmark::kMillisecond);
 
+BENCHMARK(RangesSize);
+
 BENCHMARK_MAIN();
diff --git a/src/core/group/internal/group.cc b/src/core/group/internal/group.cc
index d231a79..53ebe89 100644
--- a/src/core/group/internal/group.cc
+++ b/src/core/group/internal/group.cc
@@ -68,11 +68,11 @@ RangesUnion Group::cases() const {
     RangesUnion data;
     for (auto raw_code : codes) {
         auto common_code = raw_code.to_common_code().unwrap();
-        data[common_code >> 32].emplace_back(static_cast<uint32_t>(common_code));
+        data.ranges(common_code >> 32).emplace_back(static_cast<uint32_t>(common_code));
     }
 
     for (int head = 0; head < 16; ++head) {
-        std::stable_sort(data[head].begin(), data[head].end());
+        std::stable_sort(data.ranges(head).begin(), data.ranges(head).end());
     }
     return data;
 }
diff --git a/src/core/group/internal/group_cases.cc b/src/core/group/internal/group_cases.cc
index 6499986..e937e8d 100644
--- a/src/core/group/internal/group_cases.cc
+++ b/src/core/group/internal/group_cases.cc
@@ -119,15 +119,15 @@ CommonCode GroupCases::fast_obtain_code(CaseInfo info) {
 
     auto case_id = info.case_id();
     for (;;) {
-        if (case_id >= cases[head].size()) {
-            case_id -= cases[head].size();
+        if (case_id >= cases.ranges(head).size()) {
+            case_id -= cases.ranges(head).size();
             ++head;
         } else {
             break;
         }
     }
 
-    auto range = cases[head][case_id];
+    auto range = cases.ranges(head)[case_id];
     return CommonCode::unsafe_create(head << 32 | range);
 }
 
@@ -173,15 +173,15 @@ CommonCode GroupCases::tiny_obtain_code(CaseInfo info) {
 
     auto case_id = info.case_id();
     for (;;) {
-        if (case_id >= cases[head].size()) {
-            case_id -= cases[head].size();
+        if (case_id >= cases.ranges(head).size()) {
+            case_id -= cases.ranges(head).size();
             ++head;
         } else {
             break;
         }
     }
 
-    auto range = cases[head][case_id];
+    auto range = cases.ranges(head)[case_id];
     return CommonCode::unsafe_create(head << 32 | range);
 }
 
diff --git a/src/core/group/internal/group_union.cc b/src/core/group/internal/group_union.cc
index 75afa5c..6590352 100644
--- a/src/core/group/internal/group_union.cc
+++ b/src/core/group/internal/group_union.cc
@@ -7,7 +7,7 @@ using klotski::cases::RangesUnion;
 
 using klotski::cases::BASIC_RANGES_NUM;
 
-#define RANGE_DERIVE(HEAD) ranges.derive(HEAD, cases[HEAD])
+#define RANGE_DERIVE(HEAD) ranges.derive(HEAD, cases.ranges(HEAD))
 
 RangesUnion GroupUnion::cases() const {
     auto [n, n_2x1, n_1x1] = BLOCK_NUM[type_id_];
@@ -19,10 +19,10 @@ RangesUnion GroupUnion::cases() const {
     ranges.reverse();
 
     RangesUnion cases;
-    cases[0x0].reserve(s_a); cases[0x1].reserve(s_b); cases[0x2].reserve(s_a);
-    cases[0x4].reserve(s_c); cases[0x5].reserve(s_d); cases[0x6].reserve(s_c);
-    cases[0x8].reserve(s_c); cases[0x9].reserve(s_d); cases[0xA].reserve(s_c);
-    cases[0xC].reserve(s_a); cases[0xD].reserve(s_b); cases[0xE].reserve(s_a);
+    cases.ranges(0x0).reserve(s_a); cases.ranges(0x1).reserve(s_b); cases.ranges(0x2).reserve(s_a);
+    cases.ranges(0x4).reserve(s_c); cases.ranges(0x5).reserve(s_d); cases.ranges(0x6).reserve(s_c);
+    cases.ranges(0x8).reserve(s_c); cases.ranges(0x9).reserve(s_d); cases.ranges(0xA).reserve(s_c);
+    cases.ranges(0xC).reserve(s_a); cases.ranges(0xD).reserve(s_b); cases.ranges(0xE).reserve(s_a);
 
