shared_ptr does not destruct the object at the end of the program

I'm trying to implement a Deque using smart pointers. However, I noticed that at the end of the program the Nodes of the Deque are not destructed properly.
Here is the code:

#include<iostream>
#include<memory>


class Node
{
  int value;
  std::shared_ptr<Node> next = nullptr;
  std::shared_ptr<Node> prev = nullptr;

public:
  Node() = default;
  Node(int val): value(val) {}
  ~Node()
  {
    std::cout << "Destructor of node: " << value << std::endl;
  }
  friend class Deque;
};

class Deque
{
  using pointer = std::shared_ptr<Node>; 
  pointer head = nullptr;      // pointer to the first element of the queue
  pointer tail = nullptr;      // pointer to the last element of the queue 

public:
  Deque() = default;
  ~Deque(){ std::cout << "Dequeue destructor" << std::endl; }
  
  bool is_empty()
  {
    if (head == nullptr && tail == nullptr )
      return true;
    else
      return false;
  }
  void push_back(const pointer& val)
  {
    if (is_empty())
      {
        head = val;
        tail = val;
      }
    else
      {
        val->prev = tail;
        tail->next = val;
        tail = val;
      }
  }
};



int main()
{
  Deque DEQ;  
  auto node1 = std::make_shared< Node >(1);
  auto node2 = std::make_shared< Node >(2);
  auto node3 = std::make_shared< Node >(3);

  DEQ.push_back(node1);
  DEQ.push_back(node2);

  std::cout << "Use count node1 = " << node1.use_count() << std::endl;
  std::cout << "Use count node2 = " << node2.use_count() << std::endl;
  std::cout << "Use count node3 = " << node3.use_count() << std::endl;
 
  return 0;
}

The output is the following:

Use count node1 = 3
Use count node2 = 3
Use count node3 = 1
Destructor of node: 3
Dequeue destructor

when I push the node1 and node2 into the Deque, they are not destructed at the end of the program, while node3 is correctly destructed.
I assume the problem is that the reference count of node1 and node2 is equal to 3. Do you know how I can change my implementation in order to solve this problem? Thanks.