diff --git a/app/solver/__init__.py b/app/solver/__init__.py
index 5193d53..c40d95c 100644
--- a/app/solver/__init__.py
+++ b/app/solver/__init__.py
@@ -7,9 +7,9 @@ import numpy as np
 
 from app._typing import NDArray
 
-from ._wrap import matrix, spmatrix
-from ._wrap.glpk import ilp
-from ._wrap.glpk import set_global_options as set_glpk_options
+from ._cvxopt_wrap import matrix, spmatrix
+from ._cvxopt_wrap.glpk import ilp
+from ._cvxopt_wrap.glpk import set_global_options as set_glpk_options
 
 set_glpk_options({"msg_lev": "GLP_MSG_ERR"})
 
@@ -139,19 +139,19 @@ class _BIPSolver:
 
     @staticmethod
     def solution_mat_clusters(solution_mat: NDArray):
-        n = solution_mat.shape[0]
+        n: int = solution_mat.shape[0]
         labels = np.arange(1, n + 1)
         for i in range(n):
             for j in range(i + 1, n):
                 if solution_mat[i, j] > 0:
                     labels[j] = labels[i]
-
-        clusters = defaultdict(list)
+        # a dictionary that with empty list as default value for non-existing keys
+        clusters: dict[int, list[int]] = defaultdict(list)
         for i, label in enumerate(labels):
-            clusters[label].append(i)
+            clusters[int(label)].append(i)
         return list(clusters.values())
 
-    def solve(self, affinity_matrix, rtn_matrix=False):
+    def solve(self, affinity_matrix: NDArray, rtn_matrix=False):
         n_nodes = affinity_matrix.shape[0]
         if n_nodes <= 1:
             solution_x, sol_matrix = (
diff --git a/app/solver/_wrap/__init__.py b/app/solver/_cvxopt_wrap/__init__.py
similarity index 100%
rename from app/solver/_wrap/__init__.py
rename to app/solver/_cvxopt_wrap/__init__.py
diff --git a/app/solver/_wrap/glpk.py b/app/solver/_cvxopt_wrap/glpk.py
similarity index 100%
rename from app/solver/_wrap/glpk.py
rename to app/solver/_cvxopt_wrap/glpk.py