diff --git a/src/core/group/internal/group.cc b/src/core/group/internal/group.cc
index 9604736..95a7aba 100644
--- a/src/core/group/internal/group.cc
+++ b/src/core/group/internal/group.cc
@@ -51,6 +51,8 @@ KLSK_NOINLINE static RangesUnion group_extend(RawCode seed, const size_t reserve
         core.next_cases(curr, cases.find(curr)->second);
     }
 
+    std::cout << std::format("[{}, {}, {}]\n", codes.size(), mirrors.size(), cases.size());
+
     // std::cout << std::format("{:.5f}\n", static_cast<double>(codes.size()) / reserve);
 
     RangesUnion result {};
@@ -86,9 +88,10 @@ static RangesUnion extend_type_ver(RawCode seed, size_t reserve) {
 
 static RangesUnion extend_type_diag(RawCode seed, size_t reserve) {
     return group_extend(seed, reserve, [](const RawCode code, auto callback) {
-        if (const auto mirror = code.to_diagonal_mirror(); mirror != code) {
-            callback(mirror);
-        }
+        // if (const auto mirror = code.to_diagonal_mirror(); mirror != code) {
+        //     callback(mirror);
+        // }
+        callback(code.to_diagonal_mirror());
     });
 }
 
@@ -105,6 +108,7 @@ static RangesUnion extend_type_x(RawCode seed, size_t reserve) {
 
 RangesUnion Group::cases() const {
     if (const auto gu = GroupUnion::unsafe_create(type_id()); gu.group_num() == 1) {
+        std::cout << "[]" << std::endl;
         return gu.cases();
     }
 
diff --git a/src/core/main.cc b/src/core/main.cc
index 2726f82..51e2597 100644
--- a/src/core/main.cc
+++ b/src/core/main.cc
@@ -68,6 +68,7 @@ int main() {
             // if (group.mirror_type() == Group::MirrorType::Full) {
             // if (group.mirror_type() == Group::MirrorType::Ordinary) {
                 // std::cout << std::format("{} ({})\n", group.to_string(), group.size());
+                std::cout << std::format("{}: ", group.to_string());
                 volatile auto kk = group.cases();
                 // std::cout << group.size() << std::endl;
             // }
diff --git a/verify/mirror.py b/verify/mirror.py
new file mode 100755
index 0000000..d62b299
--- /dev/null
+++ b/verify/mirror.py
@@ -0,0 +1,50 @@
+#!/usr/bin/env python3
+
+import yaml
+from functools import cache
+from klotski import Group, GroupUnion
+
+
+def load_data(path: str) -> dict[str, list[int]]:
+    raw = yaml.safe_load(open(path).read())
+    return {x: y for x, y in raw.items() if len(y)}
+
+
+@cache
+def klotski_groups() -> dict[str, Group]:
+    groups = []
+    for type_id in range(203):
+        groups.extend(GroupUnion(type_id).groups())
+    return {str(x): x for x in groups}
+
+
+def verify_group(name: str, num_1: int, num_2: int, num_3: int) -> None:
+    group = klotski_groups()[name]
+    assert num_1 + num_2 == num_3
+    assert num_3 == group.size
+
+    is_v_mirror = group.is_vertical_mirror
+    is_h_mirror = group.is_horizontal_mirror
+    is_d_mirror = str(group) == str(group.to_vertical_mirror().to_horizontal_mirror())
+
+    if is_v_mirror and is_h_mirror:  # full mirror
+        h_mirrors = [x for x in list(group.cases()) if x.is_horizontal_mirror]
+        assert num_1 * 4 - len(h_mirrors) == num_3
+
+    elif is_h_mirror:  # horizontal mirror
+        h_mirrors = [x for x in list(group.cases()) if x.is_horizontal_mirror]
+        assert num_1 - num_2 == len(h_mirrors)
+
+    elif is_v_mirror:  # vertical mirror
+        assert num_1 == num_2
+
+    elif is_d_mirror:  # diagonal mirror
+        assert num_1 == num_2
+
+    else:  # non-mirror
+        assert num_2 == 0
+
+
+if __name__ == '__main__':
+    data = load_data('raw.yaml')
+    [verify_group(x, *y) for x, y in data.items()]