How to solve my problem: Can't set default content type for a custom content type for a list using csom (c#)?

I'm adding a custom content type and then setting it as default content type for a custom content type. I has followed the instruction on the internet. When I execute the code, my custom content type has been added but it hasn't been set as default content type (No error, exception when running). Here is my code:

List list = web.Lists.GetByTitle(lname);
                    list.ContentTypesEnabled = true;
                    list.ContentTypes.AddExistingContentType(contentType);                    
                    var ctypes = list.ContentTypes;
                    context.Load(ctypes);
                    context.ExecuteQuery();
                    var ids = new List<ContentTypeId>();
                    foreach(var content in ctypes)
                    {
                        ids.Add(GetByName(ctypes, content.Name).Id);
                    }
                    ids.Reverse();
                    list.RootFolder.UniqueContentTypeOrder = ids;
                    list.RootFolder.Update();
                    list.Update();

                    context.Load(list.RootFolder, r => r.UniqueContentTypeOrder);
                    Console.WriteLine("Content-type Added!");

The function GetByName above I use to get the ContentType by name:

  public static ContentType GetByName(ContentTypeCollection cts, string name)
        {
            var ctx = cts.Context;
            ctx.Load(cts);
            ctx.ExecuteQuery();
            return Enumerable.FirstOrDefault(cts, ct => ct.Name == name);
        }

So, where did I get it wrong? How can I solve it?

Try to set default content type for list using code below.

List aeList = context.Web.Lists.GetByTitle(lname);
var currentCtOrder = aeList.ContentTypes;
context.Load(currentCtOrder, coll => coll.Include(
                        ct => ct.Name,
                        ct => ct.Id));
context.ExecuteQuery();

IList<ContentTypeId> reverseOrder = (from ct in currentCtOrder where ct.Name.Equals("CustomContentTypeName", StringComparison.OrdinalIgnoreCase) select ct.Id).ToList();
aeList.RootFolder.UniqueContentTypeOrder = reverseOrder;
aeList.RootFolder.Update();
aeList.Update();
context.ExecuteQuery();