     RANGE_DERIVE(0x0); RANGE_DERIVE(0x1); RANGE_DERIVE(0x2);
     RANGE_DERIVE(0x4); RANGE_DERIVE(0x5); RANGE_DERIVE(0x6);
diff --git a/src/core/ranges/internal/ranges.cc b/src/core/ranges/internal/ranges.cc
index ae1c025..85cdcd9 100644
--- a/src/core/ranges/internal/ranges.cc
+++ b/src/core/ranges/internal/ranges.cc
@@ -23,23 +23,44 @@ Ranges& Ranges::operator+=(const Ranges &ranges) {
 
 RangesUnion& RangesUnion::operator+=(const RangesUnion &ranges_union) {
     for (const auto head : heads) {
-        (*this)[head] += ranges_union[head];
+        // (*this)[head] += ranges_union[head];
+        std::array<Ranges, 16>::operator[](head) += ranges_union.std::array<Ranges, 16>::operator[](head);
     }
     return *this;
 }
 
 std::vector<CommonCode> RangesUnion::codes() const {
-    size_type size = 0;
-    for (const auto head : heads) {
-        size += (*this)[head].size();
-    }
-
     std::vector<CommonCode> codes;
-    codes.reserve(size);
+    codes.reserve(size());
     for (const auto head : heads) {
-        for (const auto range : (*this)[head]) {
+        // for (const auto range : (*this)[head]) {
+        for (const auto range : ranges(head)) {
             codes.emplace_back(CommonCode::unsafe_create(head << 32 | range));
         }
     }
+    // TODO: try using std::views
     return codes;
 }
+
+// TODO: move to `.inl` file
+size_t RangesUnion::size() const {
+    size_type size = 0;
+    for (const auto head : heads) {
+        size += std::array<Ranges, 16>::operator[](head).size();
+        // size += (*this)[head].size();
+    }
+    return size;
+}
+
+uint32_t RangesUnion::operator[](size_type index) const {
+    size_t head = 0;
+    for (;;) {
+        if (index >= std::array<Ranges, 16>::operator[](head).size()) {
+            index -= std::array<Ranges, 16>::operator[](head).size();
+            ++head;
+        } else {
+            break;
+        }
+    }
+    return std::array<Ranges, 16>::operator[](head)[index];
+}
diff --git a/src/core/ranges/ranges.h b/src/core/ranges/ranges.h
index 5b9b6f0..bc79ccc 100644
--- a/src/core/ranges/ranges.h
+++ b/src/core/ranges/ranges.h
@@ -41,6 +41,18 @@ public:
 
     /// Export the RangesUnion as CommonCode list.
     [[nodiscard]] std::vector<codec::CommonCode> codes() const;
+
+    [[nodiscard]] const Ranges& ranges(const size_t head) const {
+        return std::array<Ranges, 16>::operator[](head);
+    }
+
+    Ranges& ranges(const size_t head) {
+        return std::array<Ranges, 16>::operator[](head);
+    }
+
+    [[nodiscard]] size_t size() const;
+
+    [[nodiscard]] uint32_t operator[](size_type) const;
 };
 
 } // namespace klotski::cases
diff --git a/src/core/short_code/internal/convert.cc b/src/core/short_code/internal/convert.cc
index 0b87697..7a43ff2 100644
--- a/src/core/short_code/internal/convert.cc
+++ b/src/core/short_code/internal/convert.cc
@@ -52,7 +52,7 @@ static uint32_t check_range(uint32_t head, uint32_t range) noexcept {
 
