diff --git a/src/core_test/cases/ranges_union.cc b/src/core_test/cases/ranges_union.cc
index 7d44a15..fc9a677 100644
--- a/src/core_test/cases/ranges_union.cc
+++ b/src/core_test/cases/ranges_union.cc
@@ -1,59 +1,81 @@
 #include <gtest/gtest.h>
 
+#include "group/group.h"
+#include "ranges/ranges.h"
+
 #include "helper/hash.h"
-#include "helper/cases.h"
 #include "helper/expect.h"
-#include "ranges/ranges.h"
 
+using klotski::cases::Ranges;
+using klotski::cases::AllCases;
+using klotski::cases::RangesUnion;
+
+using klotski::group::BLOCK_NUM;
+using klotski::cases::ALL_CASES_NUM_;
+
+constexpr auto Heads = RangesUnion::Heads;
 constexpr std::string_view ALL_CASES_MD5 = "3888e9fab8d3cbb50908b12b147cfb23";
 
 static_assert(std::is_base_of_v<std::array<Ranges, 16>, RangesUnion>);
 
+TEST(RangesUnion, heads) {
+    for (const auto head : RangesUnion::Heads) {
+        EXPECT_GE(head, 0);
+        EXPECT_LT(head, 16);
+        EXPECT_NE(head % 4, 3);
+    }
+    EXPECT_SORTED_AND_UNIQUE(RangesUnion::Heads);
+}
+
+TEST(RangesUnion, index) {
+    const auto &all_cases = AllCases::instance().fetch();
+    const auto codes = all_cases.codes();
+    for (size_t i = 0; i < codes.size(); ++i) {
+        EXPECT_EQ(all_cases[i], codes[i]); // test `operator[]`
+    }
+    EXPECT_EQ(all_cases.size(), ALL_CASES_NUM_);
+}
+
 TEST(RangesUnion, export) {
     std::string buffer;
     buffer.reserve(ALL_CASES_NUM_ * 10); // [\dA-F]{9} + '\n'
-    for (auto code : AllCases::instance().fetch().codes()) {
+    for (const auto code : AllCases::instance().fetch().codes()) {
         buffer += std::format("{:09X}\n", code.unwrap());
     }
     EXPECT_EQ(helper::md5(buffer), ALL_CASES_MD5);
 }
 
+TEST(RangesUnion, ranges) {
+    auto mut_cases = AllCases::instance().fetch();
+    for (const auto head : Heads) {
+        auto &ranges = mut_cases.std::array<Ranges, 16>::operator[](head);
+        EXPECT_EQ(mut_cases.ranges(head), ranges);
+    }
+
+    const auto const_cases = AllCases::instance().fetch();
+    for (const auto head : Heads) {
+        const auto &ranges = const_cases.std::array<Ranges, 16>::operator[](head);
+        EXPECT_EQ(const_cases.ranges(head), ranges);
+    }
+}
+
 TEST(RangesUnion, append) {
     RangesUnion cases;
-    for (auto [n, n_2x1, n_1x1] : BLOCK_NUM) {
-        Ranges r;
-        r.spawn(n, n_2x1, n_1x1);
-        r.reverse();
+    for (const auto [n, n_2x1, n_1x1] : BLOCK_NUM) {
+        Ranges ranges;
+        ranges.spawn(n, n_2x1, n_1x1);
+        ranges.reverse();
 
-        RangesUnion ru;
+        RangesUnion ranges_union;
         for (const auto head : Heads) {
-            r.derive(head, ru.ranges(head));
+            ranges.derive(static_cast<int>(head), ranges_union.ranges(head));
         }
-        auto &tmp = cases += ru;
+        auto &tmp = cases += ranges_union;
         EXPECT_EQ(tmp, cases); // reference of cases
     }
 
     for (const auto head : Heads) {
-        std::stable_sort(cases.ranges(head).begin(), cases.ranges(head).end());
+        std::ranges::stable_sort(cases.ranges(head).begin(), cases.ranges(head).end());
     }
     EXPECT_EQ(cases, AllCases::instance().fetch());
 }
-
-TEST(RangesUnion, index) {
-    auto &all_cases = AllCases::instance().fetch();
-
-    // EXPECT_EQ(all_cases[1035968], 0x03F7FBC40);
-    // EXPECT_EQ(all_cases[3778871], 0x13CD00030);
-    // EXPECT_EQ(all_cases[7489354], 0x2CF0F3B30);
-    // EXPECT_EQ(all_cases[10398492], 0x4FE81C000);
-    // EXPECT_EQ(all_cases[19091276], 0xA0C4CEF40);
-    // EXPECT_EQ(all_cases[21373726], 0xC06BF3100);
-    // EXPECT_EQ(all_cases[27296711], 0xE384E4400);
-    // EXPECT_EQ(all_cases[28214648], 0xEBBC10800);
-
-    const auto codes = all_cases.codes();
-    for (size_t i = 0; i < codes.size(); ++i) {
-        EXPECT_EQ(codes[i], all_cases[i]);
-    }
-
-}