 uint32_t ShortCode::fast_encode(uint64_t common_code) {
     auto head = common_code >> 32;
-    auto &ranges = (*cases_)[head]; // match available ranges
+    const auto &ranges = (*cases_).ranges(head); // match available ranges
     // TODO: try to narrow the scope by prefix
     auto target = std::lower_bound(ranges.begin(), ranges.end(), (uint32_t)common_code);
     return ALL_CASES_OFFSET[head] + (target - ranges.begin());
@@ -62,7 +62,7 @@ uint64_t ShortCode::fast_decode(uint32_t short_code) {
     auto offset = std::upper_bound(ALL_CASES_OFFSET.begin(), ALL_CASES_OFFSET.end(), short_code) - 1;
     uint64_t head = offset - ALL_CASES_OFFSET.begin();
     // return (head << 32) | AllCases::instance().fetch()[head][short_code - *offset];
-    return (head << 32) | (*cases_)[head][short_code - *offset];
+    return (head << 32) | (*cases_).ranges(head)[short_code - *offset];
 }
 
 uint32_t ShortCode::tiny_encode(uint64_t common_code) {
diff --git a/src/core_test/cases/all_cases.cc b/src/core_test/cases/all_cases.cc
index 42f4aec..4758b56 100644
--- a/src/core_test/cases/all_cases.cc
+++ b/src/core_test/cases/all_cases.cc
@@ -51,15 +51,15 @@ protected:
     static void Verify() {
         const auto &all_cases = AllCases::instance().fetch();
         for (int head = 0; head < 16; ++head) {
-            EXPECT_EQ(all_cases[head].size(), ALL_CASES_NUM[head]); // verify all cases size
-            EXPECT_EQ(helper::xxh3(all_cases[head]), ALL_CASES_XXH3[head]); // verify all cases checksum
+            EXPECT_EQ(all_cases.ranges(head).size(), ALL_CASES_NUM[head]); // verify all cases size
+            EXPECT_EQ(helper::xxh3(all_cases.ranges(head)), ALL_CASES_XXH3[head]); // verify all cases checksum
         }
     }
 };
 
 TEST_FF(AllCases, content) {
     for (auto head : Heads) {
-        auto &cases = AllCases::instance().fetch()[head];
+        auto &cases = AllCases::instance().fetch().ranges(head);
         EXPECT_SORTED_AND_UNIQUE(cases);
         EXPECT_EQ(cases.size(), ALL_CASES_NUM[head]); // size verify
         EXPECT_EQ(helper::xxh3(cases), ALL_CASES_XXH3[head]); // checksum verify
diff --git a/src/core_test/cases/ranges.cc b/src/core_test/cases/ranges.cc
index 5b4e38d..542eda9 100644
--- a/src/core_test/cases/ranges.cc
+++ b/src/core_test/cases/ranges.cc
@@ -16,7 +16,7 @@ TEST(Ranges, check) {
     for (const auto head : Heads) {
         for (auto range : BasicRanges::instance().fetch()) {
             if (Ranges::check(head, range_reverse(range)) == 0) {
-                all_cases[head].emplace_back(range); // found valid cases
+                all_cases.ranges(head).emplace_back(range); // found valid cases
             }
         }
     }
@@ -45,14 +45,14 @@ TEST(Ranges, derive) {
 
         RangesUnion cases;
         for (const auto head : Heads) {
-            ranges.derive(head, cases[head]);
-            EXPECT_SORTED_AND_UNIQUE(cases[head]); // sorted and unique
-            EXPECT_COMMON_CODES(head, cases[head]); // verify common codes
+            ranges.derive(head, cases.ranges(head));
+            EXPECT_SORTED_AND_UNIQUE(cases.ranges(head)); // sorted and unique
+            EXPECT_COMMON_CODES(head, cases.ranges(head)); // verify common codes
         }
 
         ranges.reverse();
         for (const auto head : Heads) {
-            EXPECT_SUBSET(ranges, cases[head]); // derive ranges is subset
+            EXPECT_SUBSET(ranges, cases.ranges(head)); // derive ranges is subset
         }
     }
 }
@@ -83,7 +83,7 @@ TEST(Ranges, combine) {
     RangesUnion all_cases;
     all_ranges.reserve(BASIC_RANGES_NUM_); // pre reserve
     for (const auto head : Heads) {
-        all_cases[head].reserve(ALL_CASES_NUM[head]); // pre reserve
+        all_cases.ranges(head).reserve(ALL_CASES_NUM[head]); // pre reserve
     }
 
     for (auto [n, n_2x1, n_1x1] : BLOCK_NUM) {
@@ -92,21 +92,21 @@ TEST(Ranges, combine) {
         all_ranges += ranges;
         ranges.reverse(); // reverse ranges for derive
         for (const auto head : Heads) {
-            ranges.derive(head, all_cases[head]); // derive from sub ranges
+            ranges.derive(head, all_cases.ranges(head)); // derive from sub ranges
         }
     }
 
     std::ranges::stable_sort(all_ranges.begin(), all_ranges.end());
     for (const auto head : Heads) {
-        std::ranges::stable_sort(all_cases[head].begin(), all_cases[head].end());
+        std::ranges::stable_sort(all_cases.ranges(head).begin(), all_cases.ranges(head).end());
     }
     EXPECT_EQ(all_ranges, BasicRanges::instance().fetch()); // verify all ranges
     EXPECT_EQ(all_cases, AllCases::instance().fetch()); // verify all cases
 
     all_ranges.reverse(); // reverse ranges for derive
     for (const auto head : Heads) {
-        all_cases[head].clear();
-        all_ranges.derive(head, all_cases[head]); // derive from all ranges
+        all_cases.ranges(head).clear();
+        all_ranges.derive(head, all_cases.ranges(head)); // derive from all ranges
     }
     EXPECT_EQ(all_cases, AllCases::instance().fetch()); // verify content
 }
diff --git a/src/core_test/cases/ranges_union.cc b/src/core_test/cases/ranges_union.cc
index 4c7ff25..dc9e0c5 100644
--- a/src/core_test/cases/ranges_union.cc
+++ b/src/core_test/cases/ranges_union.cc
@@ -27,14 +27,14 @@ TEST(RangesUnion, append) {
 
         RangesUnion ru;
         for (const auto head : Heads) {
-            r.derive(head, ru[head]);
+            r.derive(head, ru.ranges(head));
         }
         auto &tmp = cases += ru;
         EXPECT_EQ(tmp, cases); // reference of cases
     }
 
     for (const auto head : Heads) {
-        std::stable_sort(cases[head].begin(), cases[head].end());
+        std::stable_sort(cases.ranges(head).begin(), cases.ranges(head).end());
     }
     EXPECT_EQ(cases, AllCases::instance().fetch());
 }
diff --git a/src/core_test/mover/mover.cc b/src/core_test/mover/mover.cc
index b9f0622..63998c6 100644
--- a/src/core_test/mover/mover.cc
+++ b/src/core_test/mover/mover.cc
@@ -38,7 +38,7 @@ TEST(Core, core) {
     // codes.reserve(klotski::cases::ALL_CASES_NUM_);
 
     for (uint64_t head = 0; head < 16; ++head) {
-        for (const auto range : AllCases::instance().fetch()[head]) {
+        for (const auto range : AllCases::instance().fetch().ranges(head)) {
             auto common_code = CommonCode::unsafe_create(head << 32 | range);
             auto raw_code = common_code.to_raw_code().unwrap();
 
@@ -73,7 +73,7 @@ TEST(Core, mask) {
     raw_codes.reserve(klotski::cases::ALL_CASES_NUM_);
 
     for (uint64_t head = 0; head < 16; ++head) {
-        for (const auto range : AllCases::instance().fetch()[head]) {
+        for (const auto range : AllCases::instance().fetch().ranges(head)) {
             auto common_code = CommonCode::unsafe_create(head << 32 | range);
             auto raw_code = common_code.to_raw_code().unwrap();
             raw_codes.emplace_back(raw_code);
@@ -173,7 +173,7 @@ TEST(Core, next_cases) {
     std::vector<RawCode> raw_codes;
 
     for (uint64_t head = 0; head < 16; ++head) {
-        for (const auto range : AllCases::instance().fetch()[head]) {
+        for (const auto range : AllCases::instance().fetch().ranges(head)) {
             auto common_code = CommonCode::unsafe_create(head << 32 | range);
 
             auto raw_code = common_code.to_raw_